WaveProp1D-Veri.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "fb5220c2",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "8e060377",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Plotting a UnitIntervalMesh:\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from dolfin import *\n",
    "import numpy as np\n",
    "parameters[\"form_compiler\"][\"representation\"] = 'quadrature'\n",
    "import warnings\n",
    "from ffc.quadrature.deprecation import QuadratureRepresentationDeprecationWarning\n",
    "warnings.simplefilter(\"once\", QuadratureRepresentationDeprecationWarning)\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# Form compiler options\n",
    "parameters[\"form_compiler\"][\"cpp_optimize\"] = True\n",
    "parameters[\"form_compiler\"][\"optimize\"] = True\n",
    "\n",
    "# Define mesh\n",
    "N_mesh = 25\n",
    "mesh = UnitIntervalMesh(N_mesh)\n",
    "#mesh = RectangleMesh(Point(0., 0.), Point(1., 0.1), 50, 5)\n",
    "\n",
    "print(\"Plotting a UnitIntervalMesh:\")\n",
    "plt.figure()\n",
    "plot(mesh, title=\"UnitIntervalMesh\")\n",
    "\n",
    "tol = 1E-12\n",
    "# Sub domain for clamp at left end\n",
    "def left(x, on_boundary):\n",
    "    return near(x[0], 0.,tol) and on_boundary\n",
    "\n",
    "# Sub domain for rotation at right end\n",
    "def right(x, on_boundary):\n",
    "    return near(x[0], 1.,tol) and on_boundary\n",
    "\n",
    "def left_and_right(x, on_boundary):\n",
    "    return on_boundary"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "5ac35593",
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "id": "5c1420ec",
   "metadata": {},
   "source": [
    "# Set up boundary domains"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "3dac1292",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Create mesh function over the cell facets\n",
    "boundary_subdomains = MeshFunction(\"size_t\", mesh, mesh.topology().dim() - 1)\n",
    "boundary_subdomains.set_all(0)\n",
    "force_boundary = AutoSubDomain(right)\n",
    "force_boundary.mark(boundary_subdomains, 3)\n",
    "\n",
    "# Define measure for boundary condition integral\n",
    "dss = ds(subdomain_data=boundary_subdomains)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "68f90b91",
   "metadata": {},
   "outputs": [],
   "source": [
    "E = Constant(70e3)\n",
    "nu = Constant(0.3)\n",
    "lmbda = E*nu/(1+nu)/(1-2*nu)\n",
    "mu = E/2./(1+nu)\n",
    "sig0 = Constant((1e1))  # yield strength\n",
    "Et = E/100.  # tangent modulus\n",
    "H = E*Et/(E-Et)  # hardening modulus\n",
    "rho = Constant(10e4)\n",
    "\n",
    "Nitermax, tol = 200, 1e-8  # parameters of the Newton-Raphson procedure\n",
    "Nincr = 500\n",
    "load_steps = np.linspace(0, 1, Nincr+1)[1:]\n",
    "\n",
    "dt = Constant(load_steps[1]-load_steps[0])\n",
    "dt_ = float(dt)\n",
    "\n",
    "# Newmark-beta method\n",
    "betaN = Constant(0.25)\n",
    "gammaN = Constant(0.5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "98bdd5ce",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(26923.076923076922, 0.002, 0.7337993857053428)"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "float(mu), float(dt), float(sqrt(2*mu/rho))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "c9000a1e",
   "metadata": {},
   "outputs": [],
   "source": [
    "deg_u = 2\n",
    "deg_stress = 2\n",
    "V = FunctionSpace(mesh, \"CG\", deg_u)\n",
    "We = VectorElement(\"Quadrature\", mesh.ufl_cell(), degree=deg_stress, dim=1, quad_scheme='default')\n",
    "W = FunctionSpace(mesh, We)\n",
    "W0e = FiniteElement(\"Quadrature\", mesh.ufl_cell(), degree=deg_stress, quad_scheme='default')\n",
    "W0 = FunctionSpace(mesh, W0e)\n",
    "# Define function space for stresses\n",
    "Vsig = VectorFunctionSpace(mesh, \"DG\", 0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "c1fafcf2",
   "metadata": {},
   "outputs": [],
   "source": [
    "sig = Function(W)\n",
    "sig_old = Function(W)\n",
    "beta = Function(W0)\n",
    "beta1 = Function(V)\n",
    "gamma0 = Function(W0)\n",
    "gamma0.interpolate(Constant(1e-6))\n",
    "u = Function(V, name=\"Total displacement\")\n",
    "u_pre = Function(V)\n",
    "u_old = Function(V)\n",
    "u_d_old = Function(V)\n",
    "u_dd_old = Function(V)\n",
    "du = Function(V, name=\"Iteration correction\")\n",
    "Du = Function(V, name=\"Current increment\")\n",
    "v = TrialFunction(V)\n",
    "u_ = TestFunction(V)\n",
    "\n",
    "sig_out = Function(Vsig, name=\"sigma\")\n",
    "eps_out = Function(Vsig, name=\"epsilon\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "03770583",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Set up boundary condition at left end\n",
    "# bc_expression = Expression( (\"t <= tc ? x[0]*1e-6*pow(t,1) : x[0]*0.5e-6\"), tc=0.5, t=0, degree=2) # Constant(0.0)\n",
    "# t*x[0]*(1-t*x[0]/L)/L -BC1\n",
    "# t*x[0]*(1-t*x[0]*x[0]/L)/L -BC2\n",
    "# \"t*t*x[0]*(1-x[0]*x[0]/L)/L\" - 0 BC\n",
    "bc_expression = Expression((\"t*x[0]*(1-t*x[0]*x[0]/L)/L\"), L=1, t=0, degree=2)\n",
    "bc = DirichletBC(V, bc_expression, left_and_right)\n",
    "\n",
    "zero = Constant(0.0)\n",
    "bc_newton = DirichletBC(V, zero, left_and_right)\n",
    "\n",
    "# bc = [DirichletBC(V.sub(1), 0, facets, 1), DirichletBC(V.sub(0), 0, facets, 3)]\n",
    "n = FacetNormal(mesh)\n",
    "\n",
    "q_lim = float(2/sqrt(3)*sig0*mu*2)\n",
    "# loading = Expression(\"q*t\", q=q_lim, t=0, degree=2)\n",
    "loading = Expression((\"t <= tc ? q*t*(1-t)*4 : 0\"), q=0.2*q_lim, t=0, tc=0.7, degree=2)\n",
    "\n",
    "# DEFINING SOURCE TERM\n",
    "# source = Expression((\"t <= tc && x[0]<0.55 && x[0]>0.45  ? q*t*(1-t)*4 : 0\"), q=0.2*q_lim, t=0, tc=1.2, degree=2)\n",
    "# source = Constant(0.0)\n",
    "\n",
    "# MMS - Nonlinear\n",
    "# \"(2*eps0*eps0*(G0*t*t-rho*x[0]*x[0])*pow(L,4)-4*pow(L,3)*eps0*rho*t*x[0]*x[0]+8*t*t*(eps0*x[0]-1/4)*rho*pow(x[0],2)*L*L+8*L*rho*pow(t,3)*pow(x[0],3)-8*rho*pow(t,4)*pow(x[0],4))/(L*L*pow(L*L*eps0-2*t*t*x[0]+L*t,2))\"\n",
    "\n",
    "# MMS - linear\n",
    "# (2*G0*t*t-2*rho*x[0]*x[0])/L/L - BC1\n",
    "# 6*x[0]*(G0*t*t-(1/3)*rho*x[0]*x[0])/L/L - BC2\n",
    "# (2*(rho*(-x[0]*x[0]+L)+3*G0*t*t))*x[0]/L/L - 0 BC case\n",
    "\n",
    "source = Expression(\\\n",
    "    (\"6*x[0]*(G0*t*t-(1/3)*rho*x[0]*x[0])/L/L\")\\\n",
    "    ,G0=float(mu), rho=float(rho), t=0, L=1, degree=2)\n",
    "\n",
    "# (2*eps0*eps0*(G0*t*t-rho*x*x)*pow(L,4)\n",
    "#  -4*pow(L,3)*eps0*rho*t*x*x\n",
    "#  +8*x*x*t*t*rho*(x*eps0-1/4)*L*L\n",
    "#  +8*L*rho*pow(t,3)*pow(x,3)\n",
    "#  -8*rho*pow(t,4)*pow(x,4)\n",
    "# )\n",
    "# /(L*L*pow(L*L*eps0-2*t*2*x+L*t,2))\n",
    "\n",
    "\n",
    "def F_ext(v):\n",
    "    return dot(loading,v)*dss(3)\n",
    "    # return loading*dot(n, v)*dss(3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "32d057f4",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Update formula for acceleration\n",
    "# a = 1/(2*beta)*((u - u0 - v0*dt)/(0.5*dt*dt) - (1-2*beta)*a0)\n",
    "def update_a(u, u_old, v_old, a_old, ufl=True):\n",
    "    if ufl:\n",
    "        dt_ = dt\n",
    "        betaN_ = betaN\n",
    "    else:\n",
    "        dt_ = float(dt)\n",
    "        betaN_ = float(betaN)\n",
    "    return (u-u_old-dt_*v_old)/betaN_/dt_**2 - (1-2*betaN_)/2/betaN_*a_old\n",
    "\n",
    "# Update formula for velocity\n",
    "# v = dt * ((1-gamma)*a0 + gamma*a) + v0\n",
    "def update_v(a, u_old, v_old, a_old, ufl=True):\n",
    "    if ufl:\n",
    "        dt_ = dt\n",
    "        gamma_ = gammaN\n",
    "    else:\n",
    "        dt_ = float(dt)\n",
    "        gamma_ = float(gammaN)\n",
    "    return v_old + dt_*((1-gamma_)*a_old + gamma_*a)\n",
    "\n",
    "def update_fields(u, u_old, v_old, a_old):\n",
    "    \"\"\"Update fields at the end of each time step.\"\"\"\n",
    "\n",
    "    # Get vectors (references)\n",
    "    u_vec, u0_vec  = u.vector(), u_old.vector()\n",
    "    v0_vec, a0_vec = v_old.vector(), a_old.vector()\n",
    "\n",
    "    # use update functions using vector arguments\n",
    "    a_vec = update_a(u_vec, u0_vec, v0_vec, a0_vec, ufl=False)\n",
    "    v_vec = update_v(a_vec, u0_vec, v0_vec, a0_vec, ufl=False)\n",
    "\n",
    "    # Update (u_old <- u)\n",
    "    v_old.vector()[:], a_old.vector()[:] = v_vec, a_vec\n",
    "    u_old.vector()[:] = u.vector()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "62e495fb",
   "metadata": {},
   "outputs": [],
   "source": [
    "def eps(v):\n",
    "    e = 0.5*grad(v)\n",
    "    return e\n",
    "\n",
    "def sigma(eps_el):\n",
    "    return 2*mu*eps_el\n",
    "\n",
    "def sigma_out(r):\n",
    "    return 2.0*mu*sym(grad(r))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "b885ed37",
   "metadata": {},
   "outputs": [],
   "source": [
    "def proj_sig(old_u,old_sig,old_Du):\n",
    "    eps_old = eps(old_u)\n",
    "    beta = sig0/(abs(eps_old[0])+sig0)\n",
    "    beta = 1\n",
    "    # beta = gamma0\n",
    "    # beta /= (eps_old[0]+as_tensor(gamma0[0]))\n",
    "    return 2*mu*beta*eps(old_Du)+old_sig, beta\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "ff5fb1e8",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "e7b3bccf",
   "metadata": {},
   "outputs": [],
   "source": [
    "def sigma_tang(e):\n",
    "    return 2*mu*beta*e"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "d335c3ff",
   "metadata": {},
   "outputs": [],
   "source": [
    "metadata = {\"quadrature_degree\": deg_stress, \"quadrature_scheme\": \"default\"}\n",
    "dxm = dx(metadata=metadata)\n",
    "\n",
    "# a_Newton = inner(eps(v), sigma_tang(eps(u_)))*dxm\n",
    "\n",
    "# a_Newton = inner(eps(u_), sigma_tang(eps(v)))*dxm\n",
    "\n",
    "a_Newton = rho*inner(u_,v)/(betaN*dt*dt)*dxm + inner(2*eps(u_), sigma_tang(eps(v)) )*dxm\n",
    "# F_ext(u_) + \\\n",
    "res = (-rho)*inner(u_,u)/(betaN*dt*dt)*dxm + \\\n",
    "      -inner(2*eps(u_), sig)*dxm + \\\n",
    "      inner(u_,source)*dxm + \\\n",
    "      rho*inner(u_old+dt*u_d_old,u_)*1./(betaN*dt*dt)*dxm + \\\n",
    "      (1.-2*betaN)/(2*betaN)*rho*inner(u_dd_old,u_)*dxm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "4c3dff0c",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "1eda1d1b",
   "metadata": {},
   "outputs": [],
   "source": [
    "def local_project(v, V, u=None):\n",
    "    dv = TrialFunction(V)\n",
    "    v_ = TestFunction(V)\n",
    "    a_proj = inner(dv, v_)*dxm\n",
    "    b_proj = inner(v, v_)*dxm\n",
    "    solver = LocalSolver(a_proj, b_proj)\n",
    "    solver.factorize()\n",
    "    if u is None:\n",
    "        u = Function(V)\n",
    "        solver.solve_local_rhs(u)\n",
    "        return u\n",
    "    else:\n",
    "        solver.solve_local_rhs(u)\n",
    "        return"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "6cb1cd5d",
   "metadata": {},
   "outputs": [],
   "source": [
    "file_results = XDMFFile(\"nonlinearElas1DVeri__results.xdmf\")\n",
    "file_results.parameters[\"flush_output\"] = True\n",
    "file_results.parameters[\"functions_share_mesh\"] = True"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "83036715",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "cb409e71",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1,)"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sig_out.ufl_shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "eaea524e",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "U at the left and right 0.0   0.001996\n",
      "Source at the left and right 0.0   0.6461538461538462\n",
      "Increment: 1    Initial Residual: 988416.4788815634\n",
      "    Residual: 9.542432974001306e-10   0\n",
      "U at the left and right 0.0   0.003984\n",
      "Source at the left and right 0.0   2.5846153846153848\n",
      "Increment: 2    Initial Residual: 936756.2576847442\n",
      "    Residual: 6.338962764077097e-10   0\n",
      "U at the left and right 0.0   0.005964\n",
      "Source at the left and right 0.0   5.815384615384616\n",
      "Increment: 3    Initial Residual: 852497.9124045362\n",
      "    Residual: 8.211845743393076e-10   0\n",
      "U at the left and right 0.0   0.007936\n",
      "Source at the left and right 0.0   10.338461538461539\n",
      "Increment: 4    Initial Residual: 748077.3411010453\n",
      "    Residual: 1.4598407088760814e-09   0\n",
      "U at the left and right 0.0   0.0099\n",
      "Source at the left and right 0.0   16.153846153846153\n",
      "Increment: 5    Initial Residual: 631193.7004122089\n",
      "    Residual: 9.746524767042341e-10   0\n",
      "U at the left and right 0.0   0.011856\n",
      "Source at the left and right 0.0   23.261538461538464\n",
      "Increment: 6    Initial Residual: 519473.0868933464\n",
      "    Residual: 1.172581012821947e-09   0\n",
      "U at the left and right 0.0   0.013804\n",
      "Source at the left and right 0.0   31.661538461538463\n",
      "Increment: 7    Initial Residual: 425485.854675058\n",
      "    Residual: 9.830893107023169e-10   0\n",
      "U at the left and right 0.0   0.015744\n",
      "Source at the left and right 0.0   41.353846153846156\n",
      "Increment: 8    Initial Residual: 390343.5347369054\n",
      "    Residual: 9.050308613494395e-10   0\n",
      "U at the left and right 0.0   0.017676\n",
      "Source at the left and right 0.0   52.338461538461544\n",
      "Increment: 9    Initial Residual: 434151.0533998564\n",
      "    Residual: 9.692056224068343e-10   0\n",
      "U at the left and right 0.0   0.0196\n",
      "Source at the left and right 0.0   64.61538461538461\n",
      "Increment: 10    Initial Residual: 534896.2882363651\n",
      "    Residual: 1.105179401699426e-09   0\n",
      "U at the left and right 0.0   0.021515999999999997\n",
      "Source at the left and right 0.0   78.18461538461537\n",
      "Increment: 11    Initial Residual: 679961.1104078752\n",
      "    Residual: 3.0453511685004957e-09   0\n",
      "U at the left and right 0.0   0.023424\n",
      "Source at the left and right 0.0   93.04615384615386\n",
      "Increment: 12    Initial Residual: 843157.6131145868\n",
      "    Residual: 4.512877151417086e-09   0\n",
      "U at the left and right 0.0   0.025324000000000003\n",
      "Source at the left and right 0.0   109.20000000000002\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/aangniu/anaconda3/envs/fenicsproject/lib/python3.9/site-packages/ffc/jitcompiler.py:234: QuadratureRepresentationDeprecationWarning: \n",
      "*** ===================================================== ***\n",
      "*** FFC: quadrature representation is deprecated! It will ***\n",
      "*** likely be removed in 2018.2.0 release. Use uflacs     ***\n",
      "*** representation instead.                               ***\n",
      "*** ===================================================== ***\n",
      "  issue_deprecation_warning()\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Increment: 13    Initial Residual: 1012061.8595743714\n",
      "    Residual: 9.367636486091116e-10   0\n",
      "U at the left and right 0.0   0.027216\n",
      "Source at the left and right 0.0   126.64615384615385\n",
      "Increment: 14    Initial Residual: 1185247.7240458194\n",
      "    Residual: 1.1480345229685784e-09   0\n",
      "U at the left and right 0.0   0.029099999999999997\n",
      "Source at the left and right 0.0   145.38461538461536\n",
      "Increment: 15    Initial Residual: 1361874.7956436963\n",
      "    Residual: 1.8360803713541833e-09   0\n",
      "U at the left and right 0.0   0.030976\n",
      "Source at the left and right 0.0   165.41538461538462\n",
      "Increment: 16    Initial Residual: 1536891.202771349\n",
      "    Residual: 1.4794367629963479e-09   0\n",
      "U at the left and right 0.0   0.032844\n",
      "Source at the left and right 0.0   186.73846153846156\n",
      "Increment: 17    Initial Residual: 1708620.6546380203\n",
      "    Residual: 1.8314612939199752e-09   0\n",
      "U at the left and right 0.0   0.034704000000000006\n",
      "Source at the left and right 0.0   209.35384615384618\n",
      "Increment: 18    Initial Residual: 1876526.1623574318\n",
      "    Residual: 7.43282429172885e-09   0\n",
      "U at the left and right 0.0   0.036556\n",
      "Source at the left and right 0.0   233.2615384615384\n",
      "Increment: 19    Initial Residual: 2042406.682752479\n",
      "    Residual: 3.2093489431054847e-09   0\n",
      "U at the left and right 0.0   0.0384\n",
      "Source at the left and right 0.0   258.46153846153845\n",
      "Increment: 20    Initial Residual: 2207056.380955625\n",
      "    Residual: 1.5930193689889285e-09   0\n",
      "U at the left and right 0.0   0.040236\n",
      "Source at the left and right 0.0   284.95384615384614\n",
      "Increment: 21    Initial Residual: 2363347.8742142804\n",
      "    Residual: 3.2072368343258067e-09   0\n",
      "U at the left and right 0.0   0.042064\n",
      "Source at the left and right 0.0   312.7384615384615\n",
      "Increment: 22    Initial Residual: 2512648.7473886446\n",
      "    Residual: 4.4967066300632354e-09   0\n",
      "U at the left and right 0.0   0.043884\n",
      "Source at the left and right 0.0   341.8153846153846\n",
      "Increment: 23    Initial Residual: 2658307.6146116704\n",
      "    Residual: 5.35383927056888e-09   0\n",
      "U at the left and right 0.0   0.045696\n",
      "Source at the left and right 0.0   372.1846153846154\n",
      "Increment: 24    Initial Residual: 2800188.1550692976\n",
      "    Residual: 1.909353242588314e-09   0\n",
      "U at the left and right 0.0   0.0475\n",
      "Source at the left and right 0.0   403.8461538461538\n",
      "Increment: 25    Initial Residual: 2938423.661938752\n",
      "    Residual: 4.439073606612538e-09   0\n",
      "U at the left and right 0.0   0.049296\n",
      "Source at the left and right 0.0   436.80000000000007\n",
      "Increment: 26    Initial Residual: 3071272.3587741596\n",
      "    Residual: 2.5822167532540433e-09   0\n",
      "U at the left and right 0.0   0.051084\n",
      "Source at the left and right 0.0   471.04615384615386\n",
      "Increment: 27    Initial Residual: 3197419.6637650137\n",
      "    Residual: 8.046143313696363e-09   0\n",
      "U at the left and right 0.0   0.052864\n",
      "Source at the left and right 0.0   506.5846153846154\n",
      "Increment: 28    Initial Residual: 3317122.66198451\n",
      "    Residual: 6.563801019923039e-09   0\n",
      "U at the left and right 0.0   0.054636\n",
      "Source at the left and right 0.0   543.4153846153847\n",
      "Increment: 29    Initial Residual: 3432172.8963253177\n",
      "    Residual: 1.9961069570251563e-09   0\n",
      "U at the left and right 0.0   0.05639999999999999\n",
      "Source at the left and right 0.0   581.5384615384614\n",
      "Increment: 30    Initial Residual: 3543139.9189680605\n",
      "    Residual: 3.759692251206176e-09   0\n",
      "U at the left and right 0.0   0.058156\n",
      "Source at the left and right 0.0   620.953846153846\n",
      "Increment: 31    Initial Residual: 3651359.3693409036\n",
      "    Residual: 7.171599581493735e-09   0\n",
      "U at the left and right 0.0   0.059904\n",
      "Source at the left and right 0.0   661.6615384615385\n",
      "Increment: 32    Initial Residual: 3755150.373900553\n",
      "    Residual: 6.722921839906327e-09   0\n",
      "U at the left and right 0.0   0.061644\n",
      "Source at the left and right 0.0   703.6615384615385\n",
      "Increment: 33    Initial Residual: 3853337.2724848683\n",
      "    Residual: 8.738131264594945e-09   0\n",
      "U at the left and right 0.0   0.063376\n",
      "Source at the left and right 0.0   746.9538461538463\n",
      "Increment: 34    Initial Residual: 3948521.477736399\n",
      "    Residual: 6.749077253339693e-09   0\n",
      "U at the left and right 0.0   0.0651\n",
      "Source at the left and right 0.0   791.5384615384617\n",
      "Increment: 35    Initial Residual: 4041366.4722864414\n",
      "    Residual: 6.478593721043564e-09   0\n",
      "U at the left and right 0.0   0.066816\n",
      "Source at the left and right 0.0   837.4153846153847\n",
      "Increment: 36    Initial Residual: 4133305.822520636\n",
      "    Residual: 5.816107614336906e-09   0\n",
      "U at the left and right 0.0   0.068524\n",
      "Source at the left and right 0.0   884.5846153846153\n",
      "Increment: 37    Initial Residual: 4222335.399028523\n",
      "    Residual: 1.2979133736499337e-08   0\n",
      "U at the left and right 0.0   0.070224\n",
      "Source at the left and right 0.0   933.0461538461536\n",
      "Increment: 38    Initial Residual: 4305069.956873219\n",
      "    Residual: 6.223594026930472e-09   0\n",
      "U at the left and right 0.0   0.07191600000000001\n",
      "Source at the left and right 0.0   982.8000000000001\n",
      "Increment: 39    Initial Residual: 4383147.98937934\n",
      "    Residual: 6.375266970178609e-09   0\n",
      "U at the left and right 0.0   0.0736\n",
      "Source at the left and right 0.0   1033.8461538461538\n",
      "Increment: 40    Initial Residual: 4460384.115002015\n",
      "    Residual: 4.1191945813955114e-09   0\n",
      "U at the left and right 0.0   0.07527600000000001\n",
      "Source at the left and right 0.0   1086.1846153846154\n",
      "Increment: 41    Initial Residual: 4537695.220540087\n",
      "    Residual: 1.0223359987186338e-08   0\n",
      "U at the left and right 0.0   0.07694400000000001\n",
      "Source at the left and right 0.0   1139.8153846153846\n",
      "Increment: 42    Initial Residual: 4615071.051776568\n",
      "    Residual: 2.2888566790976576e-08   0\n",
      "U at the left and right 0.0   0.07860400000000001\n",
      "Source at the left and right 0.0   1194.738461538462\n",
      "Increment: 43    Initial Residual: 4693798.524619639\n",
      "    Residual: 7.073608008661919e-09   0\n",
      "U at the left and right 0.0   0.080256\n",
      "Source at the left and right 0.0   1250.953846153846\n",
      "Increment: 44    Initial Residual: 4771997.7788108885\n",
      "    Residual: 3.4218976406145536e-09   0\n",
      "U at the left and right 0.0   0.0819\n",
      "Source at the left and right 0.0   1308.461538461538\n",
      "Increment: 45    Initial Residual: 4847990.699825458\n",
      "    Residual: 6.622384606547603e-09   0\n",
      "U at the left and right 0.0   0.083536\n",
      "Source at the left and right 0.0   1367.2615384615383\n",
      "Increment: 46    Initial Residual: 4920852.21757241\n",
      "    Residual: 1.013013996081757e-08   0\n",
      "U at the left and right 0.0   0.085164\n",
      "Source at the left and right 0.0   1427.353846153846\n",
      "Increment: 47    Initial Residual: 4991477.552678689\n",
      "    Residual: 8.538887286974233e-09   0\n",
      "U at the left and right 0.0   0.086784\n",
      "Source at the left and right 0.0   1488.7384615384617\n",
      "Increment: 48    Initial Residual: 5060540.365781788\n",
      "    Residual: 8.621024238678449e-09   0\n",
      "U at the left and right 0.0   0.088396\n",
      "Source at the left and right 0.0   1551.4153846153847\n",
      "Increment: 49    Initial Residual: 5126167.539329986\n",
      "    Residual: 1.1044127145438848e-08   0\n",
      "U at the left and right 0.0   0.09000000000000001\n",
      "Source at the left and right 0.0   1615.3846153846152\n",
      "Increment: 50    Initial Residual: 5191217.355102873\n",
      "    Residual: 8.088980226796217e-09   0\n",
      "U at the left and right 0.0   0.09159600000000001\n",
      "Source at the left and right 0.0   1680.646153846154\n",
      "Increment: 51    Initial Residual: 5259232.950447231\n",
      "    Residual: 4.386865459712402e-09   0\n",
      "U at the left and right 0.0   0.09318400000000002\n",
      "Source at the left and right 0.0   1747.2000000000003\n",
      "Increment: 52    Initial Residual: 5328880.801950345\n",
      "    Residual: 1.1505697947559726e-08   0\n",
      "U at the left and right 0.0   0.094764\n",
      "Source at the left and right 0.0   1815.0461538461539\n",
      "Increment: 53    Initial Residual: 5397415.920048255\n",
      "    Residual: 1.2585783146079237e-08   0\n",
      "U at the left and right 0.0   0.096336\n",
      "Source at the left and right 0.0   1884.1846153846154\n",
      "Increment: 54    Initial Residual: 5464649.9759327\n",
      "    Residual: 3.036454392019865e-08   0\n",
      "U at the left and right 0.0   0.0979\n",
      "Source at the left and right 0.0   1954.6153846153848\n",
      "Increment: 55    Initial Residual: 5529759.40174053\n",
      "    Residual: 6.0401492617432245e-09   0\n",
      "U at the left and right 0.0   0.099456\n",
      "Source at the left and right 0.0   2026.3384615384616\n",
      "Increment: 56    Initial Residual: 5592500.374911247\n",
      "    Residual: 1.0908308229523226e-08   0\n",
      "U at the left and right 0.0   0.10100400000000001\n",
      "Source at the left and right 0.0   2099.353846153846\n",
      "Increment: 57    Initial Residual: 5655291.502911426\n",
      "    Residual: 1.690869932562607e-08   0\n",
      "U at the left and right 0.0   0.10254400000000001\n",
      "Source at the left and right 0.0   2173.661538461539\n",
      "Increment: 58    Initial Residual: 5717726.182686304\n",
      "    Residual: 5.778704605061029e-09   0\n",
      "U at the left and right 0.0   0.104076\n",
      "Source at the left and right 0.0   2249.2615384615387\n",
      "Increment: 59    Initial Residual: 5777764.4479234805\n",
      "    Residual: 9.798270376632369e-09   0\n",
      "U at the left and right 0.0   0.1056\n",
      "Source at the left and right 0.0   2326.1538461538457\n",
      "Increment: 60    Initial Residual: 5832729.531582\n",
      "    Residual: 8.748981276553094e-09   0\n",
      "U at the left and right 0.0   0.107116\n",
      "Source at the left and right 0.0   2404.338461538461\n",
      "Increment: 61    Initial Residual: 5882618.899961869\n",
      "    Residual: 6.875406513099279e-09   0\n",
      "U at the left and right 0.0   0.108624\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Source at the left and right 0.0   2483.815384615384\n",
      "Increment: 62    Initial Residual: 5929579.378880966\n",
      "    Residual: 1.332637669635395e-08   0\n",
      "U at the left and right 0.0   0.110124\n",
      "Source at the left and right 0.0   2564.584615384615\n",
      "Increment: 63    Initial Residual: 5975132.695105455\n",
      "    Residual: 3.117149317856796e-08   0\n",
      "U at the left and right 0.0   0.111616\n",
      "Source at the left and right 0.0   2646.646153846154\n",
      "Increment: 64    Initial Residual: 6022834.961793241\n",
      "    Residual: 2.2713819665067946e-08   0\n",
      "U at the left and right 0.0   0.1131\n",
      "Source at the left and right 0.0   2730.0\n",
      "Increment: 65    Initial Residual: 6074338.412250049\n",
      "    Residual: 1.9080751807007825e-08   0\n",
      "U at the left and right 0.0   0.11457600000000001\n",
      "Source at the left and right 0.0   2814.646153846154\n",
      "Increment: 66    Initial Residual: 6126870.527388312\n",
      "    Residual: 5.830071878409439e-09   0\n",
      "U at the left and right 0.0   0.11604400000000001\n",
      "Source at the left and right 0.0   2900.5846153846155\n",
      "Increment: 67    Initial Residual: 6178367.934107803\n",
      "    Residual: 4.126360747413949e-08   0\n",
      "U at the left and right 0.0   0.11750400000000001\n",
      "Source at the left and right 0.0   2987.815384615385\n",
      "Increment: 68    Initial Residual: 6230215.064495331\n",
      "    Residual: 2.4186386298175135e-08   0\n",
      "U at the left and right 0.0   0.118956\n",
      "Source at the left and right 0.0   3076.338461538462\n",
      "Increment: 69    Initial Residual: 6279593.649695043\n",
      "    Residual: 3.7470545944364467e-08   0\n",
      "U at the left and right 0.0   0.12040000000000001\n",
      "Source at the left and right 0.0   3166.1538461538466\n",
      "Increment: 70    Initial Residual: 6322171.323438933\n",
      "    Residual: 4.112938656995152e-08   0\n",
      "U at the left and right 0.0   0.12183600000000001\n",
      "Source at the left and right 0.0   3257.261538461539\n",
      "Increment: 71    Initial Residual: 6358889.254048633\n",
      "    Residual: 2.2270345390305332e-08   0\n",
      "U at the left and right 0.0   0.12326400000000001\n",
      "Source at the left and right 0.0   3349.661538461539\n",
      "Increment: 72    Initial Residual: 6391047.840694393\n",
      "    Residual: 9.850690048796209e-09   0\n",
      "U at the left and right 0.0   0.12468399999999999\n",
      "Source at the left and right 0.0   3443.353846153846\n",
      "Increment: 73    Initial Residual: 6419884.855918655\n",
      "    Residual: 2.3232951848009078e-08   0\n",
      "U at the left and right 0.0   0.12609599999999999\n",
      "Source at the left and right 0.0   3538.338461538461\n",
      "Increment: 74    Initial Residual: 6448633.257175464\n",
      "    Residual: 5.321084450979795e-08   0\n",
      "U at the left and right 0.0   0.1275\n",
      "Source at the left and right 0.0   3634.6153846153843\n",
      "Increment: 75    Initial Residual: 6482707.97259261\n",
      "    Residual: 4.4267222711056776e-08   0\n",
      "U at the left and right 0.0   0.12889599999999998\n",
      "Source at the left and right 0.0   3732.1846153846145\n",
      "Increment: 76    Initial Residual: 6522408.825045914\n",
      "    Residual: 3.867582613558017e-08   0\n",
      "U at the left and right 0.0   0.13028399999999998\n",
      "Source at the left and right 0.0   3831.046153846153\n",
      "Increment: 77    Initial Residual: 6561694.028724294\n",
      "    Residual: 4.440538808635037e-08   0\n",
      "U at the left and right 0.0   0.131664\n",
      "Source at the left and right 0.0   3931.2000000000003\n",
      "Increment: 78    Initial Residual: 6598502.927986519\n",
      "    Residual: 4.982793368173925e-09   0\n",
      "U at the left and right 0.0   0.133036\n",
      "Source at the left and right 0.0   4032.6461538461535\n",
      "Increment: 79    Initial Residual: 6635801.332344169\n",
      "    Residual: 3.596461026864057e-08   0\n",
      "U at the left and right 0.0   0.1344\n",
      "Source at the left and right 0.0   4135.384615384615\n",
      "Increment: 80    Initial Residual: 6674533.409880512\n",
      "    Residual: 8.614733815193176e-09   0\n",
      "U at the left and right 0.0   0.135756\n",
      "Source at the left and right 0.0   4239.415384615386\n",
      "Increment: 81    Initial Residual: 6714160.841135979\n",
      "    Residual: 3.8376818928935595e-08   0\n",
      "U at the left and right 0.0   0.137104\n",
      "Source at the left and right 0.0   4344.738461538462\n",
      "Increment: 82    Initial Residual: 6756868.669750475\n",
      "    Residual: 2.9652790119746643e-08   0\n",
      "U at the left and right 0.0   0.138444\n",
      "Source at the left and right 0.0   4451.3538461538465\n",
      "Increment: 83    Initial Residual: 6799532.504155161\n",
      "    Residual: 1.9080751807007825e-08   0\n",
      "U at the left and right 0.0   0.139776\n",
      "Source at the left and right 0.0   4559.261538461538\n",
      "Increment: 84    Initial Residual: 6836217.6618909845\n",
      "    Residual: 4.424027307522901e-08   0\n",
      "U at the left and right 0.0   0.1411\n",
      "Source at the left and right 0.0   4668.461538461539\n",
      "Increment: 85    Initial Residual: 6867919.884991729\n",
      "    Residual: 3.905174484985416e-08   0\n",
      "U at the left and right 0.0   0.14241600000000001\n",
      "Source at the left and right 0.0   4778.953846153848\n",
      "Increment: 86    Initial Residual: 6898199.935985558\n",
      "    Residual: 1.6043366097800635e-08   0\n",
      "U at the left and right 0.0   0.14372400000000002\n",
      "Source at the left and right 0.0   4890.738461538463\n",
      "Increment: 87    Initial Residual: 6927711.198842314\n",
      "    Residual: 2.6201465905895828e-08   0\n",
      "U at the left and right 0.0   0.14502400000000001\n",
      "Source at the left and right 0.0   5003.815384615384\n",
      "Increment: 88    Initial Residual: 6955308.808919202\n",
      "    Residual: 2.7120522742273353e-08   0\n",
      "U at the left and right 0.0   0.146316\n",
      "Source at the left and right 0.0   5118.1846153846145\n",
      "Increment: 89    Initial Residual: 6982752.28872915\n",
      "    Residual: 3.0378823038749564e-08   0\n",
      "U at the left and right 0.0   0.1476\n",
      "Source at the left and right 0.0   5233.846153846152\n",
      "Increment: 90    Initial Residual: 7011462.120917172\n",
      "    Residual: 2.155664749276397e-08   0\n",
      "U at the left and right 0.0   0.148876\n",
      "Source at the left and right 0.0   5350.799999999999\n",
      "Increment: 91    Initial Residual: 7041104.797649405\n",
      "    Residual: 5.88080614354381e-08   0\n",
      "U at the left and right 0.0   0.150144\n",
      "Source at the left and right 0.0   5469.046153846153\n",
      "Increment: 92    Initial Residual: 7073643.564949107\n",
      "    Residual: 5.848268267891592e-08   0\n",
      "U at the left and right 0.0   0.151404\n",
      "Source at the left and right 0.0   5588.584615384615\n",
      "Increment: 93    Initial Residual: 7110565.432516844\n",
      "    Residual: 5.126717182115042e-08   0\n",
      "U at the left and right 0.0   0.15265600000000001\n",
      "Source at the left and right 0.0   5709.415384615384\n",
      "Increment: 94    Initial Residual: 7147548.926536615\n",
      "    Residual: 2.6060396022411476e-08   0\n",
      "U at the left and right 0.0   0.1539\n",
      "Source at the left and right 0.0   5831.538461538461\n",
      "Increment: 95    Initial Residual: 7181485.186984447\n",
      "    Residual: 4.74449212299315e-08   0\n",
      "U at the left and right 0.0   0.15513600000000002\n",
      "Source at the left and right 0.0   5954.953846153847\n",
      "Increment: 96    Initial Residual: 7218787.138786669\n",
      "    Residual: 2.5201699003083276e-08   0\n",
      "U at the left and right 0.0   0.156364\n",
      "Source at the left and right 0.0   6079.661538461538\n",
      "Increment: 97    Initial Residual: 7262134.724813975\n",
      "    Residual: 1.3790179877505496e-08   0\n",
      "U at the left and right 0.0   0.157584\n",
      "Source at the left and right 0.0   6205.661538461539\n",
      "Increment: 98    Initial Residual: 7305963.651630275\n",
      "    Residual: 5.1053129410988637e-08   0\n",
      "U at the left and right 0.0   0.15879600000000002\n",
      "Source at the left and right 0.0   6332.953846153845\n",
      "Increment: 99    Initial Residual: 7345637.663576589\n",
      "    Residual: 1.137777392088493e-08   0\n",
      "U at the left and right 0.0   0.16000000000000003\n",
      "Source at the left and right 0.0   6461.538461538461\n",
      "Increment: 100    Initial Residual: 7376871.688189467\n",
      "    Residual: 5.6873620962562724e-08   0\n",
      "U at the left and right 0.0   0.161196\n",
      "Source at the left and right 0.0   6591.415384615386\n",
      "Increment: 101    Initial Residual: 7394437.294047784\n",
      "    Residual: 3.404745163476264e-08   0\n",
      "U at the left and right 0.0   0.16238400000000003\n",
      "Source at the left and right 0.0   6722.584615384616\n",
      "Increment: 102    Initial Residual: 7399570.126937016\n",
      "    Residual: 5.206043210327075e-08   0\n",
      "U at the left and right 0.0   0.16356400000000001\n",
      "Source at the left and right 0.0   6855.046153846155\n",
      "Increment: 103    Initial Residual: 7403415.063868759\n",
      "    Residual: 2.2039114620907665e-08   0\n",
      "U at the left and right 0.0   0.16473600000000002\n",
      "Source at the left and right 0.0   6988.800000000001\n",
      "Increment: 104    Initial Residual: 7413480.841264875\n",
      "    Residual: 3.091654306780143e-08   0\n",
      "U at the left and right 0.0   0.1659\n",
      "Source at the left and right 0.0   7123.846153846152\n",
      "Increment: 105    Initial Residual: 7428128.422656131\n",
      "    Residual: 2.4758996512849712e-08   0\n",
      "U at the left and right 0.0   0.167056\n",
      "Source at the left and right 0.0   7260.184615384615\n",
      "Increment: 106    Initial Residual: 7447156.769065008\n",
      "    Residual: 3.6657334499094917e-08   0\n",
      "U at the left and right 0.0   0.168204\n",
      "Source at the left and right 0.0   7397.815384615384\n",
      "Increment: 107    Initial Residual: 7475190.557695245\n",
      "    Residual: 1.679611280269123e-08   0\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "U at the left and right 0.0   0.169344\n",
      "Source at the left and right 0.0   7536.738461538462\n",
      "Increment: 108    Initial Residual: 7510748.526089219\n",
      "    Residual: 5.0118655141717605e-08   0\n",
      "U at the left and right 0.0   0.17047600000000002\n",
      "Source at the left and right 0.0   7676.953846153845\n",
      "Increment: 109    Initial Residual: 7546649.750144593\n",
      "    Residual: 5.4052826146409193e-08   0\n",
      "U at the left and right 0.0   0.1716\n",
      "Source at the left and right 0.0   7818.461538461539\n",
      "Increment: 110    Initial Residual: 7581199.844236756\n",
      "    Residual: 2.7752787667794786e-08   0\n",
      "U at the left and right 0.0   0.172716\n",
      "Source at the left and right 0.0   7961.261538461538\n",
      "Increment: 111    Initial Residual: 7611215.2890056865\n",
      "    Residual: 4.1191945813955114e-08   0\n",
      "U at the left and right 0.0   0.173824\n",
      "Source at the left and right 0.0   8105.3538461538465\n",
      "Increment: 112    Initial Residual: 7631812.128984576\n",
      "    Residual: 8.90302490314782e-08   0\n",
      "U at the left and right 0.0   0.174924\n",
      "Source at the left and right 0.0   8250.738461538462\n",
      "Increment: 113    Initial Residual: 7648168.8871655045\n",
      "    Residual: 4.6856263180957426e-08   0\n",
      "U at the left and right 0.0   0.176016\n",
      "Source at the left and right 0.0   8397.415384615384\n",
      "Increment: 114    Initial Residual: 7670289.684074508\n",
      "    Residual: 4.668704367985682e-08   0\n",
      "U at the left and right 0.0   0.1771\n",
      "Source at the left and right 0.0   8545.384615384615\n",
      "Increment: 115    Initial Residual: 7697785.690298342\n",
      "    Residual: 1.4622061018000899e-08   0\n",
      "U at the left and right 0.0   0.178176\n",
      "Source at the left and right 0.0   8694.646153846155\n",
      "Increment: 116    Initial Residual: 7722639.940769974\n",
      "    Residual: 3.4581425595997505e-08   0\n",
      "U at the left and right 0.0   0.17924400000000001\n",
      "Source at the left and right 0.0   8845.2\n",
      "Increment: 117    Initial Residual: 7742207.019432052\n",
      "    Residual: 8.628315384586358e-08   0\n",
      "U at the left and right 0.0   0.18030400000000002\n",
      "Source at the left and right 0.0   8997.046153846155\n",
      "Increment: 118    Initial Residual: 7756943.127806202\n",
      "    Residual: 6.065405849304574e-08   0\n",
      "U at the left and right 0.0   0.18135600000000002\n",
      "Source at the left and right 0.0   9150.184615384616\n",
      "Increment: 119    Initial Residual: 7767647.364748563\n",
      "    Residual: 1.0507654944716915e-07   0\n",
      "U at the left and right 0.0   0.1824\n",
      "Source at the left and right 0.0   9304.615384615383\n",
      "Increment: 120    Initial Residual: 7779457.606521989\n",
      "    Residual: 2.5729629739264595e-08   0\n",
      "U at the left and right 0.0   0.183436\n",
      "Source at the left and right 0.0   9460.33846153846\n",
      "Increment: 121    Initial Residual: 7798631.246038597\n",
      "    Residual: 4.820662751640515e-08   0\n",
      "U at the left and right 0.0   0.184464\n",
      "Source at the left and right 0.0   9617.353846153845\n",
      "Increment: 122    Initial Residual: 7820482.6424843995\n",
      "    Residual: 4.830324083525665e-08   0\n",
      "U at the left and right 0.0   0.185484\n",
      "Source at the left and right 0.0   9775.661538461538\n",
      "Increment: 123    Initial Residual: 7836077.643772302\n",
      "    Residual: 3.9176480129925914e-08   0\n",
      "U at the left and right 0.0   0.186496\n",
      "Source at the left and right 0.0   9935.261538461536\n",
      "Increment: 124    Initial Residual: 7849307.987678476\n",
      "    Residual: 9.516708689268792e-08   0\n",
      "U at the left and right 0.0   0.1875\n",
      "Source at the left and right 0.0   10096.153846153846\n",
      "Increment: 125    Initial Residual: 7866078.016854157\n",
      "    Residual: 2.5602902833169837e-08   0\n",
      "U at the left and right 0.0   0.188496\n",
      "Source at the left and right 0.0   10258.33846153846\n",
      "Increment: 126    Initial Residual: 7884603.504577104\n",
      "    Residual: 5.520394430131108e-08   0\n",
      "U at the left and right 0.0   0.189484\n",
      "Source at the left and right 0.0   10421.815384615384\n",
      "Increment: 127    Initial Residual: 7905784.985392355\n",
      "    Residual: 9.689112328339209e-08   0\n",
      "U at the left and right 0.0   0.190464\n",
      "Source at the left and right 0.0   10586.584615384616\n",
      "Increment: 128    Initial Residual: 7934227.302362113\n",
      "    Residual: 1.246807553277456e-07   0\n",
      "U at the left and right 0.0   0.191436\n",
      "Source at the left and right 0.0   10752.646153846154\n",
      "Increment: 129    Initial Residual: 7966893.887920576\n",
      "    Residual: 5.7031627343575894e-08   0\n",
      "U at the left and right 0.0   0.19240000000000002\n",
      "Source at the left and right 0.0   10920.0\n",
      "Increment: 130    Initial Residual: 7999135.929038347\n",
      "    Residual: 6.185412376120809e-08   0\n",
      "U at the left and right 0.0   0.193356\n",
      "Source at the left and right 0.0   11088.646153846155\n",
      "Increment: 131    Initial Residual: 8034638.296660612\n",
      "    Residual: 6.2540928658429e-08   0\n",
      "U at the left and right 0.0   0.194304\n",
      "Source at the left and right 0.0   11258.584615384616\n",
      "Increment: 132    Initial Residual: 8072303.618376281\n",
      "    Residual: 3.584382198364626e-08   0\n",
      "U at the left and right 0.0   0.195244\n",
      "Source at the left and right 0.0   11429.815384615385\n",
      "Increment: 133    Initial Residual: 8099929.730665714\n",
      "    Residual: 4.1999963507530764e-08   0\n",
      "U at the left and right 0.0   0.19617600000000002\n",
      "Source at the left and right 0.0   11602.338461538462\n",
      "Increment: 134    Initial Residual: 8110363.714351212\n",
      "    Residual: 3.885970645588835e-08   0\n",
      "U at the left and right 0.0   0.1971\n",
      "Source at the left and right 0.0   11776.153846153848\n",
      "Increment: 135    Initial Residual: 8111763.883636984\n",
      "    Residual: 6.536531129988502e-08   0\n",
      "U at the left and right 0.0   0.198016\n",
      "Source at the left and right 0.0   11951.26153846154\n",
      "Increment: 136    Initial Residual: 8112254.022823618\n",
      "    Residual: 7.309844038608183e-08   0\n",
      "U at the left and right 0.0   0.19892400000000002\n",
      "Source at the left and right 0.0   12127.66153846154\n",
      "Increment: 137    Initial Residual: 8113939.313492582\n",
      "    Residual: 5.309559764139404e-08   0\n",
      "U at the left and right 0.0   0.199824\n",
      "Source at the left and right 0.0   12305.353846153848\n",
      "Increment: 138    Initial Residual: 8123131.644630691\n",
      "    Residual: 4.8383978038506725e-08   0\n",
      "U at the left and right 0.0   0.200716\n",
      "Source at the left and right 0.0   12484.338461538464\n",
      "Increment: 139    Initial Residual: 8140111.956997586\n",
      "    Residual: 5.47127242808515e-08   0\n",
      "U at the left and right 0.0   0.2016\n",
      "Source at the left and right 0.0   12664.615384615387\n",
      "Increment: 140    Initial Residual: 8152900.954413739\n",
      "    Residual: 4.011719961360068e-08   0\n",
      "U at the left and right 0.0   0.20247600000000002\n",
      "Source at the left and right 0.0   12846.184615384618\n",
      "Increment: 141    Initial Residual: 8156789.045348011\n",
      "    Residual: 3.871155180058614e-08   0\n",
      "U at the left and right 0.0   0.20334400000000002\n",
      "Source at the left and right 0.0   13029.046153846157\n",
      "Increment: 142    Initial Residual: 8161655.585117689\n",
      "    Residual: 7.591135980049663e-08   0\n",
      "U at the left and right 0.0   0.20420400000000002\n",
      "Source at the left and right 0.0   13213.200000000004\n",
      "Increment: 143    Initial Residual: 8171900.363226297\n",
      "    Residual: 7.585706697631781e-08   0\n",
      "U at the left and right 0.0   0.20505600000000002\n",
      "Source at the left and right 0.0   13398.646153846155\n",
      "Increment: 144    Initial Residual: 8184003.076768298\n",
      "    Residual: 5.7691280355838885e-08   0\n",
      "U at the left and right 0.0   0.20589999999999997\n",
      "Source at the left and right 0.0   13585.384615384612\n",
      "Increment: 145    Initial Residual: 8200671.012185741\n",
      "    Residual: 7.468458004547476e-08   0\n",
      "U at the left and right 0.0   0.20673599999999998\n",
      "Source at the left and right 0.0   13773.415384615384\n",
      "Increment: 146    Initial Residual: 8225143.823711666\n",
      "    Residual: 9.608997107565936e-08   0\n",
      "U at the left and right 0.0   0.20756399999999997\n",
      "Source at the left and right 0.0   13962.738461538458\n",
      "Increment: 147    Initial Residual: 8253397.85595368\n",
      "    Residual: 7.021610185107531e-08   0\n",
      "U at the left and right 0.0   0.20838399999999999\n",
      "Source at the left and right 0.0   14153.353846153845\n",
      "Increment: 148    Initial Residual: 8282557.148788337\n",
      "    Residual: 9.089345715913519e-08   0\n",
      "U at the left and right 0.0   0.20919599999999997\n",
      "Source at the left and right 0.0   14345.261538461535\n",
      "Increment: 149    Initial Residual: 8314994.127897719\n",
      "    Residual: 8.073820125474587e-08   0\n",
      "U at the left and right 0.0   0.21\n",
      "Source at the left and right 0.0   14538.461538461537\n",
      "Increment: 150    Initial Residual: 8342976.5298158\n",
      "    Residual: 6.165221793495901e-08   0\n",
      "U at the left and right 0.0   0.21079599999999998\n",
      "Source at the left and right 0.0   14732.953846153843\n",
      "Increment: 151    Initial Residual: 8353211.644115438\n",
      "    Residual: 1.0016481449963535e-07   0\n",
      "U at the left and right 0.0   0.21158399999999997\n",
      "Source at the left and right 0.0   14928.738461538458\n",
      "Increment: 152    Initial Residual: 8350363.9745325195\n",
      "    Residual: 1.2282781944712603e-07   0\n",
      "U at the left and right 0.0   0.21236399999999997\n",
      "Source at the left and right 0.0   15125.815384615382\n",
      "Increment: 153    Initial Residual: 8348511.143197963\n",
      "    Residual: 4.604163428510828e-08   0\n",
      "U at the left and right 0.0   0.213136\n",
      "Source at the left and right 0.0   15324.184615384613\n",
      "Increment: 154    Initial Residual: 8350381.290482011\n",
      "    Residual: 6.663188348176974e-08   0\n",
      "U at the left and right 0.0   0.21389999999999998\n",
      "Source at the left and right 0.0   15523.846153846154\n",
      "Increment: 155    Initial Residual: 8354757.462923802\n",
      "    Residual: 1.0423014251520168e-07   0\n",
      "U at the left and right 0.0   0.21465599999999999\n",
      "Source at the left and right 0.0   15724.800000000001\n",
      "Increment: 156    Initial Residual: 8365113.911575961\n",
      "    Residual: 5.66922298037044e-08   0\n",
      "U at the left and right 0.0   0.21540399999999998\n",
      "Source at the left and right 0.0   15927.046153846157\n",
      "Increment: 157    Initial Residual: 8376268.708003783\n",
      "    Residual: 7.055498462015243e-08   0\n",
      "U at the left and right 0.0   0.21614399999999998\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Source at the left and right 0.0   16130.584615384614\n",
      "Increment: 158    Initial Residual: 8381761.699417271\n",
      "    Residual: 5.4074885660474635e-08   0\n",
      "U at the left and right 0.0   0.21687599999999999\n",
      "Source at the left and right 0.0   16335.415384615384\n",
      "Increment: 159    Initial Residual: 8392098.336858682\n",
      "    Residual: 5.6542863088326675e-08   0\n",
      "U at the left and right 0.0   0.2176\n",
      "Source at the left and right 0.0   16541.53846153846\n",
      "Increment: 160    Initial Residual: 8418529.495963829\n",
      "    Residual: 8.259418907694895e-08   0\n",
      "U at the left and right 0.0   0.21831599999999998\n",
      "Source at the left and right 0.0   16748.953846153847\n",
      "Increment: 161    Initial Residual: 8452203.723587023\n",
      "    Residual: 9.879923582357048e-08   0\n",
      "U at the left and right 0.0   0.219024\n",
      "Source at the left and right 0.0   16957.661538461543\n",
      "Increment: 162    Initial Residual: 8478266.681861915\n",
      "    Residual: 5.4400719204955674e-08   0\n",
      "U at the left and right 0.0   0.21972399999999997\n",
      "Source at the left and right 0.0   17167.66153846154\n",
      "Increment: 163    Initial Residual: 8496108.963974748\n",
      "    Residual: 8.411343350958519e-08   0\n",
      "U at the left and right 0.0   0.22041599999999997\n",
      "Source at the left and right 0.0   17378.953846153847\n",
      "Increment: 164    Initial Residual: 8506700.485054918\n",
      "    Residual: 6.49993771181041e-08   0\n",
      "U at the left and right 0.0   0.2211\n",
      "Source at the left and right 0.0   17591.53846153846\n",
      "Increment: 165    Initial Residual: 8506416.503424961\n",
      "    Residual: 1.0808157977762824e-07   0\n",
      "U at the left and right 0.0   0.221776\n",
      "Source at the left and right 0.0   17805.415384615386\n",
      "Increment: 166    Initial Residual: 8502444.744724885\n",
      "    Residual: 4.219826593700495e-08   0\n",
      "U at the left and right 0.0   0.22244399999999998\n",
      "Source at the left and right 0.0   18020.584615384618\n",
      "Increment: 167    Initial Residual: 8504750.644062595\n",
      "    Residual: 5.1281973339379596e-08   0\n",
      "U at the left and right 0.0   0.223104\n",
      "Source at the left and right 0.0   18237.046153846153\n",
      "Increment: 168    Initial Residual: 8508857.19119758\n",
      "    Residual: 6.757706379023096e-08   0\n",
      "U at the left and right 0.0   0.22375599999999998\n",
      "Source at the left and right 0.0   18454.800000000003\n",
      "Increment: 169    Initial Residual: 8512673.088526275\n",
      "    Residual: 1.4250757079278448e-07   0\n",
      "U at the left and right 0.0   0.2244\n",
      "Source at the left and right 0.0   18673.846153846156\n",
      "Increment: 170    Initial Residual: 8530708.717502264\n",
      "    Residual: 1.046816516766214e-07   0\n",
      "U at the left and right 0.0   0.22503599999999999\n",
      "Source at the left and right 0.0   18894.18461538462\n",
      "Increment: 171    Initial Residual: 8566402.421122842\n",
      "    Residual: 8.200399718686944e-08   0\n",
      "U at the left and right 0.0   0.225664\n",
      "Source at the left and right 0.0   19115.81538461539\n",
      "Increment: 172    Initial Residual: 8603001.329957299\n",
      "    Residual: 7.984427828100625e-08   0\n",
      "U at the left and right 0.0   0.22628399999999999\n",
      "Source at the left and right 0.0   19338.73846153846\n",
      "Increment: 173    Initial Residual: 8628348.2211574\n",
      "    Residual: 3.705446843817413e-08   0\n",
      "U at the left and right 0.0   0.226896\n",
      "Source at the left and right 0.0   19562.95384615385\n",
      "Increment: 174    Initial Residual: 8640276.910894807\n",
      "    Residual: 4.8553982368622254e-08   0\n",
      "U at the left and right 0.0   0.22749999999999998\n",
      "Source at the left and right 0.0   19788.461538461543\n",
      "Increment: 175    Initial Residual: 8636741.569862038\n",
      "    Residual: 9.551847005631956e-08   0\n",
      "U at the left and right 0.0   0.228096\n",
      "Source at the left and right 0.0   20015.261538461535\n",
      "Increment: 176    Initial Residual: 8623933.896728469\n",
      "    Residual: 3.338502408738233e-08   0\n",
      "U at the left and right 0.0   0.228684\n",
      "Source at the left and right 0.0   20243.353846153845\n",
      "Increment: 177    Initial Residual: 8621058.128497243\n",
      "    Residual: 1.2002865686154862e-07   0\n",
      "U at the left and right 0.0   0.229264\n",
      "Source at the left and right 0.0   20472.738461538458\n",
      "Increment: 178    Initial Residual: 8633231.593710562\n",
      "    Residual: 6.324084893377483e-08   0\n",
      "U at the left and right 0.0   0.22983599999999998\n",
      "Source at the left and right 0.0   20703.415384615382\n",
      "Increment: 179    Initial Residual: 8645161.85587321\n",
      "    Residual: 8.7613648372827e-08   0\n",
      "U at the left and right 0.0   0.2304\n",
      "Source at the left and right 0.0   20935.38461538461\n",
      "Increment: 180    Initial Residual: 8651668.400796851\n",
      "    Residual: 8.365329940947003e-08   0\n",
      "U at the left and right 0.0   0.230956\n",
      "Source at the left and right 0.0   21168.64615384615\n",
      "Increment: 181    Initial Residual: 8661693.380727725\n",
      "    Residual: 1.4962444258615864e-07   0\n",
      "U at the left and right 0.0   0.231504\n",
      "Source at the left and right 0.0   21403.199999999997\n",
      "Increment: 182    Initial Residual: 8673686.858558055\n",
      "    Residual: 8.495989867896204e-08   0\n",
      "U at the left and right 0.0   0.232044\n",
      "Source at the left and right 0.0   21639.04615384615\n",
      "Increment: 183    Initial Residual: 8681588.551029839\n",
      "    Residual: 1.1759030923937197e-07   0\n",
      "U at the left and right 0.0   0.232576\n",
      "Source at the left and right 0.0   21876.184615384613\n",
      "Increment: 184    Initial Residual: 8691520.243620707\n",
      "    Residual: 9.760242808622456e-08   0\n",
      "U at the left and right 0.0   0.2331\n",
      "Source at the left and right 0.0   22114.615384615383\n",
      "Increment: 185    Initial Residual: 8702964.720092602\n",
      "    Residual: 1.0961947599806954e-07   0\n",
      "U at the left and right 0.0   0.233616\n",
      "Source at the left and right 0.0   22354.33846153846\n",
      "Increment: 186    Initial Residual: 8706669.39565246\n",
      "    Residual: 8.612594024611184e-08   0\n",
      "U at the left and right 0.0   0.234124\n",
      "Source at the left and right 0.0   22595.35384615385\n",
      "Increment: 187    Initial Residual: 8709312.000536276\n",
      "    Residual: 7.721557217901248e-08   0\n",
      "U at the left and right 0.0   0.234624\n",
      "Source at the left and right 0.0   22837.661538461536\n",
      "Increment: 188    Initial Residual: 8724578.1264528\n",
      "    Residual: 9.270285917914886e-08   0\n",
      "U at the left and right 0.0   0.235116\n",
      "Source at the left and right 0.0   23081.26153846154\n",
      "Increment: 189    Initial Residual: 8744380.261091134\n",
      "    Residual: 6.891787052154541e-08   0\n",
      "U at the left and right 0.0   0.2356\n",
      "Source at the left and right 0.0   23326.153846153844\n",
      "Increment: 190    Initial Residual: 8752146.299680578\n",
      "    Residual: 1.6563932653826258e-07   0\n",
      "U at the left and right 0.0   0.236076\n",
      "Source at the left and right 0.0   23572.33846153846\n",
      "Increment: 191    Initial Residual: 8752227.906459251\n",
      "    Residual: 3.2342514682906375e-08   0\n",
      "U at the left and right 0.0   0.236544\n",
      "Source at the left and right 0.0   23819.815384615387\n",
      "Increment: 192    Initial Residual: 8755130.636521874\n",
      "    Residual: 9.600756839751106e-08   0\n",
      "U at the left and right 0.0   0.237004\n",
      "Source at the left and right 0.0   24068.584615384614\n",
      "Increment: 193    Initial Residual: 8760499.062125927\n",
      "    Residual: 5.8680713184264916e-08   0\n",
      "U at the left and right 0.0   0.237456\n",
      "Source at the left and right 0.0   24318.64615384615\n",
      "Increment: 194    Initial Residual: 8771957.394743226\n",
      "    Residual: 8.749476955501769e-08   0\n",
      "U at the left and right 0.0   0.2379\n",
      "Source at the left and right 0.0   24570.0\n",
      "Increment: 195    Initial Residual: 8795415.431832237\n",
      "    Residual: 7.106180435767505e-08   0\n",
      "U at the left and right 0.0   0.238336\n",
      "Source at the left and right 0.0   24822.646153846155\n",
      "Increment: 196    Initial Residual: 8816181.81460865\n",
      "    Residual: 1.2159021681045042e-07   0\n",
      "U at the left and right 0.0   0.238764\n",
      "Source at the left and right 0.0   25076.584615384614\n",
      "Increment: 197    Initial Residual: 8817903.190036114\n",
      "    Residual: 1.069846040068148e-07   0\n",
      "U at the left and right 0.0   0.239184\n",
      "Source at the left and right 0.0   25331.81538461538\n",
      "Increment: 198    Initial Residual: 8813779.032664347\n",
      "    Residual: 5.8265374301437486e-08   0\n",
      "U at the left and right 0.0   0.239596\n",
      "Source at the left and right 0.0   25588.338461538464\n",
      "Increment: 199    Initial Residual: 8820609.151003301\n",
      "    Residual: 1.1007744310120034e-07   0\n",
      "U at the left and right 0.0   0.24\n",
      "Source at the left and right 0.0   25846.153846153844\n",
      "Increment: 200    Initial Residual: 8834507.879240002\n",
      "    Residual: 1.296212337025588e-07   0\n",
      "U at the left and right 0.0   0.240396\n",
      "Source at the left and right 0.0   26105.261538461542\n",
      "Increment: 201    Initial Residual: 8851519.56853234\n",
      "    Residual: 1.0119752981386986e-07   0\n",
      "U at the left and right 0.0   0.240784\n",
      "Source at the left and right 0.0   26365.661538461543\n",
      "Increment: 202    Initial Residual: 8875103.924122687\n",
      "    Residual: 1.1952537465495347e-07   0\n",
      "U at the left and right 0.0   0.24116400000000002\n",
      "Source at the left and right 0.0   26627.353846153845\n",
      "Increment: 203    Initial Residual: 8897138.64102649\n",
      "    Residual: 1.3352060950510092e-07   0\n",
      "U at the left and right 0.0   0.241536\n",
      "Source at the left and right 0.0   26890.338461538464\n",
      "Increment: 204    Initial Residual: 8907947.16123454\n",
      "    Residual: 1.103293008721131e-07   0\n",
      "U at the left and right 0.0   0.2419\n",
      "Source at the left and right 0.0   27154.61538461539\n",
      "Increment: 205    Initial Residual: 8916446.21891889\n",
      "    Residual: 7.096409127693154e-08   0\n",
      "U at the left and right 0.0   0.242256\n",
      "Source at the left and right 0.0   27420.18461538462\n",
      "Increment: 206    Initial Residual: 8927313.294317482\n",
      "    Residual: 1.0196599998659844e-07   0\n",
      "U at the left and right 0.0   0.24260400000000001\n",
      "Source at the left and right 0.0   27687.046153846153\n",
      "Increment: 207    Initial Residual: 8926174.072441323\n",
      "    Residual: 9.284776956861561e-08   0\n",
      "U at the left and right 0.0   0.242944\n",
      "Source at the left and right 0.0   27955.200000000004\n",
      "Increment: 208    Initial Residual: 8910745.518859867\n",
      "    Residual: 9.719278105102098e-08   0\n",
      "U at the left and right 0.0   0.24327600000000002\n",
      "Source at the left and right 0.0   28224.64615384615\n",
      "Increment: 209    Initial Residual: 8902579.251571765\n",
      "    Residual: 9.30437397510561e-08   0\n",
      "U at the left and right 0.0   0.2436\n",
      "Source at the left and right 0.0   28495.38461538461\n",
      "Increment: 210    Initial Residual: 8911407.167627413\n",
      "    Residual: 8.592933419674145e-08   0\n",
      "U at the left and right 0.0   0.24391600000000002\n",
      "Source at the left and right 0.0   28767.415384615386\n",
      "Increment: 211    Initial Residual: 8929587.805681698\n",
      "    Residual: 6.971868601520696e-08   0\n",
      "U at the left and right 0.0   0.24422400000000002\n",
      "Source at the left and right 0.0   29040.73846153846\n",
      "Increment: 212    Initial Residual: 8956322.987607272\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "    Residual: 9.174827337436632e-08   0\n",
      "U at the left and right 0.0   0.24452400000000002\n",
      "Source at the left and right 0.0   29315.35384615384\n",
      "Increment: 213    Initial Residual: 8983481.843134845\n",
      "    Residual: 1.4549214142216408e-07   0\n",
      "U at the left and right 0.0   0.24481600000000003\n",
      "Source at the left and right 0.0   29591.261538461535\n",
      "Increment: 214    Initial Residual: 8989351.517144622\n",
      "    Residual: 1.3454629996233998e-07   0\n",
      "U at the left and right 0.0   0.2451\n",
      "Source at the left and right 0.0   29868.46153846154\n",
      "Increment: 215    Initial Residual: 8974048.808273645\n",
      "    Residual: 7.958313521589434e-08   0\n",
      "U at the left and right 0.0   0.245376\n",
      "Source at the left and right 0.0   30146.953846153847\n",
      "Increment: 216    Initial Residual: 8963211.385077802\n",
      "    Residual: 1.1777825043550501e-07   0\n",
      "U at the left and right 0.0   0.24564400000000003\n",
      "Source at the left and right 0.0   30426.73846153846\n",
      "Increment: 217    Initial Residual: 8964504.002780577\n",
      "    Residual: 4.734197641588313e-08   0\n",
      "U at the left and right 0.0   0.245904\n",
      "Source at the left and right 0.0   30707.81538461538\n",
      "Increment: 218    Initial Residual: 8965211.434021644\n",
      "    Residual: 9.118879855604429e-08   0\n",
      "U at the left and right 0.0   0.246156\n",
      "Source at the left and right 0.0   30990.184615384613\n",
      "Increment: 219    Initial Residual: 8966598.052571328\n",
      "    Residual: 1.3994032056666932e-07   0\n",
      "U at the left and right 0.0   0.24640000000000004\n",
      "Source at the left and right 0.0   31273.846153846156\n",
      "Increment: 220    Initial Residual: 8975731.428444618\n",
      "    Residual: 9.831520334181672e-08   0\n",
      "U at the left and right 0.0   0.24663600000000002\n",
      "Source at the left and right 0.0   31558.800000000003\n",
      "Increment: 221    Initial Residual: 8985640.496059794\n",
      "    Residual: 9.179552976347672e-08   0\n",
      "U at the left and right 0.0   0.24686400000000003\n",
      "Source at the left and right 0.0   31845.046153846153\n",
      "Increment: 222    Initial Residual: 8995202.46411879\n",
      "    Residual: 6.313103187859925e-08   0\n",
      "U at the left and right 0.0   0.24708400000000003\n",
      "Source at the left and right 0.0   32132.584615384614\n",
      "Increment: 223    Initial Residual: 9017189.560043788\n",
      "    Residual: 8.760869830935387e-08   0\n",
      "U at the left and right 0.0   0.24729600000000002\n",
      "Source at the left and right 0.0   32421.415384615386\n",
      "Increment: 224    Initial Residual: 9044280.881486123\n",
      "    Residual: 1.3859193947612248e-07   0\n",
      "U at the left and right 0.0   0.24750000000000003\n",
      "Source at the left and right 0.0   32711.53846153846\n",
      "Increment: 225    Initial Residual: 9056040.447221745\n",
      "    Residual: 8.214666348397711e-08   0\n",
      "U at the left and right 0.0   0.24769600000000003\n",
      "Source at the left and right 0.0   33002.95384615385\n",
      "Increment: 226    Initial Residual: 9060510.312305585\n",
      "    Residual: 1.2080657516622545e-07   0\n",
      "U at the left and right 0.0   0.24788400000000002\n",
      "Source at the left and right 0.0   33295.66153846154\n",
      "Increment: 227    Initial Residual: 9075833.106665902\n",
      "    Residual: 1.051240025099418e-07   0\n",
      "U at the left and right 0.0   0.24806400000000003\n",
      "Source at the left and right 0.0   33589.661538461536\n",
      "Increment: 228    Initial Residual: 9094242.593187435\n",
      "    Residual: 2.017770055808532e-07   0\n",
      "U at the left and right 0.0   0.24823600000000004\n",
      "Source at the left and right 0.0   33884.95384615385\n",
      "Increment: 229    Initial Residual: 9103426.007260079\n",
      "    Residual: 1.1840622928226603e-07   0\n",
      "U at the left and right 0.0   0.24840000000000004\n",
      "Source at the left and right 0.0   34181.53846153846\n",
      "Increment: 230    Initial Residual: 9108227.195479497\n",
      "    Residual: 1.0751835770653048e-07   0\n",
      "U at the left and right 0.0   0.24855600000000003\n",
      "Source at the left and right 0.0   34479.41538461539\n",
      "Increment: 231    Initial Residual: 9107811.835948925\n",
      "    Residual: 1.1892883528134335e-07   0\n",
      "U at the left and right 0.0   0.24870400000000004\n",
      "Source at the left and right 0.0   34778.58461538462\n",
      "Increment: 232    Initial Residual: 9098575.006208928\n",
      "    Residual: 1.1340740650809385e-07   0\n",
      "U at the left and right 0.0   0.24884400000000004\n",
      "Source at the left and right 0.0   35079.04615384615\n",
      "Increment: 233    Initial Residual: 9099202.945924291\n",
      "    Residual: 1.7993094295355414e-07   0\n",
      "U at the left and right 0.0   0.24897600000000003\n",
      "Source at the left and right 0.0   35380.8\n",
      "Increment: 234    Initial Residual: 9124873.95231161\n",
      "    Residual: 1.1843186507444047e-07   0\n",
      "U at the left and right 0.0   0.24910000000000002\n",
      "Source at the left and right 0.0   35683.846153846156\n",
      "Increment: 235    Initial Residual: 9155277.500424609\n",
      "    Residual: 1.2499514785136708e-07   0\n",
      "U at the left and right 0.0   0.24921600000000002\n",
      "Source at the left and right 0.0   35988.18461538462\n",
      "Increment: 236    Initial Residual: 9167177.53783038\n",
      "    Residual: 1.5221070719042156e-07   0\n",
      "U at the left and right 0.0   0.24932400000000002\n",
      "Source at the left and right 0.0   36293.81538461539\n",
      "Increment: 237    Initial Residual: 9168133.360524874\n",
      "    Residual: 1.057574092504183e-07   0\n",
      "U at the left and right 0.0   0.24942400000000003\n",
      "Source at the left and right 0.0   36600.738461538465\n",
      "Increment: 238    Initial Residual: 9166559.43489515\n",
      "    Residual: 1.0635850594496314e-07   0\n",
      "U at the left and right 0.0   0.24951600000000002\n",
      "Source at the left and right 0.0   36908.953846153854\n",
      "Increment: 239    Initial Residual: 9158508.720943574\n",
      "    Residual: 9.093638881097841e-08   0\n",
      "U at the left and right 0.0   0.2496\n",
      "Source at the left and right 0.0   37218.46153846153\n",
      "Increment: 240    Initial Residual: 9154824.634082045\n",
      "    Residual: 7.731660299195818e-08   0\n",
      "U at the left and right 0.0   0.249676\n",
      "Source at the left and right 0.0   37529.261538461535\n",
      "Increment: 241    Initial Residual: 9166559.7163117\n",
      "    Residual: 1.0558093131161025e-07   0\n",
      "U at the left and right 0.0   0.249744\n",
      "Source at the left and right 0.0   37841.35384615384\n",
      "Increment: 242    Initial Residual: 9178953.469727725\n",
      "    Residual: 1.0363657849191279e-07   0\n",
      "U at the left and right 0.0   0.249804\n",
      "Source at the left and right 0.0   38154.73846153846\n",
      "Increment: 243    Initial Residual: 9184052.034841008\n",
      "    Residual: 1.4308158197944378e-07   0\n",
      "U at the left and right 0.0   0.249856\n",
      "Source at the left and right 0.0   38469.41538461538\n",
      "Increment: 244    Initial Residual: 9201342.22010611\n",
      "    Residual: 1.22262472543672e-07   0\n",
      "U at the left and right 0.0   0.2499\n",
      "Source at the left and right 0.0   38785.38461538461\n",
      "Increment: 245    Initial Residual: 9232570.020558419\n",
      "    Residual: 1.3808093903381845e-07   0\n",
      "U at the left and right 0.0   0.249936\n",
      "Source at the left and right 0.0   39102.64615384615\n",
      "Increment: 246    Initial Residual: 9252207.003643\n",
      "    Residual: 1.6795338175475617e-07   0\n",
      "U at the left and right 0.0   0.249964\n",
      "Source at the left and right 0.0   39421.2\n",
      "Increment: 247    Initial Residual: 9253376.383399855\n",
      "    Residual: 1.374261055366101e-07   0\n",
      "U at the left and right 0.0   0.249984\n",
      "Source at the left and right 0.0   39741.046153846146\n",
      "Increment: 248    Initial Residual: 9250137.185056979\n",
      "    Residual: 1.057574092504183e-07   0\n",
      "U at the left and right 0.0   0.249996\n",
      "Source at the left and right 0.0   40062.18461538461\n",
      "Increment: 249    Initial Residual: 9245430.132805772\n",
      "    Residual: 1.1672039589799143e-07   0\n",
      "U at the left and right 0.0   0.25\n",
      "Source at the left and right 0.0   40384.61538461538\n",
      "Increment: 250    Initial Residual: 9242199.72231014\n",
      "    Residual: 1.033138594172403e-07   0\n",
      "U at the left and right 0.0   0.249996\n",
      "Source at the left and right 0.0   40708.338461538464\n",
      "Increment: 251    Initial Residual: 9258305.5793669\n",
      "    Residual: 8.77323661080054e-08   0\n",
      "U at the left and right 0.0   0.249984\n",
      "Source at the left and right 0.0   41033.35384615384\n",
      "Increment: 252    Initial Residual: 9287961.525621675\n",
      "    Residual: 1.5722534634297838e-07   0\n",
      "U at the left and right 0.0   0.249964\n",
      "Source at the left and right 0.0   41359.661538461536\n",
      "Increment: 253    Initial Residual: 9299219.868235884\n",
      "    Residual: 1.0156541315770877e-07   0\n",
      "U at the left and right 0.0   0.249936\n",
      "Source at the left and right 0.0   41687.261538461535\n",
      "Increment: 254    Initial Residual: 9289368.12412249\n",
      "    Residual: 1.1903818174651588e-07   0\n",
      "U at the left and right 0.0   0.2499\n",
      "Source at the left and right 0.0   42016.153846153844\n",
      "Increment: 255    Initial Residual: 9283774.647989253\n",
      "    Residual: 1.3556423018074603e-07   0\n",
      "U at the left and right 0.0   0.249856\n",
      "Source at the left and right 0.0   42346.338461538464\n",
      "Increment: 256    Initial Residual: 9286320.04012154\n",
      "    Residual: 1.4288139566449179e-07   0\n",
      "U at the left and right 0.0   0.249804\n",
      "Source at the left and right 0.0   42677.81538461539\n",
      "Increment: 257    Initial Residual: 9288437.907638833\n",
      "    Residual: 1.1376249158894582e-07   0\n",
      "U at the left and right 0.0   0.249744\n",
      "Source at the left and right 0.0   43010.584615384614\n",
      "Increment: 258    Initial Residual: 9298624.04533401\n",
      "    Residual: 9.095546304061892e-08   0\n",
      "U at the left and right 0.0   0.249676\n",
      "Source at the left and right 0.0   43344.64615384616\n",
      "Increment: 259    Initial Residual: 9315617.46294575\n",
      "    Residual: 9.63457592214203e-08   0\n",
      "U at the left and right 0.0   0.2496\n",
      "Source at the left and right 0.0   43680.0\n",
      "Increment: 260    Initial Residual: 9323039.353169449\n",
      "    Residual: 1.4261708437570887e-07   0\n",
      "U at the left and right 0.0   0.249516\n",
      "Source at the left and right 0.0   44016.64615384616\n",
      "Increment: 261    Initial Residual: 9328300.866275666\n",
      "    Residual: 7.859612139255607e-08   0\n",
      "U at the left and right 0.0   0.249424\n",
      "Source at the left and right 0.0   44354.58461538462\n",
      "Increment: 262    Initial Residual: 9351633.086570678\n",
      "    Residual: 1.4606926915945303e-07   0\n",
      "U at the left and right 0.0   0.249324\n",
      "Source at the left and right 0.0   44693.81538461539\n",
      "Increment: 263    Initial Residual: 9381387.498104027\n",
      "    Residual: 1.5748441680382353e-07   0\n",
      "U at the left and right 0.0   0.249216\n",
      "Source at the left and right 0.0   45034.338461538464\n",
      "Increment: 264    Initial Residual: 9395818.12951267\n",
      "    Residual: 1.3943115145214888e-07   0\n",
      "U at the left and right 0.0   0.2491\n",
      "Source at the left and right 0.0   45376.15384615385\n",
      "Increment: 265    Initial Residual: 9406235.581480138\n",
      "    Residual: 1.2169004459147845e-07   0\n",
      "U at the left and right 0.0   0.248976\n",
      "Source at the left and right 0.0   45719.26153846154\n",
      "Increment: 266    Initial Residual: 9426661.014588613\n",
      "    Residual: 1.2568024749540722e-07   0\n",
      "U at the left and right 0.0   0.248844\n",
      "Source at the left and right 0.0   46063.66153846154\n",
      "Increment: 267    Initial Residual: 9446777.928767508\n",
      "    Residual: 1.5106385181927176e-07   0\n",
      "U at the left and right 0.0   0.248704\n",
      "Source at the left and right 0.0   46409.35384615385\n",
      "Increment: 268    Initial Residual: 9464035.729415473\n",
      "    Residual: 1.0796515362294519e-07   0\n",
      "U at the left and right 0.0   0.248556\n",
      "Source at the left and right 0.0   46756.338461538464\n",
      "Increment: 269    Initial Residual: 9484880.710985273\n",
      "    Residual: 1.7121397331641503e-07   0\n",
      "U at the left and right 0.0   0.2484\n",
      "Source at the left and right 0.0   47104.61538461539\n",
      "Increment: 270    Initial Residual: 9491271.560663166\n",
      "    Residual: 1.7637194043048941e-07   0\n",
      "U at the left and right 0.0   0.24823599999999998\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Source at the left and right 0.0   47454.18461538463\n",
      "Increment: 271    Initial Residual: 9469779.950468775\n",
      "    Residual: 1.4925878949071022e-07   0\n",
      "U at the left and right 0.0   0.248064\n",
      "Source at the left and right 0.0   47805.04615384616\n",
      "Increment: 272    Initial Residual: 9449650.213875603\n",
      "    Residual: 1.3463330048870399e-07   0\n",
      "U at the left and right 0.0   0.247884\n",
      "Source at the left and right 0.0   48157.200000000004\n",
      "Increment: 273    Initial Residual: 9455353.698305247\n",
      "    Residual: 1.0153979012913191e-07   0\n",
      "U at the left and right 0.0   0.247696\n",
      "Source at the left and right 0.0   48510.64615384616\n",
      "Increment: 274    Initial Residual: 9471794.496758088\n",
      "    Residual: 1.1828529999746772e-07   0\n",
      "U at the left and right 0.0   0.2475\n",
      "Source at the left and right 0.0   48865.384615384624\n",
      "Increment: 275    Initial Residual: 9486269.09130834\n",
      "    Residual: 1.0608495911485066e-07   0\n",
      "U at the left and right 0.0   0.247296\n",
      "Source at the left and right 0.0   49221.41538461539\n",
      "Increment: 276    Initial Residual: 9504538.906646678\n",
      "    Residual: 1.3430756518135838e-07   0\n",
      "U at the left and right 0.0   0.247084\n",
      "Source at the left and right 0.0   49578.738461538465\n",
      "Increment: 277    Initial Residual: 9517229.970474433\n",
      "    Residual: 1.3725243016926928e-07   0\n",
      "U at the left and right 0.0   0.246864\n",
      "Source at the left and right 0.0   49937.353846153856\n",
      "Increment: 278    Initial Residual: 9513256.535007961\n",
      "    Residual: 1.6114033743963316e-07   0\n",
      "U at the left and right 0.0   0.246636\n",
      "Source at the left and right 0.0   50297.26153846155\n",
      "Increment: 279    Initial Residual: 9512442.857716\n",
      "    Residual: 1.7507873606040848e-07   0\n",
      "U at the left and right 0.0   0.24639999999999998\n",
      "Source at the left and right 0.0   50658.461538461546\n",
      "Increment: 280    Initial Residual: 9527175.054659659\n",
      "    Residual: 1.8082773614803905e-07   0\n",
      "U at the left and right 0.0   0.24615599999999999\n",
      "Source at the left and right 0.0   51020.95384615386\n",
      "Increment: 281    Initial Residual: 9535703.765470626\n",
      "    Residual: 1.8477073731779486e-07   0\n",
      "U at the left and right 0.0   0.24590399999999998\n",
      "Source at the left and right 0.0   51384.73846153847\n",
      "Increment: 282    Initial Residual: 9532883.509591714\n",
      "    Residual: 1.714721422157806e-07   0\n",
      "U at the left and right 0.0   0.245644\n",
      "Source at the left and right 0.0   51749.81538461539\n",
      "Increment: 283    Initial Residual: 9545365.284515107\n",
      "    Residual: 1.428935361518673e-07   0\n",
      "U at the left and right 0.0   0.24537599999999998\n",
      "Source at the left and right 0.0   52116.18461538463\n",
      "Increment: 284    Initial Residual: 9575546.794843053\n",
      "    Residual: 1.1730598438777973e-07   0\n",
      "U at the left and right 0.0   0.24509999999999998\n",
      "Source at the left and right 0.0   52483.846153846156\n",
      "Increment: 285    Initial Residual: 9601889.064410985\n",
      "    Residual: 2.0661092734131288e-07   0\n",
      "U at the left and right 0.0   0.24481599999999998\n",
      "Source at the left and right 0.0   52852.80000000002\n",
      "Increment: 286    Initial Residual: 9624164.729062783\n",
      "    Residual: 2.0764525517190018e-07   0\n",
      "U at the left and right 0.0   0.244524\n",
      "Source at the left and right 0.0   53223.04615384617\n",
      "Increment: 287    Initial Residual: 9643727.276251996\n",
      "    Residual: 2.0262206322595545e-07   0\n",
      "U at the left and right 0.0   0.244224\n",
      "Source at the left and right 0.0   53594.58461538462\n",
      "Increment: 288    Initial Residual: 9644634.603453364\n",
      "    Residual: 8.682803825144965e-08   0\n",
      "U at the left and right 0.0   0.243916\n",
      "Source at the left and right 0.0   53967.415384615364\n",
      "Increment: 289    Initial Residual: 9634666.52425719\n",
      "    Residual: 1.80135698793671e-07   0\n",
      "U at the left and right 0.0   0.2436\n",
      "Source at the left and right 0.0   54341.53846153845\n",
      "Increment: 290    Initial Residual: 9646341.510874426\n",
      "    Residual: 2.5414187340795784e-07   0\n",
      "U at the left and right 0.0   0.24327600000000002\n",
      "Source at the left and right 0.0   54716.95384615383\n",
      "Increment: 291    Initial Residual: 9676975.705732057\n",
      "    Residual: 1.4619094781837301e-07   0\n",
      "U at the left and right 0.0   0.242944\n",
      "Source at the left and right 0.0   55093.661538461536\n",
      "Increment: 292    Initial Residual: 9695191.501211042\n",
      "    Residual: 2.5555430354786994e-07   0\n",
      "U at the left and right 0.0   0.24260400000000001\n",
      "Source at the left and right 0.0   55471.661538461536\n",
      "Increment: 293    Initial Residual: 9699736.78442647\n",
      "    Residual: 1.4334201132678198e-07   0\n",
      "U at the left and right 0.0   0.242256\n",
      "Source at the left and right 0.0   55850.95384615383\n",
      "Increment: 294    Initial Residual: 9705405.792302435\n",
      "    Residual: 1.5742657634447448e-07   0\n",
      "U at the left and right 0.0   0.2419\n",
      "Source at the left and right 0.0   56231.538461538454\n",
      "Increment: 295    Initial Residual: 9706703.01858084\n",
      "    Residual: 2.510704715215336e-07   0\n",
      "U at the left and right 0.0   0.241536\n",
      "Source at the left and right 0.0   56613.41538461538\n",
      "Increment: 296    Initial Residual: 9705831.08386008\n",
      "    Residual: 1.0274560678227006e-07   0\n",
      "U at the left and right 0.0   0.24116400000000002\n",
      "Source at the left and right 0.0   56996.58461538461\n",
      "Increment: 297    Initial Residual: 9722765.496650876\n",
      "    Residual: 9.343444703562644e-08   0\n",
      "U at the left and right 0.0   0.240784\n",
      "Source at the left and right 0.0   57381.04615384614\n",
      "Increment: 298    Initial Residual: 9746862.96100457\n",
      "    Residual: 1.819156940761559e-07   0\n",
      "U at the left and right 0.0   0.240396\n",
      "Source at the left and right 0.0   57766.799999999996\n",
      "Increment: 299    Initial Residual: 9751465.645897008\n",
      "    Residual: 1.641348700974897e-07   0\n",
      "U at the left and right 0.0   0.24\n",
      "Source at the left and right 0.0   58153.84615384615\n",
      "Increment: 300    Initial Residual: 9751295.064679658\n",
      "    Residual: 1.7740656139119324e-07   0\n",
      "U at the left and right 0.0   0.239596\n",
      "Source at the left and right 0.0   58542.18461538461\n",
      "Increment: 301    Initial Residual: 9770769.675909499\n",
      "    Residual: 1.9411541923152372e-07   0\n",
      "U at the left and right 0.0   0.239184\n",
      "Source at the left and right 0.0   58931.81538461537\n",
      "Increment: 302    Initial Residual: 9794922.974684445\n",
      "    Residual: 2.0828962233496405e-07   0\n",
      "U at the left and right 0.0   0.238764\n",
      "Source at the left and right 0.0   59322.73846153845\n",
      "Increment: 303    Initial Residual: 9807815.4672101\n",
      "    Residual: 2.310731239035949e-07   0\n",
      "U at the left and right 0.0   0.238336\n",
      "Source at the left and right 0.0   59714.95384615383\n",
      "Increment: 304    Initial Residual: 9823236.527193392\n",
      "    Residual: 1.6945464790864866e-07   0\n",
      "U at the left and right 0.0   0.2379\n",
      "Source at the left and right 0.0   60108.46153846153\n",
      "Increment: 305    Initial Residual: 9843503.555940416\n",
      "    Residual: 1.3967354871569338e-07   0\n",
      "U at the left and right 0.0   0.237456\n",
      "Source at the left and right 0.0   60503.26153846153\n",
      "Increment: 306    Initial Residual: 9857489.541049251\n",
      "    Residual: 1.5860125397802405e-07   0\n",
      "U at the left and right 0.0   0.237004\n",
      "Source at the left and right 0.0   60899.35384615384\n",
      "Increment: 307    Initial Residual: 9880700.594324248\n",
      "    Residual: 1.3791437761287873e-07   0\n",
      "U at the left and right 0.0   0.236544\n",
      "Source at the left and right 0.0   61296.73846153845\n",
      "Increment: 308    Initial Residual: 9925138.8687217\n",
      "    Residual: 1.5996803854480391e-07   0\n",
      "U at the left and right 0.0   0.236076\n",
      "Source at the left and right 0.0   61695.41538461539\n",
      "Increment: 309    Initial Residual: 9958953.143422771\n",
      "    Residual: 2.1430742261579265e-07   0\n",
      "U at the left and right 0.0   0.2356\n",
      "Source at the left and right 0.0   62095.38461538462\n",
      "Increment: 310    Initial Residual: 9958225.24962068\n",
      "    Residual: 3.0437439872019356e-07   0\n",
      "U at the left and right 0.0   0.235116\n",
      "Source at the left and right 0.0   62496.646153846144\n",
      "Increment: 311    Initial Residual: 9947894.870720271\n",
      "    Residual: 1.9109595467405312e-07   0\n",
      "U at the left and right 0.0   0.234624\n",
      "Source at the left and right 0.0   62899.200000000004\n",
      "Increment: 312    Initial Residual: 9946277.612496221\n",
      "    Residual: 1.268275341989859e-07   0\n",
      "U at the left and right 0.0   0.234124\n",
      "Source at the left and right 0.0   63303.04615384615\n",
      "Increment: 313    Initial Residual: 9943282.375450287\n",
      "    Residual: 1.2918555337434163e-07   0\n",
      "U at the left and right 0.0   0.233616\n",
      "Source at the left and right 0.0   63708.18461538463\n",
      "Increment: 314    Initial Residual: 9945451.903915383\n",
      "    Residual: 1.7381583373678036e-07   0\n",
      "U at the left and right 0.0   0.2331\n",
      "Source at the left and right 0.0   64114.61538461538\n",
      "Increment: 315    Initial Residual: 9962434.679865312\n",
      "    Residual: 1.493778700862001e-07   0\n",
      "U at the left and right 0.0   0.232576\n",
      "Source at the left and right 0.0   64522.33846153846\n",
      "Increment: 316    Initial Residual: 9972702.338673947\n",
      "    Residual: 1.9678914319064008e-07   0\n",
      "U at the left and right 0.0   0.232044\n",
      "Source at the left and right 0.0   64931.35384615384\n",
      "Increment: 317    Initial Residual: 9966922.814464688\n",
      "    Residual: 1.8213964904594623e-07   0\n",
      "U at the left and right 0.0   0.231504\n",
      "Source at the left and right 0.0   65341.661538461536\n",
      "Increment: 318    Initial Residual: 9974663.349803068\n",
      "    Residual: 1.5404874926906327e-07   0\n",
      "U at the left and right 0.0   0.230956\n",
      "Source at the left and right 0.0   65753.26153846155\n",
      "Increment: 319    Initial Residual: 10003362.585812233\n",
      "    Residual: 9.331833608355634e-08   0\n",
      "U at the left and right 0.0   0.2304\n",
      "Source at the left and right 0.0   66166.15384615384\n",
      "Increment: 320    Initial Residual: 10024638.935142277\n",
      "    Residual: 1.3526959460500856e-07   0\n",
      "U at the left and right 0.0   0.22983599999999998\n",
      "Source at the left and right 0.0   66580.33846153846\n",
      "Increment: 321    Initial Residual: 10035783.52359502\n",
      "    Residual: 1.3515412758046192e-07   0\n",
      "U at the left and right 0.0   0.229264\n",
      "Source at the left and right 0.0   66995.81538461539\n",
      "Increment: 322    Initial Residual: 10056965.891389962\n",
      "    Residual: 1.3779797954992712e-07   0\n",
      "U at the left and right 0.0   0.228684\n",
      "Source at the left and right 0.0   67412.5846153846\n",
      "Increment: 323    Initial Residual: 10081802.614723083\n",
      "    Residual: 2.0851644827658728e-07   0\n",
      "U at the left and right 0.0   0.228096\n",
      "Source at the left and right 0.0   67830.64615384617\n",
      "Increment: 324    Initial Residual: 10099647.439287318\n",
      "    Residual: 1.8704518989672052e-07   0\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "U at the left and right 0.0   0.22749999999999998\n",
      "Source at the left and right 0.0   68250.0\n",
      "Increment: 325    Initial Residual: 10125646.71167753\n",
      "    Residual: 1.3492289708163181e-07   0\n",
      "U at the left and right 0.0   0.226896\n",
      "Source at the left and right 0.0   68670.64615384616\n",
      "Increment: 326    Initial Residual: 10153887.904968759\n",
      "    Residual: 1.5587346472229056e-07   0\n",
      "U at the left and right 0.0   0.22628399999999999\n",
      "Source at the left and right 0.0   69092.58461538462\n",
      "Increment: 327    Initial Residual: 10154569.986655599\n",
      "    Residual: 1.3762162224997487e-07   0\n",
      "U at the left and right 0.0   0.225664\n",
      "Source at the left and right 0.0   69515.81538461539\n",
      "Increment: 328    Initial Residual: 10139624.179100579\n",
      "    Residual: 2.1223531698851106e-07   0\n",
      "U at the left and right 0.0   0.22503599999999999\n",
      "Source at the left and right 0.0   69940.33846153847\n",
      "Increment: 329    Initial Residual: 10147307.02137468\n",
      "    Residual: 1.1058842844365087e-07   0\n",
      "U at the left and right 0.0   0.2244\n",
      "Source at the left and right 0.0   70366.15384615384\n",
      "Increment: 330    Initial Residual: 10174131.256892998\n",
      "    Residual: 2.3707602287377894e-07   0\n",
      "U at the left and right 0.0   0.22375599999999998\n",
      "Source at the left and right 0.0   70793.26153846153\n",
      "Increment: 331    Initial Residual: 10198552.613712475\n",
      "    Residual: 1.926555047020452e-07   0\n",
      "U at the left and right 0.0   0.223104\n",
      "Source at the left and right 0.0   71221.66153846154\n",
      "Increment: 332    Initial Residual: 10227937.914647773\n",
      "    Residual: 1.4176920043742678e-07   0\n",
      "U at the left and right 0.0   0.22244399999999998\n",
      "Source at the left and right 0.0   71651.35384615384\n",
      "Increment: 333    Initial Residual: 10261796.511529936\n",
      "    Residual: 2.0800834824067405e-07   0\n",
      "U at the left and right 0.0   0.221776\n",
      "Source at the left and right 0.0   72082.33846153847\n",
      "Increment: 334    Initial Residual: 10279578.228126585\n",
      "    Residual: 2.1994992225059138e-07   0\n",
      "U at the left and right 0.0   0.2211\n",
      "Source at the left and right 0.0   72514.61538461539\n",
      "Increment: 335    Initial Residual: 10291420.12317401\n",
      "    Residual: 2.0169961566301527e-07   0\n",
      "U at the left and right 0.0   0.22041599999999997\n",
      "Source at the left and right 0.0   72948.18461538461\n",
      "Increment: 336    Initial Residual: 10323565.54231372\n",
      "    Residual: 2.3000462413479583e-07   0\n",
      "U at the left and right 0.0   0.21972399999999997\n",
      "Source at the left and right 0.0   73383.04615384617\n",
      "Increment: 337    Initial Residual: 10358528.9714289\n",
      "    Residual: 2.6770948000865755e-07   0\n",
      "U at the left and right 0.0   0.219024\n",
      "Source at the left and right 0.0   73819.20000000001\n",
      "Increment: 338    Initial Residual: 10368261.052162567\n",
      "    Residual: 2.006735427786274e-07   0\n",
      "U at the left and right 0.0   0.21831599999999998\n",
      "Source at the left and right 0.0   74256.64615384617\n",
      "Increment: 339    Initial Residual: 10371393.890486263\n",
      "    Residual: 1.3892635960723206e-07   0\n",
      "U at the left and right 0.0   0.2176\n",
      "Source at the left and right 0.0   74695.38461538462\n",
      "Increment: 340    Initial Residual: 10386986.89770312\n",
      "    Residual: 2.444539921957689e-07   0\n",
      "U at the left and right 0.0   0.21687599999999999\n",
      "Source at the left and right 0.0   75135.4153846154\n",
      "Increment: 341    Initial Residual: 10398697.16700415\n",
      "    Residual: 1.9775643110255892e-07   0\n",
      "U at the left and right 0.0   0.21614399999999998\n",
      "Source at the left and right 0.0   75576.73846153848\n",
      "Increment: 342    Initial Residual: 10404722.035619428\n",
      "    Residual: 2.526408826280708e-07   0\n",
      "U at the left and right 0.0   0.21540399999999998\n",
      "Source at the left and right 0.0   76019.35384615386\n",
      "Increment: 343    Initial Residual: 10421548.407589804\n",
      "    Residual: 2.0554185834992142e-07   0\n",
      "U at the left and right 0.0   0.21465599999999999\n",
      "Source at the left and right 0.0   76463.26153846156\n",
      "Increment: 344    Initial Residual: 10434952.320885288\n",
      "    Residual: 2.5307309365687953e-07   0\n",
      "U at the left and right 0.0   0.21389999999999998\n",
      "Source at the left and right 0.0   76908.46153846156\n",
      "Increment: 345    Initial Residual: 10430397.121309381\n",
      "    Residual: 2.57422681173035e-07   0\n",
      "U at the left and right 0.0   0.21313599999999996\n",
      "Source at the left and right 0.0   77354.95384615385\n",
      "Increment: 346    Initial Residual: 10437853.089240769\n",
      "    Residual: 1.9811575749407526e-07   0\n",
      "U at the left and right 0.0   0.21236399999999997\n",
      "Source at the left and right 0.0   77802.73846153848\n",
      "Increment: 347    Initial Residual: 10474708.59399756\n",
      "    Residual: 1.7959801867591064e-07   0\n",
      "U at the left and right 0.0   0.21158399999999997\n",
      "Source at the left and right 0.0   78251.8153846154\n",
      "Increment: 348    Initial Residual: 10510273.03595657\n",
      "    Residual: 2.4519089865541955e-07   0\n",
      "U at the left and right 0.0   0.21079599999999998\n",
      "Source at the left and right 0.0   78702.18461538463\n",
      "Increment: 349    Initial Residual: 10528164.689428136\n",
      "    Residual: 2.67690039683306e-07   0\n",
      "U at the left and right 0.0   0.20999999999999996\n",
      "Source at the left and right 0.0   79153.84615384617\n",
      "Increment: 350    Initial Residual: 10546008.08117911\n",
      "    Residual: 1.3270611413238105e-07   0\n",
      "U at the left and right 0.0   0.20919599999999997\n",
      "Source at the left and right 0.0   79606.8\n",
      "Increment: 351    Initial Residual: 10562688.601830926\n",
      "    Residual: 2.39094285643425e-07   0\n",
      "U at the left and right 0.0   0.208384\n",
      "Source at the left and right 0.0   80061.04615384614\n",
      "Increment: 352    Initial Residual: 10568700.102522608\n",
      "    Residual: 1.941176533578752e-07   0\n",
      "U at the left and right 0.0   0.20756400000000003\n",
      "Source at the left and right 0.0   80516.5846153846\n",
      "Increment: 353    Initial Residual: 10586919.995950095\n",
      "    Residual: 1.991375872627511e-07   0\n",
      "U at the left and right 0.0   0.206736\n",
      "Source at the left and right 0.0   80973.41538461538\n",
      "Increment: 354    Initial Residual: 10625745.021646675\n",
      "    Residual: 1.9751944454842515e-07   0\n",
      "U at the left and right 0.0   0.20590000000000003\n",
      "Source at the left and right 0.0   81431.53846153844\n",
      "Increment: 355    Initial Residual: 10651225.038450085\n",
      "    Residual: 2.1810453264028237e-07   0\n",
      "U at the left and right 0.0   0.20505600000000002\n",
      "Source at the left and right 0.0   81890.95384615383\n",
      "Increment: 356    Initial Residual: 10655371.857387805\n",
      "    Residual: 1.9511596911525978e-07   0\n",
      "U at the left and right 0.0   0.20420400000000002\n",
      "Source at the left and right 0.0   82351.66153846153\n",
      "Increment: 357    Initial Residual: 10670277.760544175\n",
      "    Residual: 2.9507497472037156e-07   0\n",
      "U at the left and right 0.0   0.20334400000000002\n",
      "Source at the left and right 0.0   82813.66153846153\n",
      "Increment: 358    Initial Residual: 10697018.51227045\n",
      "    Residual: 2.6109608032089753e-07   0\n",
      "U at the left and right 0.0   0.20247600000000002\n",
      "Source at the left and right 0.0   83276.95384615385\n",
      "Increment: 359    Initial Residual: 10712426.542906003\n",
      "    Residual: 2.9172258103285425e-07   0\n",
      "U at the left and right 0.0   0.2016\n",
      "Source at the left and right 0.0   83741.53846153844\n",
      "Increment: 360    Initial Residual: 10726210.662182583\n",
      "    Residual: 2.1869230949596873e-07   0\n",
      "U at the left and right 0.0   0.200716\n",
      "Source at the left and right 0.0   84207.41538461536\n",
      "Increment: 361    Initial Residual: 10749430.928068712\n",
      "    Residual: 2.46172358135055e-07   0\n",
      "U at the left and right 0.0   0.199824\n",
      "Source at the left and right 0.0   84674.5846153846\n",
      "Increment: 362    Initial Residual: 10763227.45711156\n",
      "    Residual: 2.9121669130314997e-07   0\n",
      "U at the left and right 0.0   0.19892400000000002\n",
      "Source at the left and right 0.0   85143.04615384614\n",
      "Increment: 363    Initial Residual: 10770224.622346494\n",
      "    Residual: 2.5463796669990337e-07   0\n",
      "U at the left and right 0.0   0.198016\n",
      "Source at the left and right 0.0   85612.79999999999\n",
      "Increment: 364    Initial Residual: 10800866.848302001\n",
      "    Residual: 2.52668346578867e-07   0\n",
      "U at the left and right 0.0   0.1971\n",
      "Source at the left and right 0.0   86083.84615384616\n",
      "Increment: 365    Initial Residual: 10844645.014896447\n",
      "    Residual: 1.6663128144644623e-07   0\n",
      "U at the left and right 0.0   0.19617600000000002\n",
      "Source at the left and right 0.0   86556.1846153846\n",
      "Increment: 366    Initial Residual: 10864744.494362788\n",
      "    Residual: 2.2746398043313198e-07   0\n",
      "U at the left and right 0.0   0.195244\n",
      "Source at the left and right 0.0   87029.81538461537\n",
      "Increment: 367    Initial Residual: 10870537.852261813\n",
      "    Residual: 2.1100571730268527e-07   0\n",
      "U at the left and right 0.0   0.194304\n",
      "Source at the left and right 0.0   87504.73846153845\n",
      "Increment: 368    Initial Residual: 10888121.007854205\n",
      "    Residual: 1.6831964772317347e-07   0\n",
      "U at the left and right 0.0   0.193356\n",
      "Source at the left and right 0.0   87980.95384615385\n",
      "Increment: 369    Initial Residual: 10907103.46943611\n",
      "    Residual: 1.4104541404278985e-07   0\n",
      "U at the left and right 0.0   0.19240000000000002\n",
      "Source at the left and right 0.0   88458.46153846153\n",
      "Increment: 370    Initial Residual: 10922166.131301837\n",
      "    Residual: 1.8690602280082078e-07   0\n",
      "U at the left and right 0.0   0.191436\n",
      "Source at the left and right 0.0   88937.26153846152\n",
      "Increment: 371    Initial Residual: 10953489.633885574\n",
      "    Residual: 1.588935664819896e-07   0\n",
      "U at the left and right 0.0   0.190464\n",
      "Source at the left and right 0.0   89417.35384615384\n",
      "Increment: 372    Initial Residual: 10989879.05723838\n",
      "    Residual: 2.1717995144996552e-07   0\n",
      "U at the left and right 0.0   0.189484\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Source at the left and right 0.0   89898.73846153845\n",
      "Increment: 373    Initial Residual: 11003816.258222325\n",
      "    Residual: 1.938404253236606e-07   0\n",
      "U at the left and right 0.0   0.188496\n",
      "Source at the left and right 0.0   90381.4153846154\n",
      "Increment: 374    Initial Residual: 11015135.594628131\n",
      "    Residual: 1.9092794222998536e-07   0\n",
      "U at the left and right 0.0   0.1875\n",
      "Source at the left and right 0.0   90865.38461538462\n",
      "Increment: 375    Initial Residual: 11050380.284061145\n",
      "    Residual: 1.7652923985121377e-07   0\n",
      "U at the left and right 0.0   0.186496\n",
      "Source at the left and right 0.0   91350.64615384614\n",
      "Increment: 376    Initial Residual: 11086589.948990827\n",
      "    Residual: 1.7153535961870543e-07   0\n",
      "U at the left and right 0.0   0.185484\n",
      "Source at the left and right 0.0   91837.20000000001\n",
      "Increment: 377    Initial Residual: 11102807.231137076\n",
      "    Residual: 1.7161624391395538e-07   0\n",
      "U at the left and right 0.0   0.184464\n",
      "Source at the left and right 0.0   92325.04615384615\n",
      "Increment: 378    Initial Residual: 11117820.027565919\n",
      "    Residual: 2.0125189121373864e-07   0\n",
      "U at the left and right 0.0   0.183436\n",
      "Source at the left and right 0.0   92814.18461538463\n",
      "Increment: 379    Initial Residual: 11136094.869115163\n",
      "    Residual: 3.186048946897377e-07   0\n",
      "U at the left and right 0.0   0.1824\n",
      "Source at the left and right 0.0   93304.61538461538\n",
      "Increment: 380    Initial Residual: 11142761.314228468\n",
      "    Residual: 2.344862368979486e-07   0\n",
      "U at the left and right 0.0   0.181356\n",
      "Source at the left and right 0.0   93796.33846153846\n",
      "Increment: 381    Initial Residual: 11155923.198899807\n",
      "    Residual: 2.3650459564117601e-07   0\n",
      "U at the left and right 0.0   0.180304\n",
      "Source at the left and right 0.0   94289.35384615384\n",
      "Increment: 382    Initial Residual: 11194483.247257482\n",
      "    Residual: 1.442558242076131e-07   0\n",
      "U at the left and right 0.0   0.179244\n",
      "Source at the left and right 0.0   94783.66153846154\n",
      "Increment: 383    Initial Residual: 11230028.53377344\n",
      "    Residual: 1.9508040295216533e-07   0\n",
      "U at the left and right 0.0   0.178176\n",
      "Source at the left and right 0.0   95279.26153846155\n",
      "Increment: 384    Initial Residual: 11245155.917262593\n",
      "    Residual: 1.727446474822101e-07   0\n",
      "U at the left and right 0.0   0.17709999999999998\n",
      "Source at the left and right 0.0   95776.15384615384\n",
      "Increment: 385    Initial Residual: 11270965.779841866\n",
      "    Residual: 2.458762150713072e-07   0\n",
      "U at the left and right 0.0   0.17601599999999998\n",
      "Source at the left and right 0.0   96274.33846153846\n",
      "Increment: 386    Initial Residual: 11315935.754413266\n",
      "    Residual: 2.0466224139038442e-07   0\n",
      "U at the left and right 0.0   0.174924\n",
      "Source at the left and right 0.0   96773.81538461539\n",
      "Increment: 387    Initial Residual: 11351310.765580418\n",
      "    Residual: 3.3843293608164773e-07   0\n",
      "U at the left and right 0.0   0.17382399999999998\n",
      "Source at the left and right 0.0   97274.5846153846\n",
      "Increment: 388    Initial Residual: 11376568.455098394\n",
      "    Residual: 2.5717322419935504e-07   0\n",
      "U at the left and right 0.0   0.17271599999999998\n",
      "Source at the left and right 0.0   97776.64615384617\n",
      "Increment: 389    Initial Residual: 11405085.872864673\n",
      "    Residual: 2.439851856191685e-07   0\n",
      "U at the left and right 0.0   0.17159999999999997\n",
      "Source at the left and right 0.0   98280.0\n",
      "Increment: 390    Initial Residual: 11418729.824145582\n",
      "    Residual: 1.9548902315927884e-07   0\n",
      "U at the left and right 0.0   0.170476\n",
      "Source at the left and right 0.0   98784.64615384614\n",
      "Increment: 391    Initial Residual: 11412961.159783185\n",
      "    Residual: 1.9381357575980527e-07   0\n",
      "U at the left and right 0.0   0.169344\n",
      "Source at the left and right 0.0   99290.58461538462\n",
      "Increment: 392    Initial Residual: 11424510.881928828\n",
      "    Residual: 1.6786556568804472e-07   0\n",
      "U at the left and right 0.0   0.168204\n",
      "Source at the left and right 0.0   99797.81538461539\n",
      "Increment: 393    Initial Residual: 11460210.256045224\n",
      "    Residual: 2.2017852361129104e-07   0\n",
      "U at the left and right 0.0   0.16705599999999998\n",
      "Source at the left and right 0.0   100306.33846153846\n",
      "Increment: 394    Initial Residual: 11485349.099877957\n",
      "    Residual: 2.97271396729e-07   0\n",
      "U at the left and right 0.0   0.1659\n",
      "Source at the left and right 0.0   100816.15384615384\n",
      "Increment: 395    Initial Residual: 11499757.045570819\n",
      "    Residual: 2.876626135789037e-07   0\n",
      "U at the left and right 0.0   0.16473599999999997\n",
      "Source at the left and right 0.0   101327.26153846152\n",
      "Increment: 396    Initial Residual: 11529688.041741127\n",
      "    Residual: 2.126191284526291e-07   0\n",
      "U at the left and right 0.0   0.163564\n",
      "Source at the left and right 0.0   101839.66153846156\n",
      "Increment: 397    Initial Residual: 11564529.192937326\n",
      "    Residual: 3.1942599363546457e-07   0\n",
      "U at the left and right 0.0   0.16238399999999997\n",
      "Source at the left and right 0.0   102353.35384615386\n",
      "Increment: 398    Initial Residual: 11588407.559987223\n",
      "    Residual: 2.5750353423931384e-07   0\n",
      "U at the left and right 0.0   0.16119599999999998\n",
      "Source at the left and right 0.0   102868.33846153849\n",
      "Increment: 399    Initial Residual: 11620571.27617466\n",
      "    Residual: 3.284335171434088e-07   0\n",
      "U at the left and right 0.0   0.15999999999999998\n",
      "Source at the left and right 0.0   103384.61538461538\n",
      "Increment: 400    Initial Residual: 11659194.167265655\n",
      "    Residual: 2.443262250666389e-07   0\n",
      "U at the left and right 0.0   0.15879599999999996\n",
      "Source at the left and right 0.0   103902.18461538461\n",
      "Increment: 401    Initial Residual: 11673120.863019314\n",
      "    Residual: 1.8966081829902314e-07   0\n",
      "U at the left and right 0.0   0.15758399999999997\n",
      "Source at the left and right 0.0   104421.04615384617\n",
      "Increment: 402    Initial Residual: 11673286.286178885\n",
      "    Residual: 2.783642006884722e-07   0\n",
      "U at the left and right 0.0   0.15636399999999998\n",
      "Source at the left and right 0.0   104941.20000000001\n",
      "Increment: 403    Initial Residual: 11695169.759227877\n",
      "    Residual: 2.1513349887700246e-07   0\n",
      "U at the left and right 0.0   0.15513599999999997\n",
      "Source at the left and right 0.0   105462.64615384617\n",
      "Increment: 404    Initial Residual: 11727554.077398429\n",
      "    Residual: 2.59844005380092e-07   0\n",
      "U at the left and right 0.0   0.15389999999999995\n",
      "Source at the left and right 0.0   105985.38461538462\n",
      "Increment: 405    Initial Residual: 11746569.951824553\n",
      "    Residual: 2.3793059054065982e-07   0\n",
      "U at the left and right 0.0   0.15265599999999996\n",
      "Source at the left and right 0.0   106509.41538461538\n",
      "Increment: 406    Initial Residual: 11768981.53064013\n",
      "    Residual: 3.20753768353908e-07   0\n",
      "U at the left and right 0.0   0.15140399999999996\n",
      "Source at the left and right 0.0   107034.73846153848\n",
      "Increment: 407    Initial Residual: 11803045.98305954\n",
      "    Residual: 3.330178250772731e-07   0\n",
      "U at the left and right 0.0   0.15014399999999997\n",
      "Source at the left and right 0.0   107561.35384615386\n",
      "Increment: 408    Initial Residual: 11826734.95470094\n",
      "    Residual: 2.158660279240089e-07   0\n",
      "U at the left and right 0.0   0.14887599999999995\n",
      "Source at the left and right 0.0   108089.26153846155\n",
      "Increment: 409    Initial Residual: 11846650.779278547\n",
      "    Residual: 2.370394342443653e-07   0\n",
      "U at the left and right 0.0   0.14759999999999995\n",
      "Source at the left and right 0.0   108618.46153846156\n",
      "Increment: 410    Initial Residual: 11887203.022043185\n",
      "    Residual: 2.3583618061435865e-07   0\n",
      "U at the left and right 0.0   0.14631599999999995\n",
      "Source at the left and right 0.0   109148.95384615385\n",
      "Increment: 411    Initial Residual: 11927688.35685349\n",
      "    Residual: 1.9778274541343844e-07   0\n",
      "U at the left and right 0.0   0.14502399999999996\n",
      "Source at the left and right 0.0   109680.73846153848\n",
      "Increment: 412    Initial Residual: 11942189.845469568\n",
      "    Residual: 2.3728081493518023e-07   0\n",
      "U at the left and right 0.0   0.14372399999999996\n",
      "Source at the left and right 0.0   110213.81538461539\n",
      "Increment: 413    Initial Residual: 11957652.92696153\n",
      "    Residual: 1.6998104075416675e-07   0\n",
      "U at the left and right 0.0   0.14241599999999996\n",
      "Source at the left and right 0.0   110748.18461538461\n",
      "Increment: 414    Initial Residual: 11994141.105431989\n",
      "    Residual: 2.573687650176268e-07   0\n",
      "U at the left and right 0.0   0.14109999999999995\n",
      "Source at the left and right 0.0   111283.84615384617\n",
      "Increment: 415    Initial Residual: 12027988.582057154\n",
      "    Residual: 3.038795815338658e-07   0\n",
      "U at the left and right 0.0   0.13977599999999996\n",
      "Source at the left and right 0.0   111820.80000000002\n",
      "Increment: 416    Initial Residual: 12054805.355843911\n",
      "    Residual: 2.5128456881702025e-07   0\n",
      "U at the left and right 0.0   0.138444\n",
      "Source at the left and right 0.0   112359.04615384614\n",
      "Increment: 417    Initial Residual: 12092799.615194784\n",
      "    Residual: 2.526271495330356e-07   0\n",
      "U at the left and right 0.0   0.13710400000000003\n",
      "Source at the left and right 0.0   112898.5846153846\n",
      "Increment: 418    Initial Residual: 12124871.766181821\n",
      "    Residual: 1.99581362996096e-07   0\n",
      "U at the left and right 0.0   0.13575600000000002\n",
      "Source at the left and right 0.0   113439.41538461538\n",
      "Increment: 419    Initial Residual: 12131889.450387279\n",
      "    Residual: 2.1135893393314306e-07   0\n",
      "U at the left and right 0.0   0.13440000000000002\n",
      "Source at the left and right 0.0   113981.53846153844\n",
      "Increment: 420    Initial Residual: 12143558.805236166\n",
      "    Residual: 1.6719250608771396e-07   0\n",
      "U at the left and right 0.0   0.13303600000000002\n",
      "Source at the left and right 0.0   114524.95384615383\n",
      "Increment: 421    Initial Residual: 12178090.841810664\n",
      "    Residual: 1.596885565620125e-07   0\n",
      "U at the left and right 0.0   0.13166400000000003\n",
      "Source at the left and right 0.0   115069.66153846154\n",
      "Increment: 422    Initial Residual: 12206186.944919847\n",
      "    Residual: 2.4285921473811e-07   0\n",
      "U at the left and right 0.0   0.130284\n",
      "Source at the left and right 0.0   115615.66153846151\n",
      "Increment: 423    Initial Residual: 12220985.777555434\n",
      "    Residual: 1.9559547934242373e-07   0\n",
      "U at the left and right 0.0   0.128896\n",
      "Source at the left and right 0.0   116162.95384615385\n",
      "Increment: 424    Initial Residual: 12251534.269323666\n",
      "    Residual: 2.228256164120458e-07   0\n",
      "U at the left and right 0.0   0.1275\n",
      "Source at the left and right 0.0   116711.53846153844\n",
      "Increment: 425    Initial Residual: 12293941.259998398\n",
      "    Residual: 2.788560821178845e-07   0\n",
      "U at the left and right 0.0   0.126096\n",
      "Source at the left and right 0.0   117261.41538461536\n",
      "Increment: 426    Initial Residual: 12326410.104275312\n",
      "    Residual: 2.606971352773546e-07   0\n",
      "U at the left and right 0.0   0.12468400000000002\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Source at the left and right 0.0   117812.5846153846\n",
      "Increment: 427    Initial Residual: 12365077.132762147\n",
      "    Residual: 2.90220198560641e-07   0\n",
      "U at the left and right 0.0   0.12326400000000001\n",
      "Source at the left and right 0.0   118365.04615384614\n",
      "Increment: 428    Initial Residual: 12417316.745401883\n",
      "    Residual: 1.910914157394617e-07   0\n",
      "U at the left and right 0.0   0.12183600000000001\n",
      "Source at the left and right 0.0   118918.79999999999\n",
      "Increment: 429    Initial Residual: 12450296.721037373\n",
      "    Residual: 1.601116595628977e-07   0\n",
      "U at the left and right 0.0   0.12040000000000001\n",
      "Source at the left and right 0.0   119473.84615384616\n",
      "Increment: 430    Initial Residual: 12461156.971893426\n",
      "    Residual: 2.642200059935103e-07   0\n",
      "U at the left and right 0.0   0.118956\n",
      "Source at the left and right 0.0   120030.18461538458\n",
      "Increment: 431    Initial Residual: 12486267.44293538\n",
      "    Residual: 3.5762301798103836e-07   0\n",
      "U at the left and right 0.0   0.11750400000000001\n",
      "Source at the left and right 0.0   120587.81538461539\n",
      "Increment: 432    Initial Residual: 12523744.04414531\n",
      "    Residual: 2.9108561190929925e-07   0\n",
      "U at the left and right 0.0   0.11604400000000001\n",
      "Source at the left and right 0.0   121146.73846153845\n",
      "Increment: 433    Initial Residual: 12546191.816565862\n",
      "    Residual: 1.6343583475814255e-07   0\n",
      "U at the left and right 0.0   0.11457600000000001\n",
      "Source at the left and right 0.0   121706.95384615385\n",
      "Increment: 434    Initial Residual: 12566064.093743017\n",
      "    Residual: 1.7901754521609196e-07   0\n",
      "U at the left and right 0.0   0.1131\n",
      "Source at the left and right 0.0   122268.46153846153\n",
      "Increment: 435    Initial Residual: 12599502.050839184\n",
      "    Residual: 3.068732614889687e-07   0\n",
      "U at the left and right 0.0   0.111616\n",
      "Source at the left and right 0.0   122831.26153846152\n",
      "Increment: 436    Initial Residual: 12626948.633084074\n",
      "    Residual: 3.150954830270605e-07   0\n",
      "U at the left and right 0.0   0.110124\n",
      "Source at the left and right 0.0   123395.35384615383\n",
      "Increment: 437    Initial Residual: 12647905.161645215\n",
      "    Residual: 2.896518016380052e-07   0\n",
      "U at the left and right 0.0   0.108624\n",
      "Source at the left and right 0.0   123960.73846153845\n",
      "Increment: 438    Initial Residual: 12691197.129853861\n",
      "    Residual: 2.641412088330543e-07   0\n",
      "U at the left and right 0.0   0.107116\n",
      "Source at the left and right 0.0   124527.41538461538\n",
      "Increment: 439    Initial Residual: 12744279.161881942\n",
      "    Residual: 3.2341441944894414e-07   0\n",
      "U at the left and right 0.0   0.1056\n",
      "Source at the left and right 0.0   125095.38461538462\n",
      "Increment: 440    Initial Residual: 12770701.220050309\n",
      "    Residual: 3.525471140241915e-07   0\n",
      "U at the left and right 0.0   0.104076\n",
      "Source at the left and right 0.0   125664.64615384614\n",
      "Increment: 441    Initial Residual: 12783751.560206646\n",
      "    Residual: 2.385349660155493e-07   0\n",
      "U at the left and right 0.0   0.102544\n",
      "Source at the left and right 0.0   126235.20000000001\n",
      "Increment: 442    Initial Residual: 12808487.6807839\n",
      "    Residual: 2.9718385152785676e-07   0\n",
      "U at the left and right 0.0   0.101004\n",
      "Source at the left and right 0.0   126807.04615384615\n",
      "Increment: 443    Initial Residual: 12828128.855167631\n",
      "    Residual: 2.507455237153864e-07   0\n",
      "U at the left and right 0.0   0.09945599999999999\n",
      "Source at the left and right 0.0   127380.18461538461\n",
      "Increment: 444    Initial Residual: 12837534.433911417\n",
      "    Residual: 2.5142949888894663e-07   0\n",
      "U at the left and right 0.0   0.09789999999999999\n",
      "Source at the left and right 0.0   127954.61538461538\n",
      "Increment: 445    Initial Residual: 12865313.267085658\n",
      "    Residual: 2.1824765108328466e-07   0\n",
      "U at the left and right 0.0   0.09633599999999999\n",
      "Source at the left and right 0.0   128530.33846153846\n",
      "Increment: 446    Initial Residual: 12907392.90342818\n",
      "    Residual: 2.2725797527651586e-07   0\n",
      "U at the left and right 0.0   0.09476399999999999\n",
      "Source at the left and right 0.0   129107.35384615386\n",
      "Increment: 447    Initial Residual: 12937628.560446367\n",
      "    Residual: 1.7531637273043572e-07   0\n",
      "U at the left and right 0.0   0.09318399999999999\n",
      "Source at the left and right 0.0   129685.66153846154\n",
      "Increment: 448    Initial Residual: 12972759.337543147\n",
      "    Residual: 2.660585013877767e-07   0\n",
      "U at the left and right 0.0   0.09159599999999998\n",
      "Source at the left and right 0.0   130265.26153846155\n",
      "Increment: 449    Initial Residual: 13031472.73980108\n",
      "    Residual: 2.8167850884337483e-07   0\n",
      "U at the left and right 0.0   0.08999999999999998\n",
      "Source at the left and right 0.0   130846.15384615384\n",
      "Increment: 450    Initial Residual: 13082114.785269355\n",
      "    Residual: 3.738445286018607e-07   0\n",
      "U at the left and right 0.0   0.08839599999999997\n",
      "Source at the left and right 0.0   131428.33846153846\n",
      "Increment: 451    Initial Residual: 13104104.10866558\n",
      "    Residual: 2.4283064138490353e-07   0\n",
      "U at the left and right 0.0   0.08678399999999997\n",
      "Source at the left and right 0.0   132011.8153846154\n",
      "Increment: 452    Initial Residual: 13124630.760039425\n",
      "    Residual: 2.2230340164654988e-07   0\n",
      "U at the left and right 0.0   0.08516399999999998\n",
      "Source at the left and right 0.0   132596.58461538464\n",
      "Increment: 453    Initial Residual: 13151586.547961615\n",
      "    Residual: 3.1734466542602786e-07   0\n",
      "U at the left and right 0.0   0.08353599999999997\n",
      "Source at the left and right 0.0   133182.64615384617\n",
      "Increment: 454    Initial Residual: 13166367.973650178\n",
      "    Residual: 2.592959939565382e-07   0\n",
      "U at the left and right 0.0   0.08189999999999997\n",
      "Source at the left and right 0.0   133770.0\n",
      "Increment: 455    Initial Residual: 13185683.900801716\n",
      "    Residual: 2.150528490151704e-07   0\n",
      "U at the left and right 0.0   0.08025599999999997\n",
      "Source at the left and right 0.0   134358.64615384614\n",
      "Increment: 456    Initial Residual: 13230144.887560872\n",
      "    Residual: 2.6404267931436363e-07   0\n",
      "U at the left and right 0.0   0.07860399999999997\n",
      "Source at the left and right 0.0   134948.58461538464\n",
      "Increment: 457    Initial Residual: 13271678.654891243\n",
      "    Residual: 3.1025205274905283e-07   0\n",
      "U at the left and right 0.0   0.07694399999999997\n",
      "Source at the left and right 0.0   135539.8153846154\n",
      "Increment: 458    Initial Residual: 13292874.278247386\n",
      "    Residual: 2.1922312646812942e-07   0\n",
      "U at the left and right 0.0   0.07527599999999997\n",
      "Source at the left and right 0.0   136132.3384615385\n",
      "Increment: 459    Initial Residual: 13323761.686558723\n",
      "    Residual: 2.700450064028458e-07   0\n",
      "U at the left and right 0.0   0.07359999999999997\n",
      "Source at the left and right 0.0   136726.15384615384\n",
      "Increment: 460    Initial Residual: 13369512.560040258\n",
      "    Residual: 1.8238710857769322e-07   0\n",
      "U at the left and right 0.0   0.07191599999999997\n",
      "Source at the left and right 0.0   137321.26153846155\n",
      "Increment: 461    Initial Residual: 13401208.448428012\n",
      "    Residual: 2.3421235184622221e-07   0\n",
      "U at the left and right 0.0   0.07022399999999997\n",
      "Source at the left and right 0.0   137917.66153846157\n",
      "Increment: 462    Initial Residual: 13425833.00482463\n",
      "    Residual: 2.418499662249015e-07   0\n",
      "U at the left and right 0.0   0.06852399999999996\n",
      "Source at the left and right 0.0   138515.35384615386\n",
      "Increment: 463    Initial Residual: 13465802.469573056\n",
      "    Residual: 2.9317584959832355e-07   0\n",
      "U at the left and right 0.0   0.06681599999999996\n",
      "Source at the left and right 0.0   139114.3384615385\n",
      "Increment: 464    Initial Residual: 13503329.900469668\n",
      "    Residual: 2.2572615696101942e-07   0\n",
      "U at the left and right 0.0   0.06509999999999996\n",
      "Source at the left and right 0.0   139714.6153846154\n",
      "Increment: 465    Initial Residual: 13525787.643682556\n",
      "    Residual: 2.630487597571273e-07   0\n",
      "U at the left and right 0.0   0.06337599999999996\n",
      "Source at the left and right 0.0   140316.1846153846\n",
      "Increment: 466    Initial Residual: 13560803.799463034\n",
      "    Residual: 2.8793385414689183e-07   0\n",
      "U at the left and right 0.0   0.061643999999999956\n",
      "Source at the left and right 0.0   140919.04615384617\n",
      "Increment: 467    Initial Residual: 13610225.987537833\n",
      "    Residual: 2.2948362748506463e-07   0\n",
      "U at the left and right 0.0   0.05990399999999995\n",
      "Source at the left and right 0.0   141523.2\n",
      "Increment: 468    Initial Residual: 13641557.070290925\n",
      "    Residual: 2.9784854970513774e-07   0\n",
      "U at the left and right 0.0   0.05815599999999995\n",
      "Source at the left and right 0.0   142128.64615384617\n",
      "Increment: 469    Initial Residual: 13662179.013519485\n",
      "    Residual: 2.490587120619929e-07   0\n",
      "U at the left and right 0.0   0.05639999999999995\n",
      "Source at the left and right 0.0   142735.38461538462\n",
      "Increment: 470    Initial Residual: 13701429.700836997\n",
      "    Residual: 3.4188038604805235e-07   0\n",
      "U at the left and right 0.0   0.05463599999999995\n",
      "Source at the left and right 0.0   143343.4153846154\n",
      "Increment: 471    Initial Residual: 13743679.545237927\n",
      "    Residual: 3.1680303253932744e-07   0\n",
      "U at the left and right 0.0   0.052863999999999946\n",
      "Source at the left and right 0.0   143952.73846153848\n",
      "Increment: 472    Initial Residual: 13769002.60207652\n",
      "    Residual: 2.1933388118525787e-07   0\n",
      "U at the left and right 0.0   0.05108399999999994\n",
      "Source at the left and right 0.0   144563.35384615386\n",
      "Increment: 473    Initial Residual: 13798440.121272823\n",
      "    Residual: 1.901358389135427e-07   0\n",
      "U at the left and right 0.0   0.049295999999999944\n",
      "Source at the left and right 0.0   145175.26153846155\n",
      "Increment: 474    Initial Residual: 13834413.295659896\n",
      "    Residual: 2.0587074577284007e-07   0\n",
      "U at the left and right 0.0   0.04749999999999994\n",
      "Source at the left and right 0.0   145788.46153846156\n",
      "Increment: 475    Initial Residual: 13849632.066985132\n",
      "    Residual: 2.7878764430595714e-07   0\n",
      "U at the left and right 0.0   0.04569599999999994\n",
      "Source at the left and right 0.0   146402.95384615386\n",
      "Increment: 476    Initial Residual: 13857352.482260808\n",
      "    Residual: 3.059221004258253e-07   0\n",
      "U at the left and right 0.0   0.04388399999999994\n",
      "Source at the left and right 0.0   147018.7384615385\n",
      "Increment: 477    Initial Residual: 13892011.037713911\n",
      "    Residual: 1.7846434663241334e-07   0\n",
      "U at the left and right 0.0   0.042063999999999935\n",
      "Source at the left and right 0.0   147635.81538461542\n",
      "Increment: 478    Initial Residual: 13939223.722451337\n",
      "    Residual: 1.9900687665643743e-07   0\n",
      "U at the left and right 0.0   0.04023599999999993\n",
      "Source at the left and right 0.0   148254.1846153846\n",
      "Increment: 479    Initial Residual: 13974727.71199835\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "    Residual: 2.1762679141392216e-07   0\n",
      "U at the left and right 0.0   0.03840000000000003\n",
      "Source at the left and right 0.0   148873.84615384613\n",
      "Increment: 480    Initial Residual: 14017047.691720353\n",
      "    Residual: 2.6656007498500226e-07   0\n",
      "U at the left and right 0.0   0.03655600000000003\n",
      "Source at the left and right 0.0   149494.8\n",
      "Increment: 481    Initial Residual: 14071105.892864931\n",
      "    Residual: 3.1808176938150873e-07   0\n",
      "U at the left and right 0.0   0.034704000000000026\n",
      "Source at the left and right 0.0   150117.04615384614\n",
      "Increment: 482    Initial Residual: 14106351.24243298\n",
      "    Residual: 3.022023363845405e-07   0\n",
      "U at the left and right 0.0   0.032844000000000026\n",
      "Source at the left and right 0.0   150740.5846153846\n",
      "Increment: 483    Initial Residual: 14125616.616916247\n",
      "    Residual: 3.316868445483618e-07   0\n",
      "U at the left and right 0.0   0.030976000000000028\n",
      "Source at the left and right 0.0   151365.41538461536\n",
      "Increment: 484    Initial Residual: 14158256.990101712\n",
      "    Residual: 3.93538616260536e-07   0\n",
      "U at the left and right 0.0   0.029100000000000025\n",
      "Source at the left and right 0.0   151991.53846153844\n",
      "Increment: 485    Initial Residual: 14192528.505861282\n",
      "    Residual: 3.699402714854957e-07   0\n",
      "U at the left and right 0.0   0.027216000000000025\n",
      "Source at the left and right 0.0   152618.95384615383\n",
      "Increment: 486    Initial Residual: 14210541.640319718\n",
      "    Residual: 4.7300919128235203e-07   0\n",
      "U at the left and right 0.0   0.025324000000000024\n",
      "Source at the left and right 0.0   153247.66153846154\n",
      "Increment: 487    Initial Residual: 14241097.477428718\n",
      "    Residual: 2.3766067486608895e-07   0\n",
      "U at the left and right 0.0   0.02342400000000002\n",
      "Source at the left and right 0.0   153877.6615384615\n",
      "Increment: 488    Initial Residual: 14297736.519716073\n",
      "    Residual: 1.9538250897238886e-07   0\n",
      "U at the left and right 0.0   0.021516000000000018\n",
      "Source at the left and right 0.0   154508.95384615386\n",
      "Increment: 489    Initial Residual: 14348245.685474377\n",
      "    Residual: 2.3078767212828308e-07   0\n",
      "U at the left and right 0.0   0.019600000000000017\n",
      "Source at the left and right 0.0   155141.53846153844\n",
      "Increment: 490    Initial Residual: 14385403.632434765\n",
      "    Residual: 2.105695420661953e-07   0\n",
      "U at the left and right 0.0   0.017676000000000015\n",
      "Source at the left and right 0.0   155775.41538461536\n",
      "Increment: 491    Initial Residual: 14430658.313053688\n",
      "    Residual: 3.0874993838360115e-07   0\n",
      "U at the left and right 0.0   0.015744000000000015\n",
      "Source at the left and right 0.0   156410.5846153846\n",
      "Increment: 492    Initial Residual: 14471120.453615453\n",
      "    Residual: 2.6232895435311735e-07   0\n",
      "U at the left and right 0.0   0.013804000000000012\n",
      "Source at the left and right 0.0   157047.04615384614\n",
      "Increment: 493    Initial Residual: 14488657.11542362\n",
      "    Residual: 2.6450872808490946e-07   0\n",
      "U at the left and right 0.0   0.01185600000000001\n",
      "Source at the left and right 0.0   157684.8\n",
      "Increment: 494    Initial Residual: 14511357.10808699\n",
      "    Residual: 2.16604088445414e-07   0\n",
      "U at the left and right 0.0   0.00990000000000001\n",
      "Source at the left and right 0.0   158323.84615384616\n",
      "Increment: 495    Initial Residual: 14556199.904252548\n",
      "    Residual: 2.2307460104608657e-07   0\n",
      "U at the left and right 0.0   0.007936000000000007\n",
      "Source at the left and right 0.0   158964.18461538458\n",
      "Increment: 496    Initial Residual: 14594743.788807493\n",
      "    Residual: 2.5515519209573134e-07   0\n",
      "U at the left and right 0.0   0.005964000000000005\n",
      "Source at the left and right 0.0   159605.8153846154\n",
      "Increment: 497    Initial Residual: 14621959.320117196\n",
      "    Residual: 2.74283589932322e-07   0\n",
      "U at the left and right 0.0   0.003984000000000003\n",
      "Source at the left and right 0.0   160248.73846153845\n",
      "Increment: 498    Initial Residual: 14665067.808872879\n",
      "    Residual: 2.2261531901849304e-07   0\n",
      "U at the left and right 0.0   0.0019960000000000017\n",
      "Source at the left and right 0.0   160892.95384615386\n",
      "Increment: 499    Initial Residual: 14714708.205172151\n",
      "    Residual: 2.5784014911051995e-07   0\n",
      "U at the left and right 0.0   0.0\n",
      "Source at the left and right 0.0   161538.46153846153\n",
      "Increment: 500    Initial Residual: 14747381.785017667\n",
      "    Residual: 2.2276332677034733e-07   0\n"
     ]
    }
   ],
   "source": [
    "results = np.zeros((Nincr+1, 5))\n",
    "results_1d = np.zeros((Nincr+1, N_mesh))\n",
    "\n",
    "# Initial conditions\n",
    "u_old.interpolate( Expression((\"0\"), degree=2) )\n",
    "u_d_old.interpolate( Expression((\"0\"), degree=2) )\n",
    "# u.assign(u_old)\n",
    "\n",
    "for (i, t) in enumerate(load_steps):\n",
    "    loading.t = t\n",
    "    bc_expression.t = t\n",
    "    source.t = t\n",
    "    \n",
    "    u_pre.assign(u)\n",
    "    \n",
    "    # Prepare for U_n+1^0 from U_n\n",
    "    bc.apply(u.vector())\n",
    "    print('U at the left and right',u(0), \" \", u(1))\n",
    "    print('Source at the left and right',source(0), \" \", source(1))\n",
    "    # -- Compute components in F(U_n+1^0)\n",
    "    Du.assign(u-u_pre)\n",
    "    sig_, beta_ = proj_sig(u_pre,sig_old,Du)\n",
    "    local_project(sig_, W, sig)\n",
    "    local_project(beta_, W0, beta)\n",
    "    A, Res = assemble_system(a_Newton, res, bc_newton)\n",
    "    \n",
    "    nRes0 = Res.norm(\"l2\")\n",
    "    nRes = nRes0\n",
    "    print(\"Increment:\", str(i+1),\"   Initial Residual:\", nRes0)\n",
    "    niter = 0\n",
    "    \n",
    "    while (nRes/nRes0 > tol and nRes0>1e-10) and niter < Nitermax:\n",
    "        solve(A, du.vector(), Res, \"mumps\")\n",
    "        Du.assign(Du+du)\n",
    "        u.assign(u+du) # u^{k+1}_{n+1}\n",
    "        sig_, beta_ = proj_sig(u_pre,sig_old,Du)\n",
    "        local_project(sig_, W, sig)\n",
    "        local_project(beta_, W0, beta)\n",
    "        A, Res = assemble_system(a_Newton, res, bc_newton)\n",
    "        nRes = Res.norm(\"l2\")\n",
    "        print(\"    Residual:\", nRes,\" \",niter)\n",
    "        niter += 1\n",
    "    u.assign(u_pre+Du)\n",
    "    \n",
    "    update_fields(u, u_old, u_d_old, u_dd_old)\n",
    "    \n",
    "    sig_old.assign(sig)\n",
    "    \n",
    "# ----------------\n",
    "# Post-processing\n",
    "# ----------------\n",
    "#\n",
    "# Inside the incremental loop, the displacement and plastic strains are exported\n",
    "# at each time increment, the plastic strain must first be projected onto the\n",
    "# previously defined DG FunctionSpace. We also monitor the value of the cylinder\n",
    "# displacement on the inner boundary. The load-displacement curve is then plotted::\n",
    "\n",
    "    local_project(sig, Vsig, sig_out)\n",
    "    local_project(eps(u), Vsig, eps_out)\n",
    "    \n",
    "    file_results.write(u, t)\n",
    "    for i_x in range(N_mesh):\n",
    "        results_1d[i+1,i_x] = u(i_x/(N_mesh-1))\n",
    "    tc = 0.7;\n",
    "    if t<tc:\n",
    "        # results[i+1, :] = (u(1),t,4*t*(1-t))\n",
    "        results[i+1, :] = (u(1), sig_out(1),t,4*t*(1-t),eps_out(1))\n",
    "    else:\n",
    "        results[i+1, :] = (u(1), sig_out(1),t,0,eps_out(1))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "5f2e49b4",
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib notebook\n",
    "\n",
    "from matplotlib.animation import FuncAnimation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "263a0c08",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/javascript": [
       "/* Put everything inside the global mpl namespace */\n",
       "/* global mpl */\n",
       "window.mpl = {};\n",
       "\n",
       "mpl.get_websocket_type = function () {\n",
       "    if (typeof WebSocket !== 'undefined') {\n",
       "        return WebSocket;\n",
       "    } else if (typeof MozWebSocket !== 'undefined') {\n",
       "        return MozWebSocket;\n",
       "    } else {\n",
       "        alert(\n",
       "            'Your browser does not have WebSocket support. ' +\n",
       "                'Please try Chrome, Safari or Firefox ≥ 6. ' +\n",
       "                'Firefox 4 and 5 are also supported but you ' +\n",
       "                'have to enable WebSockets in about:config.'\n",
       "        );\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure = function (figure_id, websocket, ondownload, parent_element) {\n",
       "    this.id = figure_id;\n",
       "\n",
       "    this.ws = websocket;\n",
       "\n",
       "    this.supports_binary = this.ws.binaryType !== undefined;\n",
       "\n",
       "    if (!this.supports_binary) {\n",
       "        var warnings = document.getElementById('mpl-warnings');\n",
       "        if (warnings) {\n",
       "            warnings.style.display = 'block';\n",
       "            warnings.textContent =\n",
       "                'This browser does not support binary websocket messages. ' +\n",
       "                'Performance may be slow.';\n",
       "        }\n",
       "    }\n",
       "\n",
       "    this.imageObj = new Image();\n",
       "\n",
       "    this.context = undefined;\n",
       "    this.message = undefined;\n",
       "    this.canvas = undefined;\n",
       "    this.rubberband_canvas = undefined;\n",
       "    this.rubberband_context = undefined;\n",
       "    this.format_dropdown = undefined;\n",
       "\n",
       "    this.image_mode = 'full';\n",
       "\n",
       "    this.root = document.createElement('div');\n",
       "    this.root.setAttribute('style', 'display: inline-block');\n",
       "    this._root_extra_style(this.root);\n",
       "\n",
       "    parent_element.appendChild(this.root);\n",
       "\n",
       "    this._init_header(this);\n",
       "    this._init_canvas(this);\n",
       "    this._init_toolbar(this);\n",
       "\n",
       "    var fig = this;\n",
       "\n",
       "    this.waiting = false;\n",
       "\n",
       "    this.ws.onopen = function () {\n",
       "        fig.send_message('supports_binary', { value: fig.supports_binary });\n",
       "        fig.send_message('send_image_mode', {});\n",
       "        if (fig.ratio !== 1) {\n",
       "            fig.send_message('set_dpi_ratio', { dpi_ratio: fig.ratio });\n",
       "        }\n",
       "        fig.send_message('refresh', {});\n",
       "    };\n",
       "\n",
       "    this.imageObj.onload = function () {\n",
       "        if (fig.image_mode === 'full') {\n",
       "            // Full images could contain transparency (where diff images\n",
       "            // almost always do), so we need to clear the canvas so that\n",
       "            // there is no ghosting.\n",
       "            fig.context.clearRect(0, 0, fig.canvas.width, fig.canvas.height);\n",
       "        }\n",
       "        fig.context.drawImage(fig.imageObj, 0, 0);\n",
       "    };\n",
       "\n",
       "    this.imageObj.onunload = function () {\n",
       "        fig.ws.close();\n",
       "    };\n",
       "\n",
       "    this.ws.onmessage = this._make_on_message_function(this);\n",
       "\n",
       "    this.ondownload = ondownload;\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._init_header = function () {\n",
       "    var titlebar = document.createElement('div');\n",
       "    titlebar.classList =\n",
       "        'ui-dialog-titlebar ui-widget-header ui-corner-all ui-helper-clearfix';\n",
       "    var titletext = document.createElement('div');\n",
       "    titletext.classList = 'ui-dialog-title';\n",
       "    titletext.setAttribute(\n",
       "        'style',\n",
       "        'width: 100%; text-align: center; padding: 3px;'\n",
       "    );\n",
       "    titlebar.appendChild(titletext);\n",
       "    this.root.appendChild(titlebar);\n",
       "    this.header = titletext;\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function (_canvas_div) {};\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function (_canvas_div) {};\n",
       "\n",
       "mpl.figure.prototype._init_canvas = function () {\n",
       "    var fig = this;\n",
       "\n",
       "    var canvas_div = (this.canvas_div = document.createElement('div'));\n",
       "    canvas_div.setAttribute(\n",
       "        'style',\n",
       "        'border: 1px solid #ddd;' +\n",
       "            'box-sizing: content-box;' +\n",
       "            'clear: both;' +\n",
       "            'min-height: 1px;' +\n",
       "            'min-width: 1px;' +\n",
       "            'outline: 0;' +\n",
       "            'overflow: hidden;' +\n",
       "            'position: relative;' +\n",
       "            'resize: both;'\n",
       "    );\n",
       "\n",
       "    function on_keyboard_event_closure(name) {\n",
       "        return function (event) {\n",
       "            return fig.key_event(event, name);\n",
       "        };\n",
       "    }\n",
       "\n",
       "    canvas_div.addEventListener(\n",
       "        'keydown',\n",
       "        on_keyboard_event_closure('key_press')\n",
       "    );\n",
       "    canvas_div.addEventListener(\n",
       "        'keyup',\n",
       "        on_keyboard_event_closure('key_release')\n",
       "    );\n",
       "\n",
       "    this._canvas_extra_style(canvas_div);\n",
       "    this.root.appendChild(canvas_div);\n",
       "\n",
       "    var canvas = (this.canvas = document.createElement('canvas'));\n",
       "    canvas.classList.add('mpl-canvas');\n",
       "    canvas.setAttribute('style', 'box-sizing: content-box;');\n",
       "\n",
       "    this.context = canvas.getContext('2d');\n",
       "\n",
       "    var backingStore =\n",
       "        this.context.backingStorePixelRatio ||\n",
       "        this.context.webkitBackingStorePixelRatio ||\n",
       "        this.context.mozBackingStorePixelRatio ||\n",
       "        this.context.msBackingStorePixelRatio ||\n",
       "        this.context.oBackingStorePixelRatio ||\n",
       "        this.context.backingStorePixelRatio ||\n",
       "        1;\n",
       "\n",
       "    this.ratio = (window.devicePixelRatio || 1) / backingStore;\n",
       "\n",
       "    var rubberband_canvas = (this.rubberband_canvas = document.createElement(\n",
       "        'canvas'\n",
       "    ));\n",
       "    rubberband_canvas.setAttribute(\n",
       "        'style',\n",
       "        'box-sizing: content-box; position: absolute; left: 0; top: 0; z-index: 1;'\n",
       "    );\n",
       "\n",
       "    // Apply a ponyfill if ResizeObserver is not implemented by browser.\n",
       "    if (this.ResizeObserver === undefined) {\n",
       "        if (window.ResizeObserver !== undefined) {\n",
       "            this.ResizeObserver = window.ResizeObserver;\n",
       "        } else {\n",
       "            var obs = _JSXTOOLS_RESIZE_OBSERVER({});\n",
       "            this.ResizeObserver = obs.ResizeObserver;\n",
       "        }\n",
       "    }\n",
       "\n",
       "    this.resizeObserverInstance = new this.ResizeObserver(function (entries) {\n",
       "        var nentries = entries.length;\n",
       "        for (var i = 0; i < nentries; i++) {\n",
       "            var entry = entries[i];\n",
       "            var width, height;\n",
       "            if (entry.contentBoxSize) {\n",
       "                if (entry.contentBoxSize instanceof Array) {\n",
       "                    // Chrome 84 implements new version of spec.\n",
       "                    width = entry.contentBoxSize[0].inlineSize;\n",
       "                    height = entry.contentBoxSize[0].blockSize;\n",
       "                } else {\n",
       "                    // Firefox implements old version of spec.\n",
       "                    width = entry.contentBoxSize.inlineSize;\n",
       "                    height = entry.contentBoxSize.blockSize;\n",
       "                }\n",
       "            } else {\n",
       "                // Chrome <84 implements even older version of spec.\n",
       "                width = entry.contentRect.width;\n",
       "                height = entry.contentRect.height;\n",
       "            }\n",
       "\n",
       "            // Keep the size of the canvas and rubber band canvas in sync with\n",
       "            // the canvas container.\n",
       "            if (entry.devicePixelContentBoxSize) {\n",
       "                // Chrome 84 implements new version of spec.\n",
       "                canvas.setAttribute(\n",
       "                    'width',\n",
       "                    entry.devicePixelContentBoxSize[0].inlineSize\n",
       "                );\n",
       "                canvas.setAttribute(\n",
       "                    'height',\n",
       "                    entry.devicePixelContentBoxSize[0].blockSize\n",
       "                );\n",
       "            } else {\n",
       "                canvas.setAttribute('width', width * fig.ratio);\n",
       "                canvas.setAttribute('height', height * fig.ratio);\n",
       "            }\n",
       "            canvas.setAttribute(\n",
       "                'style',\n",
       "                'width: ' + width + 'px; height: ' + height + 'px;'\n",
       "            );\n",
       "\n",
       "            rubberband_canvas.setAttribute('width', width);\n",
       "            rubberband_canvas.setAttribute('height', height);\n",
       "\n",
       "            // And update the size in Python. We ignore the initial 0/0 size\n",
       "            // that occurs as the element is placed into the DOM, which should\n",
       "            // otherwise not happen due to the minimum size styling.\n",
       "            if (fig.ws.readyState == 1 && width != 0 && height != 0) {\n",
       "                fig.request_resize(width, height);\n",
       "            }\n",
       "        }\n",
       "    });\n",
       "    this.resizeObserverInstance.observe(canvas_div);\n",
       "\n",
       "    function on_mouse_event_closure(name) {\n",
       "        return function (event) {\n",
       "            return fig.mouse_event(event, name);\n",
       "        };\n",
       "    }\n",
       "\n",
       "    rubberband_canvas.addEventListener(\n",
       "        'mousedown',\n",
       "        on_mouse_event_closure('button_press')\n",
       "    );\n",
       "    rubberband_canvas.addEventListener(\n",
       "        'mouseup',\n",
       "        on_mouse_event_closure('button_release')\n",
       "    );\n",
       "    rubberband_canvas.addEventListener(\n",
       "        'dblclick',\n",
       "        on_mouse_event_closure('dblclick')\n",
       "    );\n",
       "    // Throttle sequential mouse events to 1 every 20ms.\n",
       "    rubberband_canvas.addEventListener(\n",
       "        'mousemove',\n",
       "        on_mouse_event_closure('motion_notify')\n",
       "    );\n",
       "\n",
       "    rubberband_canvas.addEventListener(\n",
       "        'mouseenter',\n",
       "        on_mouse_event_closure('figure_enter')\n",
       "    );\n",
       "    rubberband_canvas.addEventListener(\n",
       "        'mouseleave',\n",
       "        on_mouse_event_closure('figure_leave')\n",
       "    );\n",
       "\n",
       "    canvas_div.addEventListener('wheel', function (event) {\n",
       "        if (event.deltaY < 0) {\n",
       "            event.step = 1;\n",
       "        } else {\n",
       "            event.step = -1;\n",
       "        }\n",
       "        on_mouse_event_closure('scroll')(event);\n",
       "    });\n",
       "\n",
       "    canvas_div.appendChild(canvas);\n",
       "    canvas_div.appendChild(rubberband_canvas);\n",
       "\n",
       "    this.rubberband_context = rubberband_canvas.getContext('2d');\n",
       "    this.rubberband_context.strokeStyle = '#000000';\n",
       "\n",
       "    this._resize_canvas = function (width, height, forward) {\n",
       "        if (forward) {\n",
       "            canvas_div.style.width = width + 'px';\n",
       "            canvas_div.style.height = height + 'px';\n",
       "        }\n",
       "    };\n",
       "\n",
       "    // Disable right mouse context menu.\n",
       "    this.rubberband_canvas.addEventListener('contextmenu', function (_e) {\n",
       "        event.preventDefault();\n",
       "        return false;\n",
       "    });\n",
       "\n",
       "    function set_focus() {\n",
       "        canvas.focus();\n",
       "        canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    window.setTimeout(set_focus, 100);\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function () {\n",
       "    var fig = this;\n",
       "\n",
       "    var toolbar = document.createElement('div');\n",
       "    toolbar.classList = 'mpl-toolbar';\n",
       "    this.root.appendChild(toolbar);\n",
       "\n",
       "    function on_click_closure(name) {\n",
       "        return function (_event) {\n",
       "            return fig.toolbar_button_onclick(name);\n",
       "        };\n",
       "    }\n",
       "\n",
       "    function on_mouseover_closure(tooltip) {\n",
       "        return function (event) {\n",
       "            if (!event.currentTarget.disabled) {\n",
       "                return fig.toolbar_button_onmouseover(tooltip);\n",
       "            }\n",
       "        };\n",
       "    }\n",
       "\n",
       "    fig.buttons = {};\n",
       "    var buttonGroup = document.createElement('div');\n",
       "    buttonGroup.classList = 'mpl-button-group';\n",
       "    for (var toolbar_ind in mpl.toolbar_items) {\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) {\n",
       "            /* Instead of a spacer, we start a new button group. */\n",
       "            if (buttonGroup.hasChildNodes()) {\n",
       "                toolbar.appendChild(buttonGroup);\n",
       "            }\n",
       "            buttonGroup = document.createElement('div');\n",
       "            buttonGroup.classList = 'mpl-button-group';\n",
       "            continue;\n",
       "        }\n",
       "\n",
       "        var button = (fig.buttons[name] = document.createElement('button'));\n",
       "        button.classList = 'mpl-widget';\n",
       "        button.setAttribute('role', 'button');\n",
       "        button.setAttribute('aria-disabled', 'false');\n",
       "        button.addEventListener('click', on_click_closure(method_name));\n",
       "        button.addEventListener('mouseover', on_mouseover_closure(tooltip));\n",
       "\n",
       "        var icon_img = document.createElement('img');\n",
       "        icon_img.src = '_images/' + image + '.png';\n",
       "        icon_img.srcset = '_images/' + image + '_large.png 2x';\n",
       "        icon_img.alt = tooltip;\n",
       "        button.appendChild(icon_img);\n",
       "\n",
       "        buttonGroup.appendChild(button);\n",
       "    }\n",
       "\n",
       "    if (buttonGroup.hasChildNodes()) {\n",
       "        toolbar.appendChild(buttonGroup);\n",
       "    }\n",
       "\n",
       "    var fmt_picker = document.createElement('select');\n",
       "    fmt_picker.classList = 'mpl-widget';\n",
       "    toolbar.appendChild(fmt_picker);\n",
       "    this.format_dropdown = fmt_picker;\n",
       "\n",
       "    for (var ind in mpl.extensions) {\n",
       "        var fmt = mpl.extensions[ind];\n",
       "        var option = document.createElement('option');\n",
       "        option.selected = fmt === mpl.default_extension;\n",
       "        option.innerHTML = fmt;\n",
       "        fmt_picker.appendChild(option);\n",
       "    }\n",
       "\n",
       "    var status_bar = document.createElement('span');\n",
       "    status_bar.classList = 'mpl-message';\n",
       "    toolbar.appendChild(status_bar);\n",
       "    this.message = status_bar;\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.request_resize = function (x_pixels, y_pixels) {\n",
       "    // Request matplotlib to resize the figure. Matplotlib will then trigger a resize in the client,\n",
       "    // which will in turn request a refresh of the image.\n",
       "    this.send_message('resize', { width: x_pixels, height: y_pixels });\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.send_message = function (type, properties) {\n",
       "    properties['type'] = type;\n",
       "    properties['figure_id'] = this.id;\n",
       "    this.ws.send(JSON.stringify(properties));\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.send_draw_message = function () {\n",
       "    if (!this.waiting) {\n",
       "        this.waiting = true;\n",
       "        this.ws.send(JSON.stringify({ type: 'draw', figure_id: this.id }));\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_save = function (fig, _msg) {\n",
       "    var format_dropdown = fig.format_dropdown;\n",
       "    var format = format_dropdown.options[format_dropdown.selectedIndex].value;\n",
       "    fig.ondownload(fig, format);\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_resize = function (fig, msg) {\n",
       "    var size = msg['size'];\n",
       "    if (size[0] !== fig.canvas.width || size[1] !== fig.canvas.height) {\n",
       "        fig._resize_canvas(size[0], size[1], msg['forward']);\n",
       "        fig.send_message('refresh', {});\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_rubberband = function (fig, msg) {\n",
       "    var x0 = msg['x0'] / fig.ratio;\n",
       "    var y0 = (fig.canvas.height - msg['y0']) / fig.ratio;\n",
       "    var x1 = msg['x1'] / fig.ratio;\n",
       "    var y1 = (fig.canvas.height - msg['y1']) / fig.ratio;\n",
       "    x0 = Math.floor(x0) + 0.5;\n",
       "    y0 = Math.floor(y0) + 0.5;\n",
       "    x1 = Math.floor(x1) + 0.5;\n",
       "    y1 = Math.floor(y1) + 0.5;\n",
       "    var min_x = Math.min(x0, x1);\n",
       "    var min_y = Math.min(y0, y1);\n",
       "    var width = Math.abs(x1 - x0);\n",
       "    var height = Math.abs(y1 - y0);\n",
       "\n",
       "    fig.rubberband_context.clearRect(\n",
       "        0,\n",
       "        0,\n",
       "        fig.canvas.width / fig.ratio,\n",
       "        fig.canvas.height / fig.ratio\n",
       "    );\n",
       "\n",
       "    fig.rubberband_context.strokeRect(min_x, min_y, width, height);\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_figure_label = function (fig, msg) {\n",
       "    // Updates the figure title.\n",
       "    fig.header.textContent = msg['label'];\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_cursor = function (fig, msg) {\n",
       "    var cursor = msg['cursor'];\n",
       "    switch (cursor) {\n",
       "        case 0:\n",
       "            cursor = 'pointer';\n",
       "            break;\n",
       "        case 1:\n",
       "            cursor = 'default';\n",
       "            break;\n",
       "        case 2:\n",
       "            cursor = 'crosshair';\n",
       "            break;\n",
       "        case 3:\n",
       "            cursor = 'move';\n",
       "            break;\n",
       "    }\n",
       "    fig.rubberband_canvas.style.cursor = cursor;\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_message = function (fig, msg) {\n",
       "    fig.message.textContent = msg['message'];\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_draw = function (fig, _msg) {\n",
       "    // Request the server to send over a new figure.\n",
       "    fig.send_draw_message();\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_image_mode = function (fig, msg) {\n",
       "    fig.image_mode = msg['mode'];\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_history_buttons = function (fig, msg) {\n",
       "    for (var key in msg) {\n",
       "        if (!(key in fig.buttons)) {\n",
       "            continue;\n",
       "        }\n",
       "        fig.buttons[key].disabled = !msg[key];\n",
       "        fig.buttons[key].setAttribute('aria-disabled', !msg[key]);\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_navigate_mode = function (fig, msg) {\n",
       "    if (msg['mode'] === 'PAN') {\n",
       "        fig.buttons['Pan'].classList.add('active');\n",
       "        fig.buttons['Zoom'].classList.remove('active');\n",
       "    } else if (msg['mode'] === 'ZOOM') {\n",
       "        fig.buttons['Pan'].classList.remove('active');\n",
       "        fig.buttons['Zoom'].classList.add('active');\n",
       "    } else {\n",
       "        fig.buttons['Pan'].classList.remove('active');\n",
       "        fig.buttons['Zoom'].classList.remove('active');\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function () {\n",
       "    // Called whenever the canvas gets updated.\n",
       "    this.send_message('ack', {});\n",
       "};\n",
       "\n",
       "// A function to construct a web socket function for onmessage handling.\n",
       "// Called in the figure constructor.\n",
       "mpl.figure.prototype._make_on_message_function = function (fig) {\n",
       "    return function socket_on_message(evt) {\n",
       "        if (evt.data instanceof Blob) {\n",
       "            var img = evt.data;\n",
       "            if (img.type !== 'image/png') {\n",
       "                /* FIXME: We get \"Resource interpreted as Image but\n",
       "                 * transferred with MIME type text/plain:\" errors on\n",
       "                 * Chrome.  But how to set the MIME type?  It doesn't seem\n",
       "                 * to be part of the websocket stream */\n",
       "                img.type = 'image/png';\n",
       "            }\n",
       "\n",
       "            /* Free the memory for the previous frames */\n",
       "            if (fig.imageObj.src) {\n",
       "                (window.URL || window.webkitURL).revokeObjectURL(\n",
       "                    fig.imageObj.src\n",
       "                );\n",
       "            }\n",
       "\n",
       "            fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n",
       "                img\n",
       "            );\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        } else if (\n",
       "            typeof evt.data === 'string' &&\n",
       "            evt.data.slice(0, 21) === 'data:image/png;base64'\n",
       "        ) {\n",
       "            fig.imageObj.src = evt.data;\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        var msg = JSON.parse(evt.data);\n",
       "        var msg_type = msg['type'];\n",
       "\n",
       "        // Call the  \"handle_{type}\" callback, which takes\n",
       "        // the figure and JSON message as its only arguments.\n",
       "        try {\n",
       "            var callback = fig['handle_' + msg_type];\n",
       "        } catch (e) {\n",
       "            console.log(\n",
       "                \"No handler for the '\" + msg_type + \"' message type: \",\n",
       "                msg\n",
       "            );\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        if (callback) {\n",
       "            try {\n",
       "                // console.log(\"Handling '\" + msg_type + \"' message: \", msg);\n",
       "                callback(fig, msg);\n",
       "            } catch (e) {\n",
       "                console.log(\n",
       "                    \"Exception inside the 'handler_\" + msg_type + \"' callback:\",\n",
       "                    e,\n",
       "                    e.stack,\n",
       "                    msg\n",
       "                );\n",
       "            }\n",
       "        }\n",
       "    };\n",
       "};\n",
       "\n",
       "// from http://stackoverflow.com/questions/1114465/getting-mouse-location-in-canvas\n",
       "mpl.findpos = function (e) {\n",
       "    //this section is from http://www.quirksmode.org/js/events_properties.html\n",
       "    var targ;\n",
       "    if (!e) {\n",
       "        e = window.event;\n",
       "    }\n",
       "    if (e.target) {\n",
       "        targ = e.target;\n",
       "    } else if (e.srcElement) {\n",
       "        targ = e.srcElement;\n",
       "    }\n",
       "    if (targ.nodeType === 3) {\n",
       "        // defeat Safari bug\n",
       "        targ = targ.parentNode;\n",
       "    }\n",
       "\n",
       "    // pageX,Y are the mouse positions relative to the document\n",
       "    var boundingRect = targ.getBoundingClientRect();\n",
       "    var x = e.pageX - (boundingRect.left + document.body.scrollLeft);\n",
       "    var y = e.pageY - (boundingRect.top + document.body.scrollTop);\n",
       "\n",
       "    return { x: x, y: y };\n",
       "};\n",
       "\n",
       "/*\n",
       " * return a copy of an object with only non-object keys\n",
       " * we need this to avoid circular references\n",
       " * http://stackoverflow.com/a/24161582/3208463\n",
       " */\n",
       "function simpleKeys(original) {\n",
       "    return Object.keys(original).reduce(function (obj, key) {\n",
       "        if (typeof original[key] !== 'object') {\n",
       "            obj[key] = original[key];\n",
       "        }\n",
       "        return obj;\n",
       "    }, {});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.mouse_event = function (event, name) {\n",
       "    var canvas_pos = mpl.findpos(event);\n",
       "\n",
       "    if (name === 'button_press') {\n",
       "        this.canvas.focus();\n",
       "        this.canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    var x = canvas_pos.x * this.ratio;\n",
       "    var y = canvas_pos.y * this.ratio;\n",
       "\n",
       "    this.send_message(name, {\n",
       "        x: x,\n",
       "        y: y,\n",
       "        button: event.button,\n",
       "        step: event.step,\n",
       "        guiEvent: simpleKeys(event),\n",
       "    });\n",
       "\n",
       "    /* This prevents the web browser from automatically changing to\n",
       "     * the text insertion cursor when the button is pressed.  We want\n",
       "     * to control all of the cursor setting manually through the\n",
       "     * 'cursor' event from matplotlib */\n",
       "    event.preventDefault();\n",
       "    return false;\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function (_event, _name) {\n",
       "    // Handle any extra behaviour associated with a key event\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.key_event = function (event, name) {\n",
       "    // Prevent repeat events\n",
       "    if (name === 'key_press') {\n",
       "        if (event.key === this._key) {\n",
       "            return;\n",
       "        } else {\n",
       "            this._key = event.key;\n",
       "        }\n",
       "    }\n",
       "    if (name === 'key_release') {\n",
       "        this._key = null;\n",
       "    }\n",
       "\n",
       "    var value = '';\n",
       "    if (event.ctrlKey && event.key !== 'Control') {\n",
       "        value += 'ctrl+';\n",
       "    }\n",
       "    else if (event.altKey && event.key !== 'Alt') {\n",
       "        value += 'alt+';\n",
       "    }\n",
       "    else if (event.shiftKey && event.key !== 'Shift') {\n",
       "        value += 'shift+';\n",
       "    }\n",
       "\n",
       "    value += 'k' + event.key;\n",
       "\n",
       "    this._key_event_extra(event, name);\n",
       "\n",
       "    this.send_message(name, { key: value, guiEvent: simpleKeys(event) });\n",
       "    return false;\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onclick = function (name) {\n",
       "    if (name === 'download') {\n",
       "        this.handle_save(this, null);\n",
       "    } else {\n",
       "        this.send_message('toolbar_button', { name: name });\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onmouseover = function (tooltip) {\n",
       "    this.message.textContent = tooltip;\n",
       "};\n",
       "\n",
       "///////////////// REMAINING CONTENT GENERATED BY embed_js.py /////////////////\n",
       "// prettier-ignore\n",
       "var _JSXTOOLS_RESIZE_OBSERVER=function(A){var t,i=new WeakMap,n=new WeakMap,a=new WeakMap,r=new WeakMap,o=new Set;function s(e){if(!(this instanceof s))throw new TypeError(\"Constructor requires 'new' operator\");i.set(this,e)}function h(){throw new TypeError(\"Function is not a constructor\")}function c(e,t,i,n){e=0 in arguments?Number(arguments[0]):0,t=1 in arguments?Number(arguments[1]):0,i=2 in arguments?Number(arguments[2]):0,n=3 in arguments?Number(arguments[3]):0,this.right=(this.x=this.left=e)+(this.width=i),this.bottom=(this.y=this.top=t)+(this.height=n),Object.freeze(this)}function d(){t=requestAnimationFrame(d);var s=new WeakMap,p=new Set;o.forEach((function(t){r.get(t).forEach((function(i){var r=t instanceof window.SVGElement,o=a.get(t),d=r?0:parseFloat(o.paddingTop),f=r?0:parseFloat(o.paddingRight),l=r?0:parseFloat(o.paddingBottom),u=r?0:parseFloat(o.paddingLeft),g=r?0:parseFloat(o.borderTopWidth),m=r?0:parseFloat(o.borderRightWidth),w=r?0:parseFloat(o.borderBottomWidth),b=u+f,F=d+l,v=(r?0:parseFloat(o.borderLeftWidth))+m,W=g+w,y=r?0:t.offsetHeight-W-t.clientHeight,E=r?0:t.offsetWidth-v-t.clientWidth,R=b+v,z=F+W,M=r?t.width:parseFloat(o.width)-R-E,O=r?t.height:parseFloat(o.height)-z-y;if(n.has(t)){var k=n.get(t);if(k[0]===M&&k[1]===O)return}n.set(t,[M,O]);var S=Object.create(h.prototype);S.target=t,S.contentRect=new c(u,d,M,O),s.has(i)||(s.set(i,[]),p.add(i)),s.get(i).push(S)}))})),p.forEach((function(e){i.get(e).call(e,s.get(e),e)}))}return s.prototype.observe=function(i){if(i instanceof window.Element){r.has(i)||(r.set(i,new Set),o.add(i),a.set(i,window.getComputedStyle(i)));var n=r.get(i);n.has(this)||n.add(this),cancelAnimationFrame(t),t=requestAnimationFrame(d)}},s.prototype.unobserve=function(i){if(i instanceof window.Element&&r.has(i)){var n=r.get(i);n.has(this)&&(n.delete(this),n.size||(r.delete(i),o.delete(i))),n.size||r.delete(i),o.size||cancelAnimationFrame(t)}},A.DOMRectReadOnly=c,A.ResizeObserver=s,A.ResizeObserverEntry=h,A}; // eslint-disable-line\n",
       "mpl.toolbar_items = [[\"Home\", \"Reset original view\", \"fa fa-home icon-home\", \"home\"], [\"Back\", \"Back to previous view\", \"fa fa-arrow-left icon-arrow-left\", \"back\"], [\"Forward\", \"Forward to next view\", \"fa fa-arrow-right icon-arrow-right\", \"forward\"], [\"\", \"\", \"\", \"\"], [\"Pan\", \"Left button pans, Right button zooms\\nx/y fixes axis, CTRL fixes aspect\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\\nx/y fixes axis, CTRL fixes aspect\", \"fa fa-square-o icon-check-empty\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o icon-save\", \"download\"]];\n",
       "\n",
       "mpl.extensions = [\"eps\", \"jpeg\", \"pgf\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\", \"tif\"];\n",
       "\n",
       "mpl.default_extension = \"png\";/* global mpl */\n",
       "\n",
       "var comm_websocket_adapter = function (comm) {\n",
       "    // Create a \"websocket\"-like object which calls the given IPython comm\n",
       "    // object with the appropriate methods. Currently this is a non binary\n",
       "    // socket, so there is still some room for performance tuning.\n",
       "    var ws = {};\n",
       "\n",
       "    ws.binaryType = comm.kernel.ws.binaryType;\n",
       "    ws.readyState = comm.kernel.ws.readyState;\n",
       "    function updateReadyState(_event) {\n",
       "        if (comm.kernel.ws) {\n",
       "            ws.readyState = comm.kernel.ws.readyState;\n",
       "        } else {\n",
       "            ws.readyState = 3; // Closed state.\n",
       "        }\n",
       "    }\n",
       "    comm.kernel.ws.addEventListener('open', updateReadyState);\n",
       "    comm.kernel.ws.addEventListener('close', updateReadyState);\n",
       "    comm.kernel.ws.addEventListener('error', updateReadyState);\n",
       "\n",
       "    ws.close = function () {\n",
       "        comm.close();\n",
       "    };\n",
       "    ws.send = function (m) {\n",
       "        //console.log('sending', m);\n",
       "        comm.send(m);\n",
       "    };\n",
       "    // Register the callback with on_msg.\n",
       "    comm.on_msg(function (msg) {\n",
       "        //console.log('receiving', msg['content']['data'], msg);\n",
       "        var data = msg['content']['data'];\n",
       "        if (data['blob'] !== undefined) {\n",
       "            data = {\n",
       "                data: new Blob(msg['buffers'], { type: data['blob'] }),\n",
       "            };\n",
       "        }\n",
       "        // Pass the mpl event to the overridden (by mpl) onmessage function.\n",
       "        ws.onmessage(data);\n",
       "    });\n",
       "    return ws;\n",
       "};\n",
       "\n",
       "mpl.mpl_figure_comm = function (comm, msg) {\n",
       "    // This is the function which gets called when the mpl process\n",
       "    // starts-up an IPython Comm through the \"matplotlib\" channel.\n",
       "\n",
       "    var id = msg.content.data.id;\n",
       "    // Get hold of the div created by the display call when the Comm\n",
       "    // socket was opened in Python.\n",
       "    var element = document.getElementById(id);\n",
       "    var ws_proxy = comm_websocket_adapter(comm);\n",
       "\n",
       "    function ondownload(figure, _format) {\n",
       "        window.open(figure.canvas.toDataURL());\n",
       "    }\n",
       "\n",
       "    var fig = new mpl.figure(id, ws_proxy, ondownload, element);\n",
       "\n",
       "    // Call onopen now - mpl needs it, as it is assuming we've passed it a real\n",
       "    // web socket which is closed, not our websocket->open comm proxy.\n",
       "    ws_proxy.onopen();\n",
       "\n",
       "    fig.parent_element = element;\n",
       "    fig.cell_info = mpl.find_output_cell(\"<div id='\" + id + \"'></div>\");\n",
       "    if (!fig.cell_info) {\n",
       "        console.error('Failed to find cell for figure', id, fig);\n",
       "        return;\n",
       "    }\n",
       "    fig.cell_info[0].output_area.element.on(\n",
       "        'cleared',\n",
       "        { fig: fig },\n",
       "        fig._remove_fig_handler\n",
       "    );\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_close = function (fig, msg) {\n",
       "    var width = fig.canvas.width / fig.ratio;\n",
       "    fig.cell_info[0].output_area.element.off(\n",
       "        'cleared',\n",
       "        fig._remove_fig_handler\n",
       "    );\n",
       "    fig.resizeObserverInstance.unobserve(fig.canvas_div);\n",
       "\n",
       "    // Update the output cell to use the data from the current canvas.\n",
       "    fig.push_to_output();\n",
       "    var dataURL = fig.canvas.toDataURL();\n",
       "    // Re-enable the keyboard manager in IPython - without this line, in FF,\n",
       "    // the notebook keyboard shortcuts fail.\n",
       "    IPython.keyboard_manager.enable();\n",
       "    fig.parent_element.innerHTML =\n",
       "        '<img src=\"' + dataURL + '\" width=\"' + width + '\">';\n",
       "    fig.close_ws(fig, msg);\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.close_ws = function (fig, msg) {\n",
       "    fig.send_message('closing', msg);\n",
       "    // fig.ws.close()\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.push_to_output = function (_remove_interactive) {\n",
       "    // Turn the data on the canvas into data in the output cell.\n",
       "    var width = this.canvas.width / this.ratio;\n",
       "    var dataURL = this.canvas.toDataURL();\n",
       "    this.cell_info[1]['text/html'] =\n",
       "        '<img src=\"' + dataURL + '\" width=\"' + width + '\">';\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function () {\n",
       "    // Tell IPython that the notebook contents must change.\n",
       "    IPython.notebook.set_dirty(true);\n",
       "    this.send_message('ack', {});\n",
       "    var fig = this;\n",
       "    // Wait a second, then push the new image to the DOM so\n",
       "    // that it is saved nicely (might be nice to debounce this).\n",
       "    setTimeout(function () {\n",
       "        fig.push_to_output();\n",
       "    }, 1000);\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function () {\n",
       "    var fig = this;\n",
       "\n",
       "    var toolbar = document.createElement('div');\n",
       "    toolbar.classList = 'btn-toolbar';\n",
       "    this.root.appendChild(toolbar);\n",
       "\n",
       "    function on_click_closure(name) {\n",
       "        return function (_event) {\n",
       "            return fig.toolbar_button_onclick(name);\n",
       "        };\n",
       "    }\n",
       "\n",
       "    function on_mouseover_closure(tooltip) {\n",
       "        return function (event) {\n",
       "            if (!event.currentTarget.disabled) {\n",
       "                return fig.toolbar_button_onmouseover(tooltip);\n",
       "            }\n",
       "        };\n",
       "    }\n",
       "\n",
       "    fig.buttons = {};\n",
       "    var buttonGroup = document.createElement('div');\n",
       "    buttonGroup.classList = 'btn-group';\n",
       "    var button;\n",
       "    for (var toolbar_ind in mpl.toolbar_items) {\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) {\n",
       "            /* Instead of a spacer, we start a new button group. */\n",
       "            if (buttonGroup.hasChildNodes()) {\n",
       "                toolbar.appendChild(buttonGroup);\n",
       "            }\n",
       "            buttonGroup = document.createElement('div');\n",
       "            buttonGroup.classList = 'btn-group';\n",
       "            continue;\n",
       "        }\n",
       "\n",
       "        button = fig.buttons[name] = document.createElement('button');\n",
       "        button.classList = 'btn btn-default';\n",
       "        button.href = '#';\n",
       "        button.title = name;\n",
       "        button.innerHTML = '<i class=\"fa ' + image + ' fa-lg\"></i>';\n",
       "        button.addEventListener('click', on_click_closure(method_name));\n",
       "        button.addEventListener('mouseover', on_mouseover_closure(tooltip));\n",
       "        buttonGroup.appendChild(button);\n",
       "    }\n",
       "\n",
       "    if (buttonGroup.hasChildNodes()) {\n",
       "        toolbar.appendChild(buttonGroup);\n",
       "    }\n",
       "\n",
       "    // Add the status bar.\n",
       "    var status_bar = document.createElement('span');\n",
       "    status_bar.classList = 'mpl-message pull-right';\n",
       "    toolbar.appendChild(status_bar);\n",
       "    this.message = status_bar;\n",
       "\n",
       "    // Add the close button to the window.\n",
       "    var buttongrp = document.createElement('div');\n",
       "    buttongrp.classList = 'btn-group inline pull-right';\n",
       "    button = document.createElement('button');\n",
       "    button.classList = 'btn btn-mini btn-primary';\n",
       "    button.href = '#';\n",
       "    button.title = 'Stop Interaction';\n",
       "    button.innerHTML = '<i class=\"fa fa-power-off icon-remove icon-large\"></i>';\n",
       "    button.addEventListener('click', function (_evt) {\n",
       "        fig.handle_close(fig, {});\n",
       "    });\n",
       "    button.addEventListener(\n",
       "        'mouseover',\n",
       "        on_mouseover_closure('Stop Interaction')\n",
       "    );\n",
       "    buttongrp.appendChild(button);\n",
       "    var titlebar = this.root.querySelector('.ui-dialog-titlebar');\n",
       "    titlebar.insertBefore(buttongrp, titlebar.firstChild);\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._remove_fig_handler = function (event) {\n",
       "    var fig = event.data.fig;\n",
       "    if (event.target !== this) {\n",
       "        // Ignore bubbled events from children.\n",
       "        return;\n",
       "    }\n",
       "    fig.close_ws(fig, {});\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function (el) {\n",
       "    el.style.boxSizing = 'content-box'; // override notebook setting of border-box.\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function (el) {\n",
       "    // this is important to make the div 'focusable\n",
       "    el.setAttribute('tabindex', 0);\n",
       "    // reach out to IPython and tell the keyboard manager to turn it's self\n",
       "    // off when our div gets focus\n",
       "\n",
       "    // location in version 3\n",
       "    if (IPython.notebook.keyboard_manager) {\n",
       "        IPython.notebook.keyboard_manager.register_events(el);\n",
       "    } else {\n",
       "        // location in version 2\n",
       "        IPython.keyboard_manager.register_events(el);\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function (event, _name) {\n",
       "    var manager = IPython.notebook.keyboard_manager;\n",
       "    if (!manager) {\n",
       "        manager = IPython.keyboard_manager;\n",
       "    }\n",
       "\n",
       "    // Check for shift+enter\n",
       "    if (event.shiftKey && event.which === 13) {\n",
       "        this.canvas_div.blur();\n",
       "        // select the cell after this one\n",
       "        var index = IPython.notebook.find_cell_index(this.cell_info[0]);\n",
       "        IPython.notebook.select(index + 1);\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_save = function (fig, _msg) {\n",
       "    fig.ondownload(fig, null);\n",
       "};\n",
       "\n",
       "mpl.find_output_cell = function (html_output) {\n",
       "    // Return the cell and output element which can be found *uniquely* in the notebook.\n",
       "    // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n",
       "    // IPython event is triggered only after the cells have been serialised, which for\n",
       "    // our purposes (turning an active figure into a static one), is too late.\n",
       "    var cells = IPython.notebook.get_cells();\n",
       "    var ncells = cells.length;\n",
       "    for (var i = 0; i < ncells; i++) {\n",
       "        var cell = cells[i];\n",
       "        if (cell.cell_type === 'code') {\n",
       "            for (var j = 0; j < cell.output_area.outputs.length; j++) {\n",
       "                var data = cell.output_area.outputs[j];\n",
       "                if (data.data) {\n",
       "                    // IPython >= 3 moved mimebundle to data attribute of output\n",
       "                    data = data.data;\n",
       "                }\n",
       "                if (data['text/html'] === html_output) {\n",
       "                    return [cell, data, j];\n",
       "                }\n",
       "            }\n",
       "        }\n",
       "    }\n",
       "};\n",
       "\n",
       "// Register the function which deals with the matplotlib target/channel.\n",
       "// The kernel may be null if the page has been refreshed.\n",
       "if (IPython.notebook.kernel !== null) {\n",
       "    IPython.notebook.kernel.comm_manager.register_target(\n",
       "        'matplotlib',\n",
       "        mpl.mpl_figure_comm\n",
       "    );\n",
       "}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<img src=\"data:image/png;base64,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\" width=\"640\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/tmp/ipykernel_42471/1787257599.py:21: RuntimeWarning: invalid value encountered in true_divide\n",
      "  plt.plot(results[:N_pt, 4], 2*float(mu)*float(sig0)*np.log(1+abs(results[:N_pt, 4])/float(sig0))\\\n"
     ]
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "plt.subplot(1,4,1)\n",
    "plt.plot(results[:, 0], results[:, 1], \"-*\")\n",
    "plt.plot(results[:, 0], results[:, 3]*0.2*q_lim, \".\")\n",
    "plt.xlabel(\"Displacement\")\n",
    "plt.ylabel(\"$\\sigma_{xx,yy}$ at the right end\")\n",
    "plt.legend([\"$\\sigma_{yy}$\",\"$\\sigma_{xx}$\",\"Loads\"])\n",
    "plt.subplot(1,4,2)\n",
    "plt.plot(results[:, 2], results[:, 1], \"-.\")\n",
    "plt.plot(results[:, 2], results[:, 3]*0.2*q_lim, \".\")\n",
    "plt.xlabel(\"Loading steps\")\n",
    "plt.ylabel(\"$\\sigma_{xx}$ at the right end\")\n",
    "plt.legend([\"$\\sigma_{yy}$\",\"Loads\"])\n",
    "plt.subplot(1,4,3)\n",
    "plt.plot(results[:, 2], results[:, 0], \"-.\")\n",
    "plt.xlabel(\"Time\")\n",
    "plt.ylabel(\"Displacement at the right end\")\n",
    "plt.subplot(1,4,4)\n",
    "N_pt = 1000;\n",
    "plt.plot(results[:N_pt, 4], results[:N_pt, 1], \".-\")\n",
    "plt.plot(results[:N_pt, 4], 2*float(mu)*float(sig0)*np.log(1+abs(results[:N_pt, 4])/float(sig0))\\\n",
    "          *abs(results[:N_pt, 4])/results[:N_pt, 4], \"-\")\n",
    "plt.xlabel(\"Strain and the right end\")\n",
    "plt.ylabel(\"Stress at the right end\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "d02305e7",
   "metadata": {},
   "outputs": [],
   "source": [
    "x_grid = np.linspace(0,1,N_mesh)\n",
    "u_theo = x_grid/1*(1-x_grid**2/1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "e3d61261",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "341bd088",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/javascript": [
       "/* Put everything inside the global mpl namespace */\n",
       "/* global mpl */\n",
       "window.mpl = {};\n",
       "\n",
       "mpl.get_websocket_type = function () {\n",
       "    if (typeof WebSocket !== 'undefined') {\n",
       "        return WebSocket;\n",
       "    } else if (typeof MozWebSocket !== 'undefined') {\n",
       "        return MozWebSocket;\n",
       "    } else {\n",
       "        alert(\n",
       "            'Your browser does not have WebSocket support. ' +\n",
       "                'Please try Chrome, Safari or Firefox ≥ 6. ' +\n",
       "                'Firefox 4 and 5 are also supported but you ' +\n",
       "                'have to enable WebSockets in about:config.'\n",
       "        );\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure = function (figure_id, websocket, ondownload, parent_element) {\n",
       "    this.id = figure_id;\n",
       "\n",
       "    this.ws = websocket;\n",
       "\n",
       "    this.supports_binary = this.ws.binaryType !== undefined;\n",
       "\n",
       "    if (!this.supports_binary) {\n",
       "        var warnings = document.getElementById('mpl-warnings');\n",
       "        if (warnings) {\n",
       "            warnings.style.display = 'block';\n",
       "            warnings.textContent =\n",
       "                'This browser does not support binary websocket messages. ' +\n",
       "                'Performance may be slow.';\n",
       "        }\n",
       "    }\n",
       "\n",
       "    this.imageObj = new Image();\n",
       "\n",
       "    this.context = undefined;\n",
       "    this.message = undefined;\n",
       "    this.canvas = undefined;\n",
       "    this.rubberband_canvas = undefined;\n",
       "    this.rubberband_context = undefined;\n",
       "    this.format_dropdown = undefined;\n",
       "\n",
       "    this.image_mode = 'full';\n",
       "\n",
       "    this.root = document.createElement('div');\n",
       "    this.root.setAttribute('style', 'display: inline-block');\n",
       "    this._root_extra_style(this.root);\n",
       "\n",
       "    parent_element.appendChild(this.root);\n",
       "\n",
       "    this._init_header(this);\n",
       "    this._init_canvas(this);\n",
       "    this._init_toolbar(this);\n",
       "\n",
       "    var fig = this;\n",
       "\n",
       "    this.waiting = false;\n",
       "\n",
       "    this.ws.onopen = function () {\n",
       "        fig.send_message('supports_binary', { value: fig.supports_binary });\n",
       "        fig.send_message('send_image_mode', {});\n",
       "        if (fig.ratio !== 1) {\n",
       "            fig.send_message('set_dpi_ratio', { dpi_ratio: fig.ratio });\n",
       "        }\n",
       "        fig.send_message('refresh', {});\n",
       "    };\n",
       "\n",
       "    this.imageObj.onload = function () {\n",
       "        if (fig.image_mode === 'full') {\n",
       "            // Full images could contain transparency (where diff images\n",
       "            // almost always do), so we need to clear the canvas so that\n",
       "            // there is no ghosting.\n",
       "            fig.context.clearRect(0, 0, fig.canvas.width, fig.canvas.height);\n",
       "        }\n",
       "        fig.context.drawImage(fig.imageObj, 0, 0);\n",
       "    };\n",
       "\n",
       "    this.imageObj.onunload = function () {\n",
       "        fig.ws.close();\n",
       "    };\n",
       "\n",
       "    this.ws.onmessage = this._make_on_message_function(this);\n",
       "\n",
       "    this.ondownload = ondownload;\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._init_header = function () {\n",
       "    var titlebar = document.createElement('div');\n",
       "    titlebar.classList =\n",
       "        'ui-dialog-titlebar ui-widget-header ui-corner-all ui-helper-clearfix';\n",
       "    var titletext = document.createElement('div');\n",
       "    titletext.classList = 'ui-dialog-title';\n",
       "    titletext.setAttribute(\n",
       "        'style',\n",
       "        'width: 100%; text-align: center; padding: 3px;'\n",
       "    );\n",
       "    titlebar.appendChild(titletext);\n",
       "    this.root.appendChild(titlebar);\n",
       "    this.header = titletext;\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function (_canvas_div) {};\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function (_canvas_div) {};\n",
       "\n",
       "mpl.figure.prototype._init_canvas = function () {\n",
       "    var fig = this;\n",
       "\n",
       "    var canvas_div = (this.canvas_div = document.createElement('div'));\n",
       "    canvas_div.setAttribute(\n",
       "        'style',\n",
       "        'border: 1px solid #ddd;' +\n",
       "            'box-sizing: content-box;' +\n",
       "            'clear: both;' +\n",
       "            'min-height: 1px;' +\n",
       "            'min-width: 1px;' +\n",
       "            'outline: 0;' +\n",
       "            'overflow: hidden;' +\n",
       "            'position: relative;' +\n",
       "            'resize: both;'\n",
       "    );\n",
       "\n",
       "    function on_keyboard_event_closure(name) {\n",
       "        return function (event) {\n",
       "            return fig.key_event(event, name);\n",
       "        };\n",
       "    }\n",
       "\n",
       "    canvas_div.addEventListener(\n",
       "        'keydown',\n",
       "        on_keyboard_event_closure('key_press')\n",
       "    );\n",
       "    canvas_div.addEventListener(\n",
       "        'keyup',\n",
       "        on_keyboard_event_closure('key_release')\n",
       "    );\n",
       "\n",
       "    this._canvas_extra_style(canvas_div);\n",
       "    this.root.appendChild(canvas_div);\n",
       "\n",
       "    var canvas = (this.canvas = document.createElement('canvas'));\n",
       "    canvas.classList.add('mpl-canvas');\n",
       "    canvas.setAttribute('style', 'box-sizing: content-box;');\n",
       "\n",
       "    this.context = canvas.getContext('2d');\n",
       "\n",
       "    var backingStore =\n",
       "        this.context.backingStorePixelRatio ||\n",
       "        this.context.webkitBackingStorePixelRatio ||\n",
       "        this.context.mozBackingStorePixelRatio ||\n",
       "        this.context.msBackingStorePixelRatio ||\n",
       "        this.context.oBackingStorePixelRatio ||\n",
       "        this.context.backingStorePixelRatio ||\n",
       "        1;\n",
       "\n",
       "    this.ratio = (window.devicePixelRatio || 1) / backingStore;\n",
       "\n",
       "    var rubberband_canvas = (this.rubberband_canvas = document.createElement(\n",
       "        'canvas'\n",
       "    ));\n",
       "    rubberband_canvas.setAttribute(\n",
       "        'style',\n",
       "        'box-sizing: content-box; position: absolute; left: 0; top: 0; z-index: 1;'\n",
       "    );\n",
       "\n",
       "    // Apply a ponyfill if ResizeObserver is not implemented by browser.\n",
       "    if (this.ResizeObserver === undefined) {\n",
       "        if (window.ResizeObserver !== undefined) {\n",
       "            this.ResizeObserver = window.ResizeObserver;\n",
       "        } else {\n",
       "            var obs = _JSXTOOLS_RESIZE_OBSERVER({});\n",
       "            this.ResizeObserver = obs.ResizeObserver;\n",
       "        }\n",
       "    }\n",
       "\n",
       "    this.resizeObserverInstance = new this.ResizeObserver(function (entries) {\n",
       "        var nentries = entries.length;\n",
       "        for (var i = 0; i < nentries; i++) {\n",
       "            var entry = entries[i];\n",
       "            var width, height;\n",
       "            if (entry.contentBoxSize) {\n",
       "                if (entry.contentBoxSize instanceof Array) {\n",
       "                    // Chrome 84 implements new version of spec.\n",
       "                    width = entry.contentBoxSize[0].inlineSize;\n",
       "                    height = entry.contentBoxSize[0].blockSize;\n",
       "                } else {\n",
       "                    // Firefox implements old version of spec.\n",
       "                    width = entry.contentBoxSize.inlineSize;\n",
       "                    height = entry.contentBoxSize.blockSize;\n",
       "                }\n",
       "            } else {\n",
       "                // Chrome <84 implements even older version of spec.\n",
       "                width = entry.contentRect.width;\n",
       "                height = entry.contentRect.height;\n",
       "            }\n",
       "\n",
       "            // Keep the size of the canvas and rubber band canvas in sync with\n",
       "            // the canvas container.\n",
       "            if (entry.devicePixelContentBoxSize) {\n",
       "                // Chrome 84 implements new version of spec.\n",
       "                canvas.setAttribute(\n",
       "                    'width',\n",
       "                    entry.devicePixelContentBoxSize[0].inlineSize\n",
       "                );\n",
       "                canvas.setAttribute(\n",
       "                    'height',\n",
       "                    entry.devicePixelContentBoxSize[0].blockSize\n",
       "                );\n",
       "            } else {\n",
       "                canvas.setAttribute('width', width * fig.ratio);\n",
       "                canvas.setAttribute('height', height * fig.ratio);\n",
       "            }\n",
       "            canvas.setAttribute(\n",
       "                'style',\n",
       "                'width: ' + width + 'px; height: ' + height + 'px;'\n",
       "            );\n",
       "\n",
       "            rubberband_canvas.setAttribute('width', width);\n",
       "            rubberband_canvas.setAttribute('height', height);\n",
       "\n",
       "            // And update the size in Python. We ignore the initial 0/0 size\n",
       "            // that occurs as the element is placed into the DOM, which should\n",
       "            // otherwise not happen due to the minimum size styling.\n",
       "            if (fig.ws.readyState == 1 && width != 0 && height != 0) {\n",
       "                fig.request_resize(width, height);\n",
       "            }\n",
       "        }\n",
       "    });\n",
       "    this.resizeObserverInstance.observe(canvas_div);\n",
       "\n",
       "    function on_mouse_event_closure(name) {\n",
       "        return function (event) {\n",
       "            return fig.mouse_event(event, name);\n",
       "        };\n",
       "    }\n",
       "\n",
       "    rubberband_canvas.addEventListener(\n",
       "        'mousedown',\n",
       "        on_mouse_event_closure('button_press')\n",
       "    );\n",
       "    rubberband_canvas.addEventListener(\n",
       "        'mouseup',\n",
       "        on_mouse_event_closure('button_release')\n",
       "    );\n",
       "    rubberband_canvas.addEventListener(\n",
       "        'dblclick',\n",
       "        on_mouse_event_closure('dblclick')\n",
       "    );\n",
       "    // Throttle sequential mouse events to 1 every 20ms.\n",
       "    rubberband_canvas.addEventListener(\n",
       "        'mousemove',\n",
       "        on_mouse_event_closure('motion_notify')\n",
       "    );\n",
       "\n",
       "    rubberband_canvas.addEventListener(\n",
       "        'mouseenter',\n",
       "        on_mouse_event_closure('figure_enter')\n",
       "    );\n",
       "    rubberband_canvas.addEventListener(\n",
       "        'mouseleave',\n",
       "        on_mouse_event_closure('figure_leave')\n",
       "    );\n",
       "\n",
       "    canvas_div.addEventListener('wheel', function (event) {\n",
       "        if (event.deltaY < 0) {\n",
       "            event.step = 1;\n",
       "        } else {\n",
       "            event.step = -1;\n",
       "        }\n",
       "        on_mouse_event_closure('scroll')(event);\n",
       "    });\n",
       "\n",
       "    canvas_div.appendChild(canvas);\n",
       "    canvas_div.appendChild(rubberband_canvas);\n",
       "\n",
       "    this.rubberband_context = rubberband_canvas.getContext('2d');\n",
       "    this.rubberband_context.strokeStyle = '#000000';\n",
       "\n",
       "    this._resize_canvas = function (width, height, forward) {\n",
       "        if (forward) {\n",
       "            canvas_div.style.width = width + 'px';\n",
       "            canvas_div.style.height = height + 'px';\n",
       "        }\n",
       "    };\n",
       "\n",
       "    // Disable right mouse context menu.\n",
       "    this.rubberband_canvas.addEventListener('contextmenu', function (_e) {\n",
       "        event.preventDefault();\n",
       "        return false;\n",
       "    });\n",
       "\n",
       "    function set_focus() {\n",
       "        canvas.focus();\n",
       "        canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    window.setTimeout(set_focus, 100);\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function () {\n",
       "    var fig = this;\n",
       "\n",
       "    var toolbar = document.createElement('div');\n",
       "    toolbar.classList = 'mpl-toolbar';\n",
       "    this.root.appendChild(toolbar);\n",
       "\n",
       "    function on_click_closure(name) {\n",
       "        return function (_event) {\n",
       "            return fig.toolbar_button_onclick(name);\n",
       "        };\n",
       "    }\n",
       "\n",
       "    function on_mouseover_closure(tooltip) {\n",
       "        return function (event) {\n",
       "            if (!event.currentTarget.disabled) {\n",
       "                return fig.toolbar_button_onmouseover(tooltip);\n",
       "            }\n",
       "        };\n",
       "    }\n",
       "\n",
       "    fig.buttons = {};\n",
       "    var buttonGroup = document.createElement('div');\n",
       "    buttonGroup.classList = 'mpl-button-group';\n",
       "    for (var toolbar_ind in mpl.toolbar_items) {\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) {\n",
       "            /* Instead of a spacer, we start a new button group. */\n",
       "            if (buttonGroup.hasChildNodes()) {\n",
       "                toolbar.appendChild(buttonGroup);\n",
       "            }\n",
       "            buttonGroup = document.createElement('div');\n",
       "            buttonGroup.classList = 'mpl-button-group';\n",
       "            continue;\n",
       "        }\n",
       "\n",
       "        var button = (fig.buttons[name] = document.createElement('button'));\n",
       "        button.classList = 'mpl-widget';\n",
       "        button.setAttribute('role', 'button');\n",
       "        button.setAttribute('aria-disabled', 'false');\n",
       "        button.addEventListener('click', on_click_closure(method_name));\n",
       "        button.addEventListener('mouseover', on_mouseover_closure(tooltip));\n",
       "\n",
       "        var icon_img = document.createElement('img');\n",
       "        icon_img.src = '_images/' + image + '.png';\n",
       "        icon_img.srcset = '_images/' + image + '_large.png 2x';\n",
       "        icon_img.alt = tooltip;\n",
       "        button.appendChild(icon_img);\n",
       "\n",
       "        buttonGroup.appendChild(button);\n",
       "    }\n",
       "\n",
       "    if (buttonGroup.hasChildNodes()) {\n",
       "        toolbar.appendChild(buttonGroup);\n",
       "    }\n",
       "\n",
       "    var fmt_picker = document.createElement('select');\n",
       "    fmt_picker.classList = 'mpl-widget';\n",
       "    toolbar.appendChild(fmt_picker);\n",
       "    this.format_dropdown = fmt_picker;\n",
       "\n",
       "    for (var ind in mpl.extensions) {\n",
       "        var fmt = mpl.extensions[ind];\n",
       "        var option = document.createElement('option');\n",
       "        option.selected = fmt === mpl.default_extension;\n",
       "        option.innerHTML = fmt;\n",
       "        fmt_picker.appendChild(option);\n",
       "    }\n",
       "\n",
       "    var status_bar = document.createElement('span');\n",
       "    status_bar.classList = 'mpl-message';\n",
       "    toolbar.appendChild(status_bar);\n",
       "    this.message = status_bar;\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.request_resize = function (x_pixels, y_pixels) {\n",
       "    // Request matplotlib to resize the figure. Matplotlib will then trigger a resize in the client,\n",
       "    // which will in turn request a refresh of the image.\n",
       "    this.send_message('resize', { width: x_pixels, height: y_pixels });\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.send_message = function (type, properties) {\n",
       "    properties['type'] = type;\n",
       "    properties['figure_id'] = this.id;\n",
       "    this.ws.send(JSON.stringify(properties));\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.send_draw_message = function () {\n",
       "    if (!this.waiting) {\n",
       "        this.waiting = true;\n",
       "        this.ws.send(JSON.stringify({ type: 'draw', figure_id: this.id }));\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_save = function (fig, _msg) {\n",
       "    var format_dropdown = fig.format_dropdown;\n",
       "    var format = format_dropdown.options[format_dropdown.selectedIndex].value;\n",
       "    fig.ondownload(fig, format);\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_resize = function (fig, msg) {\n",
       "    var size = msg['size'];\n",
       "    if (size[0] !== fig.canvas.width || size[1] !== fig.canvas.height) {\n",
       "        fig._resize_canvas(size[0], size[1], msg['forward']);\n",
       "        fig.send_message('refresh', {});\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_rubberband = function (fig, msg) {\n",
       "    var x0 = msg['x0'] / fig.ratio;\n",
       "    var y0 = (fig.canvas.height - msg['y0']) / fig.ratio;\n",
       "    var x1 = msg['x1'] / fig.ratio;\n",
       "    var y1 = (fig.canvas.height - msg['y1']) / fig.ratio;\n",
       "    x0 = Math.floor(x0) + 0.5;\n",
       "    y0 = Math.floor(y0) + 0.5;\n",
       "    x1 = Math.floor(x1) + 0.5;\n",
       "    y1 = Math.floor(y1) + 0.5;\n",
       "    var min_x = Math.min(x0, x1);\n",
       "    var min_y = Math.min(y0, y1);\n",
       "    var width = Math.abs(x1 - x0);\n",
       "    var height = Math.abs(y1 - y0);\n",
       "\n",
       "    fig.rubberband_context.clearRect(\n",
       "        0,\n",
       "        0,\n",
       "        fig.canvas.width / fig.ratio,\n",
       "        fig.canvas.height / fig.ratio\n",
       "    );\n",
       "\n",
       "    fig.rubberband_context.strokeRect(min_x, min_y, width, height);\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_figure_label = function (fig, msg) {\n",
       "    // Updates the figure title.\n",
       "    fig.header.textContent = msg['label'];\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_cursor = function (fig, msg) {\n",
       "    var cursor = msg['cursor'];\n",
       "    switch (cursor) {\n",
       "        case 0:\n",
       "            cursor = 'pointer';\n",
       "            break;\n",
       "        case 1:\n",
       "            cursor = 'default';\n",
       "            break;\n",
       "        case 2:\n",
       "            cursor = 'crosshair';\n",
       "            break;\n",
       "        case 3:\n",
       "            cursor = 'move';\n",
       "            break;\n",
       "    }\n",
       "    fig.rubberband_canvas.style.cursor = cursor;\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_message = function (fig, msg) {\n",
       "    fig.message.textContent = msg['message'];\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_draw = function (fig, _msg) {\n",
       "    // Request the server to send over a new figure.\n",
       "    fig.send_draw_message();\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_image_mode = function (fig, msg) {\n",
       "    fig.image_mode = msg['mode'];\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_history_buttons = function (fig, msg) {\n",
       "    for (var key in msg) {\n",
       "        if (!(key in fig.buttons)) {\n",
       "            continue;\n",
       "        }\n",
       "        fig.buttons[key].disabled = !msg[key];\n",
       "        fig.buttons[key].setAttribute('aria-disabled', !msg[key]);\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_navigate_mode = function (fig, msg) {\n",
       "    if (msg['mode'] === 'PAN') {\n",
       "        fig.buttons['Pan'].classList.add('active');\n",
       "        fig.buttons['Zoom'].classList.remove('active');\n",
       "    } else if (msg['mode'] === 'ZOOM') {\n",
       "        fig.buttons['Pan'].classList.remove('active');\n",
       "        fig.buttons['Zoom'].classList.add('active');\n",
       "    } else {\n",
       "        fig.buttons['Pan'].classList.remove('active');\n",
       "        fig.buttons['Zoom'].classList.remove('active');\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function () {\n",
       "    // Called whenever the canvas gets updated.\n",
       "    this.send_message('ack', {});\n",
       "};\n",
       "\n",
       "// A function to construct a web socket function for onmessage handling.\n",
       "// Called in the figure constructor.\n",
       "mpl.figure.prototype._make_on_message_function = function (fig) {\n",
       "    return function socket_on_message(evt) {\n",
       "        if (evt.data instanceof Blob) {\n",
       "            var img = evt.data;\n",
       "            if (img.type !== 'image/png') {\n",
       "                /* FIXME: We get \"Resource interpreted as Image but\n",
       "                 * transferred with MIME type text/plain:\" errors on\n",
       "                 * Chrome.  But how to set the MIME type?  It doesn't seem\n",
       "                 * to be part of the websocket stream */\n",
       "                img.type = 'image/png';\n",
       "            }\n",
       "\n",
       "            /* Free the memory for the previous frames */\n",
       "            if (fig.imageObj.src) {\n",
       "                (window.URL || window.webkitURL).revokeObjectURL(\n",
       "                    fig.imageObj.src\n",
       "                );\n",
       "            }\n",
       "\n",
       "            fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n",
       "                img\n",
       "            );\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        } else if (\n",
       "            typeof evt.data === 'string' &&\n",
       "            evt.data.slice(0, 21) === 'data:image/png;base64'\n",
       "        ) {\n",
       "            fig.imageObj.src = evt.data;\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        var msg = JSON.parse(evt.data);\n",
       "        var msg_type = msg['type'];\n",
       "\n",
       "        // Call the  \"handle_{type}\" callback, which takes\n",
       "        // the figure and JSON message as its only arguments.\n",
       "        try {\n",
       "            var callback = fig['handle_' + msg_type];\n",
       "        } catch (e) {\n",
       "            console.log(\n",
       "                \"No handler for the '\" + msg_type + \"' message type: \",\n",
       "                msg\n",
       "            );\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        if (callback) {\n",
       "            try {\n",
       "                // console.log(\"Handling '\" + msg_type + \"' message: \", msg);\n",
       "                callback(fig, msg);\n",
       "            } catch (e) {\n",
       "                console.log(\n",
       "                    \"Exception inside the 'handler_\" + msg_type + \"' callback:\",\n",
       "                    e,\n",
       "                    e.stack,\n",
       "                    msg\n",
       "                );\n",
       "            }\n",
       "        }\n",
       "    };\n",
       "};\n",
       "\n",
       "// from http://stackoverflow.com/questions/1114465/getting-mouse-location-in-canvas\n",
       "mpl.findpos = function (e) {\n",
       "    //this section is from http://www.quirksmode.org/js/events_properties.html\n",
       "    var targ;\n",
       "    if (!e) {\n",
       "        e = window.event;\n",
       "    }\n",
       "    if (e.target) {\n",
       "        targ = e.target;\n",
       "    } else if (e.srcElement) {\n",
       "        targ = e.srcElement;\n",
       "    }\n",
       "    if (targ.nodeType === 3) {\n",
       "        // defeat Safari bug\n",
       "        targ = targ.parentNode;\n",
       "    }\n",
       "\n",
       "    // pageX,Y are the mouse positions relative to the document\n",
       "    var boundingRect = targ.getBoundingClientRect();\n",
       "    var x = e.pageX - (boundingRect.left + document.body.scrollLeft);\n",
       "    var y = e.pageY - (boundingRect.top + document.body.scrollTop);\n",
       "\n",
       "    return { x: x, y: y };\n",
       "};\n",
       "\n",
       "/*\n",
       " * return a copy of an object with only non-object keys\n",
       " * we need this to avoid circular references\n",
       " * http://stackoverflow.com/a/24161582/3208463\n",
       " */\n",
       "function simpleKeys(original) {\n",
       "    return Object.keys(original).reduce(function (obj, key) {\n",
       "        if (typeof original[key] !== 'object') {\n",
       "            obj[key] = original[key];\n",
       "        }\n",
       "        return obj;\n",
       "    }, {});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.mouse_event = function (event, name) {\n",
       "    var canvas_pos = mpl.findpos(event);\n",
       "\n",
       "    if (name === 'button_press') {\n",
       "        this.canvas.focus();\n",
       "        this.canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    var x = canvas_pos.x * this.ratio;\n",
       "    var y = canvas_pos.y * this.ratio;\n",
       "\n",
       "    this.send_message(name, {\n",
       "        x: x,\n",
       "        y: y,\n",
       "        button: event.button,\n",
       "        step: event.step,\n",
       "        guiEvent: simpleKeys(event),\n",
       "    });\n",
       "\n",
       "    /* This prevents the web browser from automatically changing to\n",
       "     * the text insertion cursor when the button is pressed.  We want\n",
       "     * to control all of the cursor setting manually through the\n",
       "     * 'cursor' event from matplotlib */\n",
       "    event.preventDefault();\n",
       "    return false;\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function (_event, _name) {\n",
       "    // Handle any extra behaviour associated with a key event\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.key_event = function (event, name) {\n",
       "    // Prevent repeat events\n",
       "    if (name === 'key_press') {\n",
       "        if (event.key === this._key) {\n",
       "            return;\n",
       "        } else {\n",
       "            this._key = event.key;\n",
       "        }\n",
       "    }\n",
       "    if (name === 'key_release') {\n",
       "        this._key = null;\n",
       "    }\n",
       "\n",
       "    var value = '';\n",
       "    if (event.ctrlKey && event.key !== 'Control') {\n",
       "        value += 'ctrl+';\n",
       "    }\n",
       "    else if (event.altKey && event.key !== 'Alt') {\n",
       "        value += 'alt+';\n",
       "    }\n",
       "    else if (event.shiftKey && event.key !== 'Shift') {\n",
       "        value += 'shift+';\n",
       "    }\n",
       "\n",
       "    value += 'k' + event.key;\n",
       "\n",
       "    this._key_event_extra(event, name);\n",
       "\n",
       "    this.send_message(name, { key: value, guiEvent: simpleKeys(event) });\n",
       "    return false;\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onclick = function (name) {\n",
       "    if (name === 'download') {\n",
       "        this.handle_save(this, null);\n",
       "    } else {\n",
       "        this.send_message('toolbar_button', { name: name });\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onmouseover = function (tooltip) {\n",
       "    this.message.textContent = tooltip;\n",
       "};\n",
       "\n",
       "///////////////// REMAINING CONTENT GENERATED BY embed_js.py /////////////////\n",
       "// prettier-ignore\n",
       "var _JSXTOOLS_RESIZE_OBSERVER=function(A){var t,i=new WeakMap,n=new WeakMap,a=new WeakMap,r=new WeakMap,o=new Set;function s(e){if(!(this instanceof s))throw new TypeError(\"Constructor requires 'new' operator\");i.set(this,e)}function h(){throw new TypeError(\"Function is not a constructor\")}function c(e,t,i,n){e=0 in arguments?Number(arguments[0]):0,t=1 in arguments?Number(arguments[1]):0,i=2 in arguments?Number(arguments[2]):0,n=3 in arguments?Number(arguments[3]):0,this.right=(this.x=this.left=e)+(this.width=i),this.bottom=(this.y=this.top=t)+(this.height=n),Object.freeze(this)}function d(){t=requestAnimationFrame(d);var s=new WeakMap,p=new Set;o.forEach((function(t){r.get(t).forEach((function(i){var r=t instanceof window.SVGElement,o=a.get(t),d=r?0:parseFloat(o.paddingTop),f=r?0:parseFloat(o.paddingRight),l=r?0:parseFloat(o.paddingBottom),u=r?0:parseFloat(o.paddingLeft),g=r?0:parseFloat(o.borderTopWidth),m=r?0:parseFloat(o.borderRightWidth),w=r?0:parseFloat(o.borderBottomWidth),b=u+f,F=d+l,v=(r?0:parseFloat(o.borderLeftWidth))+m,W=g+w,y=r?0:t.offsetHeight-W-t.clientHeight,E=r?0:t.offsetWidth-v-t.clientWidth,R=b+v,z=F+W,M=r?t.width:parseFloat(o.width)-R-E,O=r?t.height:parseFloat(o.height)-z-y;if(n.has(t)){var k=n.get(t);if(k[0]===M&&k[1]===O)return}n.set(t,[M,O]);var S=Object.create(h.prototype);S.target=t,S.contentRect=new c(u,d,M,O),s.has(i)||(s.set(i,[]),p.add(i)),s.get(i).push(S)}))})),p.forEach((function(e){i.get(e).call(e,s.get(e),e)}))}return s.prototype.observe=function(i){if(i instanceof window.Element){r.has(i)||(r.set(i,new Set),o.add(i),a.set(i,window.getComputedStyle(i)));var n=r.get(i);n.has(this)||n.add(this),cancelAnimationFrame(t),t=requestAnimationFrame(d)}},s.prototype.unobserve=function(i){if(i instanceof window.Element&&r.has(i)){var n=r.get(i);n.has(this)&&(n.delete(this),n.size||(r.delete(i),o.delete(i))),n.size||r.delete(i),o.size||cancelAnimationFrame(t)}},A.DOMRectReadOnly=c,A.ResizeObserver=s,A.ResizeObserverEntry=h,A}; // eslint-disable-line\n",
       "mpl.toolbar_items = [[\"Home\", \"Reset original view\", \"fa fa-home icon-home\", \"home\"], [\"Back\", \"Back to previous view\", \"fa fa-arrow-left icon-arrow-left\", \"back\"], [\"Forward\", \"Forward to next view\", \"fa fa-arrow-right icon-arrow-right\", \"forward\"], [\"\", \"\", \"\", \"\"], [\"Pan\", \"Left button pans, Right button zooms\\nx/y fixes axis, CTRL fixes aspect\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\\nx/y fixes axis, CTRL fixes aspect\", \"fa fa-square-o icon-check-empty\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o icon-save\", \"download\"]];\n",
       "\n",
       "mpl.extensions = [\"eps\", \"jpeg\", \"pgf\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\", \"tif\"];\n",
       "\n",
       "mpl.default_extension = \"png\";/* global mpl */\n",
       "\n",
       "var comm_websocket_adapter = function (comm) {\n",
       "    // Create a \"websocket\"-like object which calls the given IPython comm\n",
       "    // object with the appropriate methods. Currently this is a non binary\n",
       "    // socket, so there is still some room for performance tuning.\n",
       "    var ws = {};\n",
       "\n",
       "    ws.binaryType = comm.kernel.ws.binaryType;\n",
       "    ws.readyState = comm.kernel.ws.readyState;\n",
       "    function updateReadyState(_event) {\n",
       "        if (comm.kernel.ws) {\n",
       "            ws.readyState = comm.kernel.ws.readyState;\n",
       "        } else {\n",
       "            ws.readyState = 3; // Closed state.\n",
       "        }\n",
       "    }\n",
       "    comm.kernel.ws.addEventListener('open', updateReadyState);\n",
       "    comm.kernel.ws.addEventListener('close', updateReadyState);\n",
       "    comm.kernel.ws.addEventListener('error', updateReadyState);\n",
       "\n",
       "    ws.close = function () {\n",
       "        comm.close();\n",
       "    };\n",
       "    ws.send = function (m) {\n",
       "        //console.log('sending', m);\n",
       "        comm.send(m);\n",
       "    };\n",
       "    // Register the callback with on_msg.\n",
       "    comm.on_msg(function (msg) {\n",
       "        //console.log('receiving', msg['content']['data'], msg);\n",
       "        var data = msg['content']['data'];\n",
       "        if (data['blob'] !== undefined) {\n",
       "            data = {\n",
       "                data: new Blob(msg['buffers'], { type: data['blob'] }),\n",
       "            };\n",
       "        }\n",
       "        // Pass the mpl event to the overridden (by mpl) onmessage function.\n",
       "        ws.onmessage(data);\n",
       "    });\n",
       "    return ws;\n",
       "};\n",
       "\n",
       "mpl.mpl_figure_comm = function (comm, msg) {\n",
       "    // This is the function which gets called when the mpl process\n",
       "    // starts-up an IPython Comm through the \"matplotlib\" channel.\n",
       "\n",
       "    var id = msg.content.data.id;\n",
       "    // Get hold of the div created by the display call when the Comm\n",
       "    // socket was opened in Python.\n",
       "    var element = document.getElementById(id);\n",
       "    var ws_proxy = comm_websocket_adapter(comm);\n",
       "\n",
       "    function ondownload(figure, _format) {\n",
       "        window.open(figure.canvas.toDataURL());\n",
       "    }\n",
       "\n",
       "    var fig = new mpl.figure(id, ws_proxy, ondownload, element);\n",
       "\n",
       "    // Call onopen now - mpl needs it, as it is assuming we've passed it a real\n",
       "    // web socket which is closed, not our websocket->open comm proxy.\n",
       "    ws_proxy.onopen();\n",
       "\n",
       "    fig.parent_element = element;\n",
       "    fig.cell_info = mpl.find_output_cell(\"<div id='\" + id + \"'></div>\");\n",
       "    if (!fig.cell_info) {\n",
       "        console.error('Failed to find cell for figure', id, fig);\n",
       "        return;\n",
       "    }\n",
       "    fig.cell_info[0].output_area.element.on(\n",
       "        'cleared',\n",
       "        { fig: fig },\n",
       "        fig._remove_fig_handler\n",
       "    );\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_close = function (fig, msg) {\n",
       "    var width = fig.canvas.width / fig.ratio;\n",
       "    fig.cell_info[0].output_area.element.off(\n",
       "        'cleared',\n",
       "        fig._remove_fig_handler\n",
       "    );\n",
       "    fig.resizeObserverInstance.unobserve(fig.canvas_div);\n",
       "\n",
       "    // Update the output cell to use the data from the current canvas.\n",
       "    fig.push_to_output();\n",
       "    var dataURL = fig.canvas.toDataURL();\n",
       "    // Re-enable the keyboard manager in IPython - without this line, in FF,\n",
       "    // the notebook keyboard shortcuts fail.\n",
       "    IPython.keyboard_manager.enable();\n",
       "    fig.parent_element.innerHTML =\n",
       "        '<img src=\"' + dataURL + '\" width=\"' + width + '\">';\n",
       "    fig.close_ws(fig, msg);\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.close_ws = function (fig, msg) {\n",
       "    fig.send_message('closing', msg);\n",
       "    // fig.ws.close()\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.push_to_output = function (_remove_interactive) {\n",
       "    // Turn the data on the canvas into data in the output cell.\n",
       "    var width = this.canvas.width / this.ratio;\n",
       "    var dataURL = this.canvas.toDataURL();\n",
       "    this.cell_info[1]['text/html'] =\n",
       "        '<img src=\"' + dataURL + '\" width=\"' + width + '\">';\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function () {\n",
       "    // Tell IPython that the notebook contents must change.\n",
       "    IPython.notebook.set_dirty(true);\n",
       "    this.send_message('ack', {});\n",
       "    var fig = this;\n",
       "    // Wait a second, then push the new image to the DOM so\n",
       "    // that it is saved nicely (might be nice to debounce this).\n",
       "    setTimeout(function () {\n",
       "        fig.push_to_output();\n",
       "    }, 1000);\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function () {\n",
       "    var fig = this;\n",
       "\n",
       "    var toolbar = document.createElement('div');\n",
       "    toolbar.classList = 'btn-toolbar';\n",
       "    this.root.appendChild(toolbar);\n",
       "\n",
       "    function on_click_closure(name) {\n",
       "        return function (_event) {\n",
       "            return fig.toolbar_button_onclick(name);\n",
       "        };\n",
       "    }\n",
       "\n",
       "    function on_mouseover_closure(tooltip) {\n",
       "        return function (event) {\n",
       "            if (!event.currentTarget.disabled) {\n",
       "                return fig.toolbar_button_onmouseover(tooltip);\n",
       "            }\n",
       "        };\n",
       "    }\n",
       "\n",
       "    fig.buttons = {};\n",
       "    var buttonGroup = document.createElement('div');\n",
       "    buttonGroup.classList = 'btn-group';\n",
       "    var button;\n",
       "    for (var toolbar_ind in mpl.toolbar_items) {\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) {\n",
       "            /* Instead of a spacer, we start a new button group. */\n",
       "            if (buttonGroup.hasChildNodes()) {\n",
       "                toolbar.appendChild(buttonGroup);\n",
       "            }\n",
       "            buttonGroup = document.createElement('div');\n",
       "            buttonGroup.classList = 'btn-group';\n",
       "            continue;\n",
       "        }\n",
       "\n",
       "        button = fig.buttons[name] = document.createElement('button');\n",
       "        button.classList = 'btn btn-default';\n",
       "        button.href = '#';\n",
       "        button.title = name;\n",
       "        button.innerHTML = '<i class=\"fa ' + image + ' fa-lg\"></i>';\n",
       "        button.addEventListener('click', on_click_closure(method_name));\n",
       "        button.addEventListener('mouseover', on_mouseover_closure(tooltip));\n",
       "        buttonGroup.appendChild(button);\n",
       "    }\n",
       "\n",
       "    if (buttonGroup.hasChildNodes()) {\n",
       "        toolbar.appendChild(buttonGroup);\n",
       "    }\n",
       "\n",
       "    // Add the status bar.\n",
       "    var status_bar = document.createElement('span');\n",
       "    status_bar.classList = 'mpl-message pull-right';\n",
       "    toolbar.appendChild(status_bar);\n",
       "    this.message = status_bar;\n",
       "\n",
       "    // Add the close button to the window.\n",
       "    var buttongrp = document.createElement('div');\n",
       "    buttongrp.classList = 'btn-group inline pull-right';\n",
       "    button = document.createElement('button');\n",
       "    button.classList = 'btn btn-mini btn-primary';\n",
       "    button.href = '#';\n",
       "    button.title = 'Stop Interaction';\n",
       "    button.innerHTML = '<i class=\"fa fa-power-off icon-remove icon-large\"></i>';\n",
       "    button.addEventListener('click', function (_evt) {\n",
       "        fig.handle_close(fig, {});\n",
       "    });\n",
       "    button.addEventListener(\n",
       "        'mouseover',\n",
       "        on_mouseover_closure('Stop Interaction')\n",
       "    );\n",
       "    buttongrp.appendChild(button);\n",
       "    var titlebar = this.root.querySelector('.ui-dialog-titlebar');\n",
       "    titlebar.insertBefore(buttongrp, titlebar.firstChild);\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._remove_fig_handler = function (event) {\n",
       "    var fig = event.data.fig;\n",
       "    if (event.target !== this) {\n",
       "        // Ignore bubbled events from children.\n",
       "        return;\n",
       "    }\n",
       "    fig.close_ws(fig, {});\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function (el) {\n",
       "    el.style.boxSizing = 'content-box'; // override notebook setting of border-box.\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function (el) {\n",
       "    // this is important to make the div 'focusable\n",
       "    el.setAttribute('tabindex', 0);\n",
       "    // reach out to IPython and tell the keyboard manager to turn it's self\n",
       "    // off when our div gets focus\n",
       "\n",
       "    // location in version 3\n",
       "    if (IPython.notebook.keyboard_manager) {\n",
       "        IPython.notebook.keyboard_manager.register_events(el);\n",
       "    } else {\n",
       "        // location in version 2\n",
       "        IPython.keyboard_manager.register_events(el);\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function (event, _name) {\n",
       "    var manager = IPython.notebook.keyboard_manager;\n",
       "    if (!manager) {\n",
       "        manager = IPython.keyboard_manager;\n",
       "    }\n",
       "\n",
       "    // Check for shift+enter\n",
       "    if (event.shiftKey && event.which === 13) {\n",
       "        this.canvas_div.blur();\n",
       "        // select the cell after this one\n",
       "        var index = IPython.notebook.find_cell_index(this.cell_info[0]);\n",
       "        IPython.notebook.select(index + 1);\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_save = function (fig, _msg) {\n",
       "    fig.ondownload(fig, null);\n",
       "};\n",
       "\n",
       "mpl.find_output_cell = function (html_output) {\n",
       "    // Return the cell and output element which can be found *uniquely* in the notebook.\n",
       "    // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n",
       "    // IPython event is triggered only after the cells have been serialised, which for\n",
       "    // our purposes (turning an active figure into a static one), is too late.\n",
       "    var cells = IPython.notebook.get_cells();\n",
       "    var ncells = cells.length;\n",
       "    for (var i = 0; i < ncells; i++) {\n",
       "        var cell = cells[i];\n",
       "        if (cell.cell_type === 'code') {\n",
       "            for (var j = 0; j < cell.output_area.outputs.length; j++) {\n",
       "                var data = cell.output_area.outputs[j];\n",
       "                if (data.data) {\n",
       "                    // IPython >= 3 moved mimebundle to data attribute of output\n",
       "                    data = data.data;\n",
       "                }\n",
       "                if (data['text/html'] === html_output) {\n",
       "                    return [cell, data, j];\n",
       "                }\n",
       "            }\n",
       "        }\n",
       "    }\n",
       "};\n",
       "\n",
       "// Register the function which deals with the matplotlib target/channel.\n",
       "// The kernel may be null if the page has been refreshed.\n",
       "if (IPython.notebook.kernel !== null) {\n",
       "    IPython.notebook.kernel.comm_manager.register_target(\n",
       "        'matplotlib',\n",
       "        mpl.mpl_figure_comm\n",
       "    );\n",
       "}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<img src=\"data:image/png;base64,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\" width=\"640\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots()\n",
    "\n",
    "line1, = ax.plot([])\n",
    "line2, = ax.plot([])\n",
    "\n",
    "ax.set_xlim(0,1)\n",
    "ax.set_ylim(-1e0,1e0)\n",
    "\n",
    "ax.set_xlabel('x')\n",
    "ax.set_ylabel('Displacement')\n",
    "\n",
    "def animate(frame_num):\n",
    "    # ax.clear()\n",
    "    line1.set_data((np.linspace(0,1,N_mesh), results_1d[frame_num, :]))\n",
    "    line2.set_data(x_grid,u_theo)\n",
    "    return line1, line2\n",
    "\n",
    "ani = FuncAnimation(fig, animate, frames=Nincr, interval=1)\n",
    "\n",
    "\n",
    "plt.show()\n",
    "\n"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "fenicsproject",
   "language": "python",
   "name": "fenicsproject"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}