SNES VI and mixed systems

[colinjcotter]

I would like to set up a mixed system with VI constraints for one variable but not the other.
Is it possible to specify that using Firedrake PETSc options?

[wence-]

You always have to pass in functions that represent the bounds in the full space, but you can put "unobtainable" bounds in the slots you don't want to constrain. See https://petsc.org/main/manualpages/SNES/SNESVISetVariableBounds/

So something like:

import numpy as np
from firedrake.datatypes import ScalarType # can't remember where this one lives
MAX_REAL = np.finfo(ScalarType).max
# recreating code in petscmath.h
BOUND_POS_INF = MAX_REAL / 4
BOUND_NEG_INF = -BOUND_POS_INF
lbound = Function(W)
lbound.sub(0).interpolate(some_known_bound)
lbound.sub(1).interpolate(BOUND_NEG_INF)
... # same for upper bound

solver = ...
solver.solve(bounds=(lbound, ubound))

[danshapero]

This is my understanding of it too. I used PETSc.INFINITY and NINFINITY instead of MAX_REAL but same idea. I have some example code here if you want to see. I'd love to know if there's a way to use a VI solver for just the part of the system that needs it and other methods for the remainder.

[wence-]

Ah, I hadn't spotted that PETSc.INFINITY and PETSc.NINFINITY were exposed

[colinjcotter]

thanks!