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Module_Thickness_Skin_Newton_Arrhenius.f90
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MODULE MODULE_THICKNESS_SKIN_NEWTON_ARRHENIUS
CONTAINS
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!!!!!! SUBROUTINE THICKNESS_NEWTON_SOLVER
SUBROUTINE THICKNESS_SKIN_NEWTON_ARRHENIUS(H,P,T,BL,Ts,Dt,Dr,M,dist,ray,el,grav,sigma,nu,delta0,&
&gam,Inter_Q,z,F_err,theta,tmps)
!*****************************************************************
!Solve for the thickness in the thickenss evolution equation using the Newton
! method
!*****************************************************************
IMPLICIT NONE
! Tableaux
DOUBLE PRECISION , DIMENSION(:,:), INTENT(INOUT) :: H,P
DOUBLE PRECISION, DIMENSIOn(:,:), INTENT(IN) :: T,BL,Ts
DOUBLE PRECISION , DIMENSION(:), INTENT(IN) :: dist,ray
!Parametre du model
DOUBLE PRECISION , INTENT(IN) :: Dt,Dr,theta
DOUBLE PRECISION, INTENT(IN) :: tmps
!Nombre sans dimensions
DOUBLE PRECISION , INTENT(IN) :: el,grav,sigma,nu,delta0,gam,Inter_Q
INTEGER, INTENT(IN) :: M, z
DOUBLE PRECISION , INTENT(INOUT) :: F_err
!Variable du sous programmes
DOUBLE PRECISION, DIMENSION(:,:), ALLOCATABLE :: Coeff
DOUBLE PRECISION, DIMENSION(:), ALLOCATABLE :: fguess,ftmps
DOUBLE PRECISION, DIMENSION(:),ALLOCATABLE :: a,b,c,d,e,f,g,k,l,S
DOUBLE PRECISION, DIMENSION(:),ALLOCATABLE :: a1,b1,c1,d1,e1,f1,g1,k1,l1
DOUBLE PRECISION, DIMENSION(:), ALLOCATABLE :: Hm,qa
DOUBLE PRECISION :: U
INTEGER :: ndyke,i,N,Size,code
INTEGER :: err1,col,algo1
LOGICAL :: cho
! Taille de la grille sur laquelle on fait l'inversion
ndyke=sigma/Dr
CHO=COUNT(H(:,1)>0.D0)<ndyke
SELECT CASE (CHO)
CASE(.TRUE.)
N = ndyke+3
CASE(.FALSE.)
N = COUNT(H(:,1)>0.d0)
END SELECT
! Caracterisation du flux
ALLOCATE(qa(1:N),stat=err1)
IF (err1>1) THEN
PRINT*, 'Erreur alloc flux';STOP
END IF
InterInjectionRate:IF (mod(tmps,Inter_Q)<Inter_Q/2D0) THEN
DO i = 1,N,1
U = 2.d0/(sigma)**4.
Flux:IF (i<ndyke+1) THEN
qa(i) = U*(1-gam*H(i,2))*(sigma**2.-dist(i)**2.)
ELSE
qa(i) = 0.d0
END IF Flux
END DO
ELSE
qa(:)=0D0
ENDIF InterInjectionRate
! Calcule coefficient pression elastique
ALLOCATE(Coeff(1:N,7),stat=err1)
IF (err1>1) THEN
PRINT*, 'Erreur alloc dans coeff du systeme'; STOP
END IF
algo1=1;col=1
CALL PRESSURE_ORDER_4(M,N,Dr,P,H,dist,Coeff,algo1,col,el,delta0)
! Calcule de f tmps n et n+1
ALLOCATE(ftmps(1:N),fguess(1:N),stat=err1)
IF (err1>1) THEN
PRINT*, 'Erreur de f';STOP
END IF
col=1
CALL THICKNESS(ftmps,col,N,M,H,P,T,BL,Ts,Coeff,Dt,Dr,dist,ray,qa,el,grav,nu,delta0)
col=2
CALL THICKNESS(fguess,col,N,M,H,P,T,BL,Ts,Coeff,Dt,Dr,dist,ray,qa,el,grav,nu,delta0)
! Jacbienne
ALLOCATE(a1(1:N),b1(1:N),c1(1:N),d1(1:N),e1(1:N), stat = err1)
ALLOCATE(f1(1:N),g1(1:N),k1(1:N),l1(1:N), stat = err1)
IF (err1>1) THEN
PRINT*, 'Erreur d''allocation dans coeff du systeme'; STOP
END IF
CALL JACOBI_THICKNESS(a1,b1,c1,d1,e1,f1,g1,k1,l1,N,M,H,P,T,BL,Ts,Coeff,Dt,Dr,dist,ray,el,grav,nu,delta0)
!Systeme a inverser
ALLOCATE(a(1:N),b(1:N),c(1:N),d(1:N),e(1:N),stat = err1)
ALLOCATE(f(1:N),g(1:N),k(1:N),l(1:N),S(1:N),stat = err1)
IF (err1>1) THEN
PRINT*, 'Erreur d''allocation dans coeff du systeme'; STOP
END IF
DO i=1,N,1
a(i)=-theta*Dt*a1(i)
b(i)=-theta*Dt*b1(i)
c(i)=-theta*Dt*c1(i)
d(i)=-theta*Dt*d1(i)
e(i)=1.d0-theta*Dt*e1(i)
f(i)=-theta*Dt*f1(i)
g(i)=-theta*Dt*g1(i)
k(i)=-theta*Dt*k1(i)
l(i)=-theta*Dt*l1(i)
S(i)=H(i,1)-H(i,2)+theta*Dt*fguess(i)+(1-theta)*Dt*ftmps(i)
END DO
a(1)=0.d0;a(2)=0.d0;a(3)=0.d0;a(4)=0.d0
b(1)=0.d0;b(2)=0.d0;b(3)=0.d0
c(1)=0.d0;c(2)=0.d0
d(1)=0.d0
l(N-3)=0.d0;l(N-2)=0.d0;l(N-1)=0.d0;l(N)=0.d0
k(N-2)=0.d0;k(N-1)=0.d0;k(N)=0.d0
g(N-1)=0.d0;g(N)=0.d0
f(N)=0.d0
!Inversion de la matrice
ALLOCATE(Hm(1:N),stat=err1)
IF (err1>1) THEN
PRINT*, 'Erreur d''allocation dans vecteur Hm'; STOP
END IF
CALL NONA_DIAGO(N,Hm,a,b,c,d,e,f,g,k,l,S)
DO i=1,N,1
H(i,3)=Hm(i)+H(i,2)
END DO
H(N+1:M,3) = delta0
! Calcul de la pression
algo1=2;col=3
CALL PRESSURE_ORDER_4(M,N,Dr,P,H,dist,Coeff,algo1,col,el,delta0)
! Calcul du soeuil F_err
IF (DOT_PRODUCT(H(:,2),H(:,2)) == 0D0) THEN
F_err = ABS(MAXVAL((Hm(:))))
ELSE
Size = COUNT(H(:,2)>1D-6)
F_err = ABS(MAXVAL((H(:Size,3)-H(:Size,2))/H(:Size,2)))
ENDIF
DEALLOCATE(Hm,a,b,c,d,e,f,g,k,l,S,Coeff,qa)
DEALLOCATE(fguess,ftmps,a1,b1,c1,d1,e1,f1,g1,k1,l1)
END SUBROUTINE THICKNESS_SKIN_NEWTON_ARRHENIUS
!-------------------------------------------------------------------------------------
!-------------------------------------------------------------------------------------
! SUBROUTINE PRESSURE
!-------------------------------------------------------------------------------------
!-------------------------------------------------------------------------------------
SUBROUTINE PRESSURE_ORDER_4(M,N,Dr,P,H,dist,Coeff,algo1,col,el,delta0)
!*****************************************************************
! Calcul the coefficient of a 7 stencil elastic
!*****************************************************************
!-------------------------------------------------------------------------------------
! Variables
IMPLICIT NONE
! Tableaux
DOUBLE PRECISION, DIMENSION(:,:), INTENT(IN) :: H
DOUBLE PRECISION, DIMENSION(:,:), INTENT(INOUT) :: Coeff,P
DOUBLE PRECISION, DIMENSION(:), INTENT(IN) :: dist
! Parametres model
INTEGER , INTENT(IN) :: M,N,col,algo1
DOUBLE PRECISION, INTENT(IN) :: Dr,el,delta0
! Variables subroutines
INTEGER :: i,err1
DOUBLE PRECISION :: p1,p2,p3,p4
!-------------------------------------------------------------------------------------
! Contains
SELECT CASE(algo1)
CASE(1)
DO i=1,N,1
p1=1.d0/dist(i)**3
p2=-1.d0/(dist(i)**2)
p3=2.d0/dist(i)
p4=1.d0
Coeff(i,1)=(1.d0/(24.d0*Dr**4))*(-4.d0*p4+3.d0*p3*Dr)
Coeff(i,2)=(1.d0/(24.d0*Dr**4))*(48.d0*p4-24.d0*p3*Dr-2.d0*p2*Dr**2+2.d0*p1*Dr**3)
Coeff(i,3)=(1.d0/(24.d0*Dr**4))*(-156.d0*p4+39.d0*p3*Dr+32.d0*p2*Dr**2-16.d0*p1*Dr**3)
Coeff(i,4)=(1.d0/(24.d0*Dr**4))*(224.d0*p4-60.d0*p2*Dr**2)
Coeff(i,5)=(1.d0/(24.d0*Dr**4))*(-156.d0*p4-39*p3*Dr+32.d0*p2*Dr**2+16.d0*p1*Dr**3)
Coeff(i,6)=(1.d0/(24.d0*Dr**4))*(48.d0*p4+24.d0*p3*Dr-2.d0*p2*Dr**2-2.d0*p1*Dr**3)
Coeff(i,7)=(1.d0/(24.d0*Dr**4))*(-4.d0*p4-3.d0*p3*Dr)
END DO
CASE(2)
DO i=1,M,1
IF (i==1) THEN
P(i,col)=el*(Coeff(i,1)*H(3,col)+Coeff(i,2)*H(2,col)+Coeff(i,3)*H(1,col)+Coeff(i,4)*H(1,col)+Coeff(i,5)*H(i+1,col)&
&+Coeff(i,6)*H(i+2,col)+Coeff(i,7)*H(i+3,col))
ELSEIF (i==2) THEN
P(i,col)=el*(Coeff(i,1)*H(2,col)+Coeff(i,2)*H(1,col)+Coeff(i,3)*H(1,col)+Coeff(i,4)*H(2,col)+Coeff(i,5)*H(i+1,col)&
&+Coeff(i,6)*H(i+2,col)+Coeff(i,7)*H(i+3,col))
ELSEIF (i==3) THEN
P(i,col)=el*(Coeff(i,1)*H(1,col)+Coeff(i,2)*H(1,col)+Coeff(i,3)*H(2,col)+Coeff(i,4)*H(3,col)+Coeff(i,5)*H(i+1,col)&
&+Coeff(i,6)*H(i+2,col)+Coeff(i,7)*H(i+3,col))
ELSEIF (i==N-2) THEN
P(i,col)=Coeff(i,1)*H(i-3,col)+Coeff(i,2)*H(i-2,col)+Coeff(i,3)*H(i-1,col)+Coeff(i,4)*H(i,col)+Coeff(i,5)*H(i+1,col)&
&+Coeff(i,6)*H(i+2,col)+Coeff(i,7)*delta0
ELSEIF (i==N-1) THEN
P(i,col)=Coeff(i,1)*H(i-3,col)+Coeff(i,2)*H(i-2,col)+Coeff(i,3)*H(i-1,col)+Coeff(i,4)*H(i,col)+Coeff(i,5)*H(i+1,col)&
&+Coeff(i,6)*delta0+Coeff(i,7)*delta0
ELSEIF (i==N) THEN
P(i,col)=Coeff(i,1)*H(i-3,col)+Coeff(i,2)*H(i-2,col)+Coeff(i,3)*H(i-1,col)+Coeff(i,4)*H(i,col)+Coeff(i,5)*delta0&
&+Coeff(i,6)*delta0+Coeff(i,7)*delta0
ELSE
P(i,col)=Coeff(i,1)*H(i-3,col)+Coeff(i,2)*H(i-2,col)+Coeff(i,3)*H(i-1,col)+Coeff(i,4)*H(i,col)+Coeff(i,5)*H(i+1,col)&
&+Coeff(i,6)*H(i+2,col)+Coeff(i,7)*H(i+3,col)
END IF
IF (el==0) THEN
P(i,col)=0
END IF
END DO
END SELECT
END SUBROUTINE PRESSURE_ORDER_4
!-------------------------------------------------------------------------------------
!-------------------------------------------------------------------------------------
! SUBROUTINE THICKNESS
!-------------------------------------------------------------------------------------
!-------------------------------------------------------------------------------------
SUBROUTINE THICKNESS(f,col,N,M,H,P,T,BL,Ts,Coeff,Dt,Dr,dist,ray,qa,el,grav,nu,delta0)
!*****************************************************************
! Give the vector f
!*****************************************************************
IMPLICIT NONE
! Tableaux
DOUBLE PRECISION ,DIMENSION(:) , INTENT(INOUT) :: f
DOUBLE PRECISION ,DIMENSION(:,:), INTENT(IN) :: H,T,BL,Ts
DOUBLE PRECISION ,DIMENSION(:,:), INTENT(INOUT) :: P,Coeff
DOUBLE PRECISION ,DIMENSION(:), INTENT(IN) :: qa
DOUBLE PRECISION ,DIMENSION(:), INTENT(IN) :: dist,ray
! Prametre du model
DOUBLE PRECISION ,INTENT(IN) :: Dt,Dr
INTEGER ,INTENT(IN) :: col,N,M
DOUBLE PRECISION, PARAMETER :: pi=3.14159265358979d0
! Nombre sans dimension
DOUBLE PRECISION ,INTENT(IN) :: el,grav,nu,delta0
! Parametre pour le sous programme
DOUBLE PRECISION :: h_a,h_b,h_a2,h_b2,h_a3,h_b3,T_a,T_b
DOUBLE PRECISION :: delta_a,delta_b,delta_a2,delta_b2,delta_a3,delta_b3
DOUBLE PRECISION :: Ael,Bel,Agrav,Bgrav,phi_a,phi_b
DOUBLE PRECISION :: Ts_a,Ts_b,Ds_b,Ds_a
INTEGER :: i,err1,algo1
! Remplissage de f
algo1=2
CALL PRESSURE_ORDER_4(M,N,Dr,P,H,dist,Coeff,algo1,col,el,delta0)
!### REMPLISSAGE DE f ###!
DO i=1,N,1
IF (i .NE. N) THEN
Ael=el*(ray(i)/(dist(i)*Dr**2))
Agrav=grav*(ray(i)/(dist(i)*Dr**2))
h_a=0.5d0*(H(i+1,col)+H(i,col))
h_a2=0.5d0*(H(i+1,col)**2+H(i,col)**2)
h_a3=0.5d0*(H(i+1,col)**3+H(i,col)**3)
delta_a=0.5d0*(BL(i+1,3)+BL(i,3))
delta_a2=0.5d0*(BL(i+1,3)**2+BL(i,3)**2)
delta_a3=0.5d0*(BL(i+1,3)**3+BL(i,3)**3)
T_a=0.5d0*(T(i,3)+T(i+1,3))
Ts_a = 0.5d0*(Ts(i,3)+Ts(i+1,3))
Ds_a = T_a -Ts_a
IF (nu <1D0) THEN
phi_a = 6*sqrt(pi)*Ds_a**(-1.5d0)*delta_a3*nu*nu**(-T_a)*(-log(&
& nu))**(-1.5d0)*erf(sqrt(Ds_a)*sqrt(-log(nu))) + 12*1.0/Ds_a*&
& delta_a3*nu*nu**Ds_a*nu**(-T_a)*1.0/(-log(nu)) - 24*1.0/Ds_a*&
& delta_a3*nu*nu**(-T_a)*1.0/(-log(nu)) - 12*1.0/Ds_a*delta_a2*&
& h_a*nu*nu**Ds_a*nu**(-T_a)*1.0/(-log(nu)) + 12*1.0/Ds_a*delta_a2&
& *h_a*nu*nu**(-T_a)*1.0/(-log(nu)) - 12*sqrt(pi)*Ds_a**(-0.5d0)*&
& delta_a3*nu*nu**(-T_a)*(-log(nu))**(-1.5d0)*log(nu)*erf(sqrt(&
& Ds_a)*sqrt(-log(nu))) + 12*sqrt(pi)*Ds_a**(-0.5d0)*delta_a2*h_a&
& *nu*nu**(-T_a)*(-log(nu))**(-1.5d0)*log(nu)*erf(sqrt(Ds_a)*sqrt(&
& -log(nu))) - 3*sqrt(pi)*Ds_a**(-0.5d0)*delta_a*h_a**2*nu*nu**(&
& -T_a)*(-log(nu))**(-1.5d0)*log(nu)*erf(sqrt(Ds_a)*sqrt(-log(nu&
& ))) + 8*delta_a3*nu*nu**(-T_a)*1.0/(-log(nu))*log(nu) - 12*&
& delta_a2*h_a*nu*nu**(-T_a)*1.0/(-log(nu))*log(nu) + 6*delta_a*&
& h_a**2*nu*nu**(-T_a)*1.0/(-log(nu))*log(nu) - h_a**3*nu*nu**(-T_a&
& )*1.0/(-log(nu))*log(nu)
phi_a = -12.0d0*sqrt(pi)*T_a*delta_a**3*nu*nu**(-T_a)*(-log(nu))**&
& (-1.5d0)*(T_a - Ts_a)**(-1.5d0)*log(nu)*erf(sqrt(-log(nu))*sqrt(&
& T_a - Ts_a)) + 8.0d0*T_a*delta_a**3*nu*nu**(-T_a)*1.0/(-log(nu))*&
& 1.0/(T_a - Ts_a)*log(nu) + 12.0d0*sqrt(pi)*T_a*delta_a**2*h_a*nu*&
& nu**(-T_a)*(-log(nu))**(-1.5d0)*(T_a - Ts_a)**(-1.5d0)*log(nu)*&
& erf(sqrt(-log(nu))*sqrt(T_a - Ts_a)) - 12.0d0*T_a*delta_a**2*h_a*&
& nu*nu**(-T_a)*1.0/(-log(nu))*1.0/(T_a - Ts_a)*log(nu) - 3.0d0*&
& sqrt(pi)*T_a*delta_a*h_a**2*nu*nu**(-T_a)*(-log(nu))**(-1.5d0)*(&
& T_a - Ts_a)**(-1.5d0)*log(nu)*erf(sqrt(-log(nu))*sqrt(T_a - Ts_a&
& )) + 6.0d0*T_a*delta_a*h_a**2*nu*nu**(-T_a)*1.0/(-log(nu))*1.0/(&
& T_a - Ts_a)*log(nu) - 1.0d0*T_a*h_a**3*nu*nu**(-T_a)*1.0/(-log(nu&
& ))*1.0/(T_a - Ts_a)*log(nu) + 12.0d0*sqrt(pi)*Ts_a*delta_a**3*nu*&
& nu**(-T_a)*(-log(nu))**(-1.5d0)*(T_a - Ts_a)**(-1.5d0)*log(nu)*&
& erf(sqrt(-log(nu))*sqrt(T_a - Ts_a)) - 8.0d0*Ts_a*delta_a**3*nu*&
& nu**(-T_a)*1.0/(-log(nu))*1.0/(T_a - Ts_a)*log(nu) - 12.0d0*sqrt(&
& pi)*Ts_a*delta_a**2*h_a*nu*nu**(-T_a)*(-log(nu))**(-1.5d0)*(T_a -&
& Ts_a)**(-1.5d0)*log(nu)*erf(sqrt(-log(nu))*sqrt(T_a - Ts_a)) +&
& 12.0d0*Ts_a*delta_a**2*h_a*nu*nu**(-T_a)*1.0/(-log(nu))*1.0/(T_a&
& - Ts_a)*log(nu) + 3.0d0*sqrt(pi)*Ts_a*delta_a*h_a**2*nu*nu**(-T_a&
& )*(-log(nu))**(-1.5d0)*(T_a - Ts_a)**(-1.5d0)*log(nu)*erf(sqrt(&
& -log(nu))*sqrt(T_a - Ts_a)) - 6.0d0*Ts_a*delta_a*h_a**2*nu*nu**(&
& -T_a)*1.0/(-log(nu))*1.0/(T_a - Ts_a)*log(nu) + 1.0d0*Ts_a*h_a**3&
& *nu*nu**(-T_a)*1.0/(-log(nu))*1.0/(T_a - Ts_a)*log(nu) + 12.0d0*&
& delta_a**3*nu*nu**(-Ts_a)*1.0/(-log(nu))*1.0/(T_a - Ts_a) + 6.0d0&
& *sqrt(pi)*delta_a**3*nu*nu**(-T_a)*(-log(nu))**(-1.5d0)*(T_a -&
& Ts_a)**(-1.5d0)*erf(sqrt(-log(nu))*sqrt(T_a - Ts_a)) - 24.0d0*&
& delta_a**3*nu*nu**(-T_a)*1.0/(-log(nu))*1.0/(T_a - Ts_a) - 12.0d0&
& *delta_a**2*h_a*nu*nu**(-Ts_a)*1.0/(-log(nu))*1.0/(T_a - Ts_a) +&
& 12.0d0*delta_a**2*h_a*nu*nu**(-T_a)*1.0/(-log(nu))*1.0/(T_a -&
& Ts_a)
ELSEIF (nu .EQ. 1D0) THEN
phi_a = h_a**3
ENDIF
ENDIF
IF (i .NE. 1) THEN
Bel=el*(ray(i-1)/(dist(i)*Dr**2))
Bgrav=grav*(ray(i-1)/(dist(i)*Dr**2))
h_b=0.5d0*(H(i,col)+H(i-1,col))
h_b2=0.5d0*(H(i,col)**2+H(i-1,col)**2)
h_b3=0.5d0*(H(i,col)**3+H(i-1,col)**3)
delta_b=0.5d0*(BL(i,3)+BL(i-1,3))
delta_b2=0.5d0*(BL(i,3)**2+BL(i-1,3)**2)
delta_b3=0.5d0*(BL(i,3)**3+BL(i-1,3)**3)
T_b=0.5d0*(T(i,3)+T(i-1,3))
Ts_b = 0.5d0*(Ts(i,3)+Ts(i-1,3))
Ds_b = T_b - Ts_b
IF (nu <1D0) THEN
phi_b = 6*sqrt(pi)*Ds_b**(-1.5d0)*delta_b3*nu*nu**(-T_b)*(-log(&
& nu))**(-1.5d0)*erf(sqrt(Ds_b)*sqrt(-log(nu))) + 12*1.0/Ds_b*&
& delta_b3*nu*nu**Ds_b*nu**(-T_b)*1.0/(-log(nu)) - 24*1.0/Ds_b*&
& delta_b3*nu*nu**(-T_b)*1.0/(-log(nu)) - 12*1.0/Ds_b*delta_b2*&
& h_b*nu*nu**Ds_b*nu**(-T_b)*1.0/(-log(nu)) + 12*1.0/Ds_b*delta_b2&
& *h_b*nu*nu**(-T_b)*1.0/(-log(nu)) - 12*sqrt(pi)*Ds_b**(-0.5d0)*&
& delta_b3*nu*nu**(-T_b)*(-log(nu))**(-1.5d0)*log(nu)*erf(sqrt(&
& Ds_b)*sqrt(-log(nu))) + 12*sqrt(pi)*Ds_b**(-0.5d0)*delta_b2*h_b&
& *nu*nu**(-T_b)*(-log(nu))**(-1.5d0)*log(nu)*erf(sqrt(Ds_b)*sqrt(&
& -log(nu))) - 3*sqrt(pi)*Ds_b**(-0.5d0)*delta_b*h_b**2*nu*nu**(&
& -T_b)*(-log(nu))**(-1.5d0)*log(nu)*erf(sqrt(Ds_b)*sqrt(-log(nu&
& ))) + 8*delta_b3*nu*nu**(-T_b)*1.0/(-log(nu))*log(nu) - 12*&
& delta_b2*h_b*nu*nu**(-T_b)*1.0/(-log(nu))*log(nu) + 6*delta_b*&
& h_b**2*nu*nu**(-T_b)*1.0/(-log(nu))*log(nu) - h_b**3*nu*nu**(-T_b&
& )*1.0/(-log(nu))*log(nu)
phi_b = -12.0d0*sqrt(pi)*T_b*delta_b**3*nu*nu**(-T_b)*(-log(nu))**&
& (-1.5d0)*(T_b - Ts_b)**(-1.5d0)*log(nu)*erf(sqrt(-log(nu))*sqrt(&
& T_b - Ts_b)) + 8.0d0*T_b*delta_b**3*nu*nu**(-T_b)*1.0/(-log(nu))*&
& 1.0/(T_b - Ts_b)*log(nu) + 12.0d0*sqrt(pi)*T_b*delta_b**2*h_b*nu*&
& nu**(-T_b)*(-log(nu))**(-1.5d0)*(T_b - Ts_b)**(-1.5d0)*log(nu)*&
& erf(sqrt(-log(nu))*sqrt(T_b - Ts_b)) - 12.0d0*T_b*delta_b**2*h_b*&
& nu*nu**(-T_b)*1.0/(-log(nu))*1.0/(T_b - Ts_b)*log(nu) - 3.0d0*&
& sqrt(pi)*T_b*delta_b*h_b**2*nu*nu**(-T_b)*(-log(nu))**(-1.5d0)*(&
& T_b - Ts_b)**(-1.5d0)*log(nu)*erf(sqrt(-log(nu))*sqrt(T_b - Ts_b&
& )) + 6.0d0*T_b*delta_b*h_b**2*nu*nu**(-T_b)*1.0/(-log(nu))*1.0/(&
& T_b - Ts_b)*log(nu) - 1.0d0*T_b*h_b**3*nu*nu**(-T_b)*1.0/(-log(nu&
& ))*1.0/(T_b - Ts_b)*log(nu) + 12.0d0*sqrt(pi)*Ts_b*delta_b**3*nu*&
& nu**(-T_b)*(-log(nu))**(-1.5d0)*(T_b - Ts_b)**(-1.5d0)*log(nu)*&
& erf(sqrt(-log(nu))*sqrt(T_b - Ts_b)) - 8.0d0*Ts_b*delta_b**3*nu*&
& nu**(-T_b)*1.0/(-log(nu))*1.0/(T_b - Ts_b)*log(nu) - 12.0d0*sqrt(&
& pi)*Ts_b*delta_b**2*h_b*nu*nu**(-T_b)*(-log(nu))**(-1.5d0)*(T_b -&
& Ts_b)**(-1.5d0)*log(nu)*erf(sqrt(-log(nu))*sqrt(T_b - Ts_b)) +&
& 12.0d0*Ts_b*delta_b**2*h_b*nu*nu**(-T_b)*1.0/(-log(nu))*1.0/(T_b&
& - Ts_b)*log(nu) + 3.0d0*sqrt(pi)*Ts_b*delta_b*h_b**2*nu*nu**(-T_b&
& )*(-log(nu))**(-1.5d0)*(T_b - Ts_b)**(-1.5d0)*log(nu)*erf(sqrt(&
& -log(nu))*sqrt(T_b - Ts_b)) - 6.0d0*Ts_b*delta_b*h_b**2*nu*nu**(&
& -T_b)*1.0/(-log(nu))*1.0/(T_b - Ts_b)*log(nu) + 1.0d0*Ts_b*h_b**3&
& *nu*nu**(-T_b)*1.0/(-log(nu))*1.0/(T_b - Ts_b)*log(nu) + 12.0d0*&
& delta_b**3*nu*nu**(-Ts_b)*1.0/(-log(nu))*1.0/(T_b - Ts_b) + 6.0d0&
& *sqrt(pi)*delta_b**3*nu*nu**(-T_b)*(-log(nu))**(-1.5d0)*(T_b -&
& Ts_b)**(-1.5d0)*erf(sqrt(-log(nu))*sqrt(T_b - Ts_b)) - 24.0d0*&
& delta_b**3*nu*nu**(-T_b)*1.0/(-log(nu))*1.0/(T_b - Ts_b) - 12.0d0&
& *delta_b**2*h_b*nu*nu**(-Ts_b)*1.0/(-log(nu))*1.0/(T_b - Ts_b) +&
& 12.0d0*delta_b**2*h_b*nu*nu**(-T_b)*1.0/(-log(nu))*1.0/(T_b -&
& Ts_b)
ELSEIF (nu .EQ. 1D0) THEN
phi_b = h_b**3
ENDIF
ENDIF
IF (i==1) THEN
f(i)=Ael*phi_a*(P(2,col)-P(1,col))+Agrav*phi_a*(H(2,col)-H(1,col))&
&+qa(i)
ELSEIF (i==N) THEN
f(i)=-Bel*phi_b*(P(i,col)-P(i-1,col))-Bgrav*phi_b*(H(i,col)-H(i-1,col))&
&+qa(i)
ELSE
f(i)=Ael*phi_a*(P(i+1,col)-P(i,col))-Bel*phi_b*(P(i,col)-P(i-1,col))&
&+Agrav*phi_a*(H(i+1,col)-H(i,col))-Bgrav*phi_b*(H(i,col)-H(i-1,col))&
&+qa(i)
END IF
END DO
END SUBROUTINE THICKNESS
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!-------------------------------------------------------------------------------------
! SUBROUTINE THICKNESS
!-------------------------------------------------------------------------------------
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
SUBROUTINE JACOBI_THICKNESS(a,b,c,d,e,f,g,k,l,N,M,H,P,T,BL,Ts,Coeff,Dt,Dr,dist,ray,el,grav,nu,delta0)
!*****************************************************************
! Give the jacobian coeficient a1,b1,c1
!*****************************************************************
IMPLICIT NONE
! Tableaux
DOUBLE PRECISION ,DIMENSION(:) , INTENT(INOUT) :: a,b,c,d,e,f,g,k,l
DOUBLE PRECISION ,DIMENSION(:,:), INTENT(IN) :: H,T,BL,Ts
DOUBLE PRECISION ,DIMENSION(:,:), INTENT(INOUT) :: P,Coeff
DOUBLE PRECISION ,DIMENSION(:), INTENT(IN) :: dist,ray
! Prametre du model
DOUBLE PRECISION ,INTENT(IN) :: Dt,Dr
INTEGER ,INTENT(IN) :: N,M
! Nombre sans dimension
DOUBLE PRECISION ,INTENT(IN) :: el,grav,nu,delta0
DOUBLE PRECISION, PARAMETER :: pi=3.14159265358979d0
! Parametre pour le sous programme
DOUBLE PRECISION ,DIMENSION(:), ALLOCATABLE :: alpha,beta,gamma,lambda,kappa,delta,epsilonn
DOUBLE PRECISION ::Ael,Bel,Agrav,Bgrav,h_a,h_b,h_a2,h_b2,h_a3,h_b3,T_a,T_b
DOUBLE PRECISION ::delta_a,delta_b,delta_a2,delta_b2,delta_a3,delta_b3
DOUBLE PRECISION :: Ts_a,Ts_b,Ds_b,Ds_a
DOUBLE PRECISION :: phi_a,phi_b,dphib_dhi,dphib_dhi1,dphia_dhi,dphia_dhi1
DOUBLE PRECISION :: H1,H2,P1,P2,hi,hi2,hia,hib,hia2,hib2
INTEGER :: i,col,algo1,err1
! Allocation + remplissage pression
ALLOCATE(alpha(1:N),beta(1:N),gamma(1:N),lambda(1:N),stat=err1)
ALLOCATE(kappa(1:N),delta(1:N),epsilonn(1:N),stat=err1)
IF (err1>1) THEN !On teste si nos tableau sont bien alloués
PRINT*,"Erreur ds alloc alpha,beta.." ;STOP
END IF
algo1=2;col=2
CALL PRESSURE_ORDER_4(M,N,Dr,P,H,dist,Coeff,algo1,col,el,delta0)
alpha=Coeff(:,1)
beta=Coeff(:,2)
gamma=Coeff(:,3)
lambda=Coeff(:,4)
kappa=Coeff(:,5)
delta=Coeff(:,6)
epsilonn=Coeff(:,7)
! Remplissage de la matrice Jacobienne
DO i=1,N,1
IF1: IF (i .NE. N) THEN
Ael=el*(ray(i)/(dist(i)*Dr**2))
Agrav=grav*(ray(i)/(dist(i)*Dr**2))
h_a=0.5d0*(H(i+1,col)+H(i,col))
h_a2=0.5d0*(H(i+1,col)**2+H(i,col)**2)
h_a3=0.5d0*(H(i+1,col)**3+H(i,col)**3)
delta_a=0.5d0*(BL(i+1,3)+BL(i,3))
delta_a2=0.5d0*(BL(i+1,3)**2+BL(i,3)**2)
delta_a3=0.5d0*(BL(i+1,3)**3+BL(i,3)**3)
T_a=0.5d0*(T(i,3)+T(i+1,3))
Ts_a = 0.5d0*(Ts(i,3)+Ts(i+1,3))
Ds_a = T_a -Ts_a
hia = H(i+1,col); hia2 = H(i+1,col)**2
hi = H(i,col);hi2 = H(i,col)**2
IF (nu <1D0) THEN
phi_a = 6*sqrt(pi)*Ds_a**(-1.5d0)*delta_a3*nu*nu**(-T_a)*(-log(&
& nu))**(-1.5d0)*erf(sqrt(Ds_a)*sqrt(-log(nu))) + 12*1.0/Ds_a*&
& delta_a3*nu*nu**Ds_a*nu**(-T_a)*1.0/(-log(nu)) - 24*1.0/Ds_a*&
& delta_a3*nu*nu**(-T_a)*1.0/(-log(nu)) - 12*1.0/Ds_a*delta_a2*&
& h_a*nu*nu**Ds_a*nu**(-T_a)*1.0/(-log(nu)) + 12*1.0/Ds_a*delta_a2&
& *h_a*nu*nu**(-T_a)*1.0/(-log(nu)) - 12*sqrt(pi)*Ds_a**(-0.5d0)*&
& delta_a3*nu*nu**(-T_a)*(-log(nu))**(-1.5d0)*log(nu)*erf(sqrt(&
& Ds_a)*sqrt(-log(nu))) + 12*sqrt(pi)*Ds_a**(-0.5d0)*delta_a2*h_a&
& *nu*nu**(-T_a)*(-log(nu))**(-1.5d0)*log(nu)*erf(sqrt(Ds_a)*sqrt(&
& -log(nu))) - 3*sqrt(pi)*Ds_a**(-0.5d0)*delta_a*h_a**2*nu*nu**(&
& -T_a)*(-log(nu))**(-1.5d0)*log(nu)*erf(sqrt(Ds_a)*sqrt(-log(nu&
& ))) + 8*delta_a3*nu*nu**(-T_a)*1.0/(-log(nu))*log(nu) - 12*&
& delta_a2*h_a*nu*nu**(-T_a)*1.0/(-log(nu))*log(nu) + 6*delta_a*&
& h_a**2*nu*nu**(-T_a)*1.0/(-log(nu))*log(nu) - h_a**3*nu*nu**(-T_a&
& )*1.0/(-log(nu))*log(nu)
dphia_dhi1 = -12*1.0/Ds_a*delta_a2*nu*nu**Ds_a*nu**(-T_a)*1.0/(&
& -log(nu)) + 12*1.0/Ds_a*delta_a2*nu*nu**(-T_a)*1.0/(-log(nu)) +&
& 12*sqrt(pi)*Ds_a**(-0.5d0)*delta_a2*nu*nu**(-T_a)*(-log(nu))**(&
& -1.5d0)*log(nu)*erf(sqrt(Ds_a)*sqrt(-log(nu))) - 6*sqrt(pi)*Ds_a&
& **(-0.5d0)*delta_a*hi*nu*nu**(-T_a)*(-log(nu))**(-1.5d0)*log(nu)*&
& erf(sqrt(Ds_a)*sqrt(-log(nu))) - 6*sqrt(pi)*Ds_a**(-0.5d0)*&
& delta_a*hia*nu*nu**(-T_a)*(-log(nu))**(-1.5d0)*log(nu)*erf(sqrt(&
& Ds_a)*sqrt(-log(nu))) - 12*delta_a2*nu*nu**(-T_a)*1.0/(-log(nu&
& ))*log(nu) + 12*delta_a*hi*nu*nu**(-T_a)*1.0/(-log(nu))*log(nu) +&
& 12*delta_a*hia*nu*nu**(-T_a)*1.0/(-log(nu))*log(nu) - 3*hi**2*nu*&
& nu**(-T_a)*1.0/(-log(nu))*log(nu) - 6*hi*hia*nu*nu**(-T_a)*1.0/(&
& -log(nu))*log(nu) - 3*hia**2*nu*nu**(-T_a)*1.0/(-log(nu))*log(nu)
dphia_dhi = -12*1.0/Ds_a*delta_a2*nu*nu**Ds_a*nu**(-T_a)*1.0/(&
& -log(nu)) + 12*1.0/Ds_a*delta_a2*nu*nu**(-T_a)*1.0/(-log(nu)) +&
& 12*sqrt(pi)*Ds_a**(-0.5d0)*delta_a2*nu*nu**(-T_a)*(-log(nu))**(&
& -1.5d0)*log(nu)*erf(sqrt(Ds_a)*sqrt(-log(nu))) - 6*sqrt(pi)*Ds_a&
& **(-0.5d0)*delta_a*hi*nu*nu**(-T_a)*(-log(nu))**(-1.5d0)*log(nu)*&
& erf(sqrt(Ds_a)*sqrt(-log(nu))) - 6*sqrt(pi)*Ds_a**(-0.5d0)*&
& delta_a*hia*nu*nu**(-T_a)*(-log(nu))**(-1.5d0)*log(nu)*erf(sqrt(&
& Ds_a)*sqrt(-log(nu))) - 12*delta_a2*nu*nu**(-T_a)*1.0/(-log(nu&
& ))*log(nu) + 12*delta_a*hi*nu*nu**(-T_a)*1.0/(-log(nu))*log(nu) +&
& 12*delta_a*hia*nu*nu**(-T_a)*1.0/(-log(nu))*log(nu) - 3*hi**2*nu*&
& nu**(-T_a)*1.0/(-log(nu))*log(nu) - 6*hi*hia*nu*nu**(-T_a)*1.0/(&
& -log(nu))*log(nu) - 3*hia**2*nu*nu**(-T_a)*1.0/(-log(nu))*log(nu)
ELSEIF (nu .EQ. 1D0) THEN
phi_a = h_a**3
dphia_dhi1 = 3*hi**2 + 6*hi*hia + 3*hia**2
dphia_dhi = 3*hi**2 + 6*hi*hia + 3*hia**2
ENDIF
P1=P(i+1,2)-P(i,2); P2=P(i,2)-P(i-1,2)
H1=H(i+1,2)-H(i,2); H2=H(i,2)-H(i-1,2)
ENDIF IF1
IF2: IF (i .NE. 1) THEN
Bel=el*(ray(i-1)/(dist(i)*Dr**2))
Bgrav=grav*(ray(i-1)/(dist(i)*Dr**2))
h_b=0.5d0*(H(i,col)+H(i-1,col))
h_b2=0.5d0*(H(i,col)**2+H(i-1,col)**2)
h_b3=0.5d0*(H(i,col)**3+H(i-1,col)**3)
delta_b=0.5d0*(BL(i,3)+BL(i-1,3))
delta_b2=0.5d0*(BL(i,3)**2+BL(i-1,3)**2)
delta_b3=0.5d0*(BL(i,3)**3+BL(i-1,3)**3)
T_b=0.5d0*(T(i,3)+T(i-1,3))
Ts_b = 0.5d0*(Ts(i,3)+Ts(i-1,3))
Ds_b = T_b - Ts_b
hib = H(i-1,col); hib2 = H(i-1,col)**2
hi = H(i,col);hi2 = H(i,col)**2
IF (nu <1D0) THEN
phi_b = 6*sqrt(pi)*Ds_b**(-1.5d0)*delta_b3*nu*nu**(-T_b)*(-log(&
& nu))**(-1.5d0)*erf(sqrt(Ds_b)*sqrt(-log(nu))) + 12*1.0/Ds_b*&
& delta_b3*nu*nu**Ds_b*nu**(-T_b)*1.0/(-log(nu)) - 24*1.0/Ds_b*&
& delta_b3*nu*nu**(-T_b)*1.0/(-log(nu)) - 12*1.0/Ds_b*delta_b2*&
& h_b*nu*nu**Ds_b*nu**(-T_b)*1.0/(-log(nu)) + 12*1.0/Ds_b*delta_b2&
& *h_b*nu*nu**(-T_b)*1.0/(-log(nu)) - 12*sqrt(pi)*Ds_b**(-0.5d0)*&
& delta_b3*nu*nu**(-T_b)*(-log(nu))**(-1.5d0)*log(nu)*erf(sqrt(&
& Ds_b)*sqrt(-log(nu))) + 12*sqrt(pi)*Ds_b**(-0.5d0)*delta_b2*h_b&
& *nu*nu**(-T_b)*(-log(nu))**(-1.5d0)*log(nu)*erf(sqrt(Ds_b)*sqrt(&
& -log(nu))) - 3*sqrt(pi)*Ds_b**(-0.5d0)*delta_b*h_b**2*nu*nu**(&
& -T_b)*(-log(nu))**(-1.5d0)*log(nu)*erf(sqrt(Ds_b)*sqrt(-log(nu&
& ))) + 8*delta_b3*nu*nu**(-T_b)*1.0/(-log(nu))*log(nu) - 12*&
& delta_b2*h_b*nu*nu**(-T_b)*1.0/(-log(nu))*log(nu) + 6*delta_b*&
& h_b**2*nu*nu**(-T_b)*1.0/(-log(nu))*log(nu) - h_b**3*nu*nu**(-T_b&
& )*1.0/(-log(nu))*log(nu)
dphib_dhi = -12*1.0/Ds_b*delta_b2*nu*nu**Ds_b*nu**(-T_b)*1.0/(&
& -log(nu)) + 12*1.0/Ds_b*delta_b2*nu*nu**(-T_b)*1.0/(-log(nu)) +&
& 12*sqrt(pi)*Ds_b**(-0.5d0)*delta_b2*nu*nu**(-T_b)*(-log(nu))**(&
& -1.5d0)*log(nu)*erf(sqrt(Ds_b)*sqrt(-log(nu))) - 6*sqrt(pi)*Ds_b&
& **(-0.5d0)*delta_b*hi*nu*nu**(-T_b)*(-log(nu))**(-1.5d0)*log(nu)*&
& erf(sqrt(Ds_b)*sqrt(-log(nu))) - 6*sqrt(pi)*Ds_b**(-0.5d0)*&
& delta_b*hib*nu*nu**(-T_b)*(-log(nu))**(-1.5d0)*log(nu)*erf(sqrt(&
& Ds_b)*sqrt(-log(nu))) - 12*delta_b2*nu*nu**(-T_b)*1.0/(-log(nu&
& ))*log(nu) + 12*delta_b*hi*nu*nu**(-T_b)*1.0/(-log(nu))*log(nu) +&
& 12*delta_b*hib*nu*nu**(-T_b)*1.0/(-log(nu))*log(nu) - 3*hi**2*nu*&
& nu**(-T_b)*1.0/(-log(nu))*log(nu) - 6*hi*hib*nu*nu**(-T_b)*1.0/(&
& -log(nu))*log(nu) - 3*hib**2*nu*nu**(-T_b)*1.0/(-log(nu))*log(nu)
dphib_dhi1 = -12*1.0/Ds_b*delta_b2*nu*nu**Ds_b*nu**(-T_b)*1.0/(&
& -log(nu)) + 12*1.0/Ds_b*delta_b2*nu*nu**(-T_b)*1.0/(-log(nu)) +&
& 12*sqrt(pi)*Ds_b**(-0.5d0)*delta_b2*nu*nu**(-T_b)*(-log(nu))**(&
& -1.5d0)*log(nu)*erf(sqrt(Ds_b)*sqrt(-log(nu))) - 6*sqrt(pi)*Ds_b&
& **(-0.5d0)*delta_b*hi*nu*nu**(-T_b)*(-log(nu))**(-1.5d0)*log(nu)*&
& erf(sqrt(Ds_b)*sqrt(-log(nu))) - 6*sqrt(pi)*Ds_b**(-0.5d0)*&
& delta_b*hib*nu*nu**(-T_b)*(-log(nu))**(-1.5d0)*log(nu)*erf(sqrt(&
& Ds_b)*sqrt(-log(nu))) - 12*delta_b2*nu*nu**(-T_b)*1.0/(-log(nu&
& ))*log(nu) + 12*delta_b*hi*nu*nu**(-T_b)*1.0/(-log(nu))*log(nu) +&
& 12*delta_b*hib*nu*nu**(-T_b)*1.0/(-log(nu))*log(nu) - 3*hi**2*nu*&
& nu**(-T_b)*1.0/(-log(nu))*log(nu) - 6*hi*hib*nu*nu**(-T_b)*1.0/(&
& -log(nu))*log(nu) - 3*hib**2*nu*nu**(-T_b)*1.0/(-log(nu))*log(nu)
ELSEIF (nu .EQ. 1D0) THEN
phi_b = h_b**3
dphib_dhi1 = 3*hi**2 + 6*hi*hib + 3*hib**2
dphib_dhi = 3*hi**2 + 6*hi*hib + 3*hib**2
ENDIF
P2=P(i,2)-P(i-1,2)
H2=H(i,2)-H(i-1,2)
ENDIF IF2
IF3: IF (i==1) THEN
a(i)=0;b(i)=0;c(i)=0;d(i)=0
e(i)=Ael*dphia_dhi*P1+Ael*phi_a*((gamma(i+1)+beta(i+1))-(lambda(i)+gamma(i)))&
&+Agrav*(dphia_dhi*H1-phi_a)
f(i)=Ael*dphia_dhi1*P1+Ael*phi_a*((lambda(i+1)+alpha(i+1))-(kappa(i)+beta(i)))&
&+Agrav*(dphia_dhi1*H1+phi_a)
g(i)=Ael*phi_a*(kappa(i+1)-(delta(i)+alpha(i)))
k(i)=Ael*phi_a*(delta(i+1)-epsilonn(i))
l(i)=Ael*phi_a*epsilonn(i+1)
ELSEIF (i==2) THEN
a(i)=0;b(i)=0;c(i)=0
d(i)=-Bel*dphib_dhi1*P2+Ael*phi_a*((beta(i+1)+alpha(i+1))-(gamma(i)+beta(i)))&
&-Bel*phi_b*((gamma(i)+beta(i))-(lambda(i-1)+gamma(i-1)))&
&+Bgrav*(-dphib_dhi1*H2+phi_b)
e(i)=Ael*dphia_dhi*P1-Bel*dphib_dhi*P2+Ael*phi_a*(gamma(i+1)-(lambda(i)+alpha(i)))&
&-Bel*phi_b*((lambda(i)+alpha(i))-(kappa(i-1)+beta(i-1)))&
&+Agrav*(dphia_dhi*H1-phi_a)-Bgrav*(dphib_dhi*H2+phi_b)
f(i)=Ael*dphia_dhi1*P1+Ael*phi_a*(lambda(i+1)-kappa(i))&
&-Bel*phi_b*(kappa(i)-(delta(i-1)+alpha(i-1)))&
&+Agrav*(dphia_dhi1*H1+phi_a)
g(i)=Ael*phi_a*(kappa(i+1)-delta(i))-Bel*phi_b*(delta(i)-epsilonn(i-1))
k(i)=Ael*phi_a*(delta(i+1)-epsilonn(i))-Bel*phi_b*epsilonn(i)
l(i)=Ael*phi_a*epsilonn(i+1)
ELSEIF (i==3) THEN
a(i)=0;b(i)=0
c(i)=Ael*phi_a*(alpha(i+1)-(beta(i)+alpha(i)))-Bel*phi_b*((beta(i)+alpha(i))-(gamma(i-1)+beta(i-1)))
d(i)=-Bel*dphib_dhi1*P2+Ael*phi_a*(beta(i+1)-gamma(i))-Bel*phi_b*(gamma(i)-(lambda(i-1)+alpha(i-1)))&
&+Bgrav*(-dphib_dhi1*H2+phi_b)
e(i)=Ael*dphia_dhi*P1-Bel*dphib_dhi*P2+Ael*phi_a*(gamma(i+1)-lambda(i))-Bel*phi_b*(lambda(i)-kappa(i-1))&
&+Agrav*(dphia_dhi*H1-phi_a)-Bgrav*(dphib_dhi*H2+phi_b)
f(i)=Ael*dphia_dhi1*P1+Ael*phi_a*(lambda(i+1)-kappa(i))-Bel*phi_b*(kappa(i)-delta(i-1))&
&+Agrav*(dphia_dhi1*H1+phi_a)
g(i)=Ael*phi_a*(kappa(i+1)-delta(i))-Bel*phi_b*(delta(i)-epsilonn(i-1))
k(i)=Ael*phi_a*(delta(i+1)-epsilonn(i))-Bel*phi_b*epsilonn(i)
l(i)=Ael*phi_a*epsilonn(i+1)
ELSEIF (i==4) THEN
a(i)=0
b(i)=-Ael*phi_a*alpha(i)-Bel*phi_b*(alpha(i)-(beta(i-1)+alpha(i-1)))
c(i)=Ael*phi_a*(alpha(i+1)-beta(i))-Bel*phi_b*(beta(i)-gamma(i-1))
d(i)=-Bel*dphib_dhi1*P2+Ael*phi_a*(beta(i+1)-gamma(i))-Bel*phi_b*(gamma(i)-lambda(i-1))&
&+Bgrav*(-dphib_dhi1*H2+phi_b)
e(i)=Ael*dphia_dhi*P1-Bel*dphib_dhi*P2+Ael*phi_a*(gamma(i+1)-lambda(i))-Bel*phi_b*(lambda(i)-kappa(i-1))&
&+Agrav*(dphia_dhi*H1-phi_a)-Bgrav*(dphib_dhi*H2+phi_b)
f(i)=Ael*dphia_dhi1*P1+Ael*phi_a*(lambda(i+1)-kappa(i))-Bel*phi_b*(kappa(i)-delta(i-1))&
&+Agrav*(dphia_dhi1*H1+phi_a)
g(i)=Ael*phi_a*(kappa(i+1)-delta(i))-Bel*phi_b*(delta(i)-epsilonn(i-1))
k(i)=Ael*phi_a*(delta(i+1)-epsilonn(i))-Bel*phi_b*epsilonn(i)
l(i)=Ael*phi_a*epsilonn(i+1)
ELSEIF (i==N-3) THEN
a(i)=Bel*phi_b*alpha(i-1)
b(i)=-Ael*phi_a*alpha(i)-Bel*phi_b*(alpha(i)-beta(i-1))
c(i)=Ael*phi_a*(alpha(i+1)-beta(i))-Bel*phi_b*(beta(i)-gamma(i-1))
d(i)=-Bel*dphib_dhi1*P2+Ael*phi_a*(beta(i+1)-gamma(i))-Bel*phi_b*(gamma(i)-lambda(i-1))&
&+Bgrav*(-dphib_dhi1*H2+phi_b)
e(i)=Ael*dphia_dhi*P1-Bel*dphib_dhi*P2+Ael*phi_a*(gamma(i+1)-lambda(i))-Bel*phi_b*(lambda(i)-kappa(i-1))&
&+Agrav*(dphia_dhi*H1-phi_a)-Bgrav*(dphib_dhi*H2+phi_b)
f(i)=Ael*dphia_dhi1*P1+Ael*phi_a*(lambda(i+1)-kappa(i))-Bel*phi_b*(kappa(i)-delta(i-1))&
&+Agrav*(dphia_dhi1*H1+phi_a)
g(i)=Ael*phi_a*(kappa(i+1)-delta(i))-Bel*phi_b*(delta(i)-epsilonn(i-1))
k(i)=Ael*phi_a*(delta(i+1)-epsilonn(i))-Bel*phi_b*epsilonn(i)
l(i)=0
ELSEIF (i==N-2) THEN
a(i)=Bel*phi_b*alpha(i-1)
b(i)=-Ael*phi_a*alpha(i)-Bel*phi_b*(alpha(i)-beta(i-1))
c(i)=Ael*phi_a*(alpha(i+1)-beta(i))-Bel*phi_b*(beta(i)-gamma(i-1))
d(i)=-Bel*dphib_dhi1*P2+Ael*phi_a*(beta(i+1)-gamma(i))-Bel*phi_b*(gamma(i)-lambda(i-1))&
&+Bgrav*(-dphib_dhi1*H2+phi_b)
e(i)=Ael*dphia_dhi*P1-Bel*dphib_dhi*P2+Ael*phi_a*(gamma(i+1)-lambda(i))-Bel*phi_b*(lambda(i)-kappa(i-1))&
&+Agrav*(dphia_dhi*H1-phi_a)-Bgrav*(dphib_dhi*H2+phi_b)
f(i)=Ael*dphia_dhi1*P1+Ael*phi_a*(lambda(i+1)-kappa(i))-Bel*phi_b*(kappa(i)-delta(i-1))&
&+Agrav*(dphia_dhi1*H1+phi_a)
g(i)=Ael*phi_a*(kappa(i+1)-delta(i))-Bel*phi_b*(delta(i)-epsilonn(i-1))
k(i)=0;l(i)=0
ELSEIF (i==N-1) THEN
a(i)=Bel*phi_b*alpha(i-1)
b(i)=-Ael*phi_a*alpha(i)-Bel*phi_b*(alpha(i)-beta(i-1))
c(i)=Ael*phi_a*(alpha(i+1)-beta(i))-Bel*phi_b*(beta(i)-gamma(i-1))
d(i)=-Bel*dphib_dhi1*P2+Ael*phi_a*(beta(i+1)-gamma(i))-Bel*phi_b*(gamma(i)-lambda(i-1))&
&+Bgrav*(-dphib_dhi1*H2+phi_b)
e(i)=Ael*dphia_dhi*P1-Bel*dphib_dhi*P2+Ael*phi_a*(gamma(i+1)-lambda(i))-Bel*phi_b*(lambda(i)-kappa(i-1))&
&+Agrav*(dphia_dhi*H1-phi_a)-Bgrav*(dphib_dhi*H2+phi_b)
f(i)=Ael*dphia_dhi1*P1+Ael*phi_a*(lambda(i+1)-kappa(i))-Bel*phi_b*(kappa(i)-delta(i-1))&
&+Agrav*(dphia_dhi1*H1+phi_a)
g(i)=0.d0;k(i)=0.d0;l(i)=0.d0
ELSEIF (i==N) THEN
a(i)=Bel*phi_b*alpha(i-1)
b(i)=-Bel*phi_b*(alpha(i)-beta(i-1))
c(i)=-Bel*phi_b*(beta(i)-gamma(i-1))
d(i)=-Bel*dphib_dhi1*P2-Bel*phi_b*(gamma(i)-lambda(i-1))&
&+Bgrav*(-dphib_dhi1*H2+phi_b)
e(i)=-Bel*dphib_dhi*P2-Bel*phi_b*(lambda(i)-kappa(i-1))&
&-Bgrav*(dphib_dhi*H2+phi_b)
f(i)=0.d0;g(i)=0.d0;k(i)=0.d0;l(i)=0.d0
ELSE
a(i)=Bel*phi_b*alpha(i-1)
b(i)=-Ael*phi_a*alpha(i)-Bel*phi_b*(alpha(i)-beta(i-1))
c(i)=Ael*phi_a*(alpha(i+1)-beta(i))-Bel*phi_b*(beta(i)-gamma(i-1))
d(i)=-Bel*dphib_dhi1*P2+Ael*phi_a*(beta(i+1)-gamma(i))-Bel*phi_b*(gamma(i)-lambda(i-1))&
&+Bgrav*(-dphib_dhi1*H2+phi_b)
e(i)=Ael*dphia_dhi*P1-Bel*dphib_dhi*P2+Ael*phi_a*(gamma(i+1)-lambda(i))-Bel*phi_b*(lambda(i)-kappa(i-1))&
&+Agrav*(dphia_dhi*H1-phi_a)-Bgrav*(dphib_dhi*H2+phi_b)
f(i)=Ael*dphia_dhi1*P1+Ael*phi_a*(lambda(i+1)-kappa(i))-Bel*phi_b*(kappa(i)-delta(i-1))&
&+Agrav*(dphia_dhi1*H1+phi_a)
g(i)=Ael*phi_a*(kappa(i+1)-delta(i))-Bel*phi_b*(delta(i)-epsilonn(i-1))
k(i)=Ael*phi_a*(delta(i+1)-epsilonn(i))-Bel*phi_b*epsilonn(i)
l(i)=Ael*phi_a*epsilonn(i+1)
END IF IF3
END DO
DEALLOCATE(alpha,beta,gamma,lambda,kappa,delta,epsilonn)
END SUBROUTINE JACOBI_THICKNESS
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!-------------------------------------------------------------------------------------
! SUBROUTINE NONA DIAG
!-------------------------------------------------------------------------------------
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
SUBROUTINE NONA_DIAGO(N,Hm,a,b,c,d,e,f,g,k,l,S)
!*****************************************************************
! Solves for a vector Hm of length N the nano diagonal linear set
! M Hm = S, where A, B, C, D, E, F, G, K and L are the three main
! diagonals of matrix M(N,N), the other terms are 0.
! S is the right side vector.
!*****************************************************************
IMPLICIT NONE
INTEGER , INTENT(IN) :: N
INTEGER :: i
INTEGER :: err3,err4
DOUBLE PRECISION, DIMENSION(:), INTENT(IN) :: a,b,c,d,e,f,g,k,l,S
DOUBLE PRECISION, DIMENSION(:),INTENT(INOUT) :: Hm
DOUBLE PRECISION, DIMENSION(:), ALLOCATABLE :: zeta,alpha,beta,mu,xi,lambda,eta,omega,gamma
AllOCATE(zeta(1:N),alpha(1:N),beta(1:N),mu(1:N),xi(1:N),stat=err3)
ALLOCATE(lambda(1:N),eta(1:N),omega(1:N),gamma(1:N),stat=err4)
IF (err3>1 .OR. err4>1) THEN
PRINT*, 'Erreur d''allocation dans vecteur P,Q'; STOP
END IF
zeta(1)=b(1)
alpha(1)=c(1)
beta(1)=d(1)
mu(1)=e(1)
xi(1)=f(1)/mu(1)
lambda(1)=g(1)/mu(1)
eta(1)=k(1)/mu(1)
omega(1)=l(1)/mu(1)
gamma(1)=S(1)/mu(1)
zeta(2)=b(2)
alpha(2)=c(2)
beta(2)=d(2)
mu(2)=e(2)-xi(1)*beta(2)
xi(2)=(f(2)-lambda(1)*beta(2))/mu(2)
lambda(2)=(g(2)-eta(1)*beta(2))/mu(2)
eta(2)=(k(2)-omega(1)*beta(2))/mu(2)
omega(2)=l(2)/mu(2)
gamma(2)=(S(2)-beta(2)*gamma(1))/mu(2)
zeta(3)=b(3)
alpha(3)=c(3)
beta(3)=d(3)-xi(1)*alpha(3)
mu(3)=e(3)-lambda(1)*alpha(3)-xi(2)*beta(3)
xi(3)=(f(3)-eta(1)*alpha(3)-lambda(2)*beta(3))/mu(3)
lambda(3)=(g(3)-omega(1)*alpha(3)-eta(2)*beta(3))/mu(3)
eta(3)=(k(3)-omega(2)*beta(3))/mu(3)
omega(3)=l(3)/mu(3)
gamma(3)=(S(3)-alpha(3)*gamma(1)-beta(3)*gamma(2))/mu(3)
zeta(4)=b(4)
alpha(4)=c(4)-xi(1)*zeta(4)
beta(4)=d(4)-lambda(1)*zeta(4)-xi(2)*alpha(4)
mu(4)=e(4)-eta(1)*zeta(4)-lambda(2)*alpha(4)-xi(3)*beta(4)
xi(4)=(f(4)-omega(1)*zeta(4)-eta(2)*alpha(4)-lambda(3)*beta(4))/mu(4)
lambda(4)=(g(4)-omega(2)*alpha(4)-eta(3)*beta(4))/mu(4)
eta(4)=(k(4)-omega(3)*beta(4))/mu(4)
omega(4)=l(4)/mu(4)
gamma(4)=(S(4)-zeta(4)*gamma(1)-alpha(4)*gamma(2)-beta(4)*gamma(3))/mu(4)
DO i=5,N
zeta(i)=b(i)-a(i)*xi(i-4)
alpha(i)=c(i)-a(i)*lambda(i-4)-xi(i-3)*zeta(i)
beta(i)=d(i)-a(i)*eta(i-4)-lambda(i-3)*zeta(i)-alpha(i)*xi(i-2)
mu(i)=e(i)-a(i)*omega(i-4)-zeta(i)*eta(i-3)-lambda(i-2)*alpha(i)-beta(i)*xi(i-1)
xi(i)=(f(i)-omega(i-3)*zeta(i)-eta(i-2)*alpha(i)-lambda(i-1)*beta(i))/mu(i)
lambda(i)=(g(i)-alpha(i)*omega(i-2)-eta(i-1)*beta(i))/mu(i)
eta(i)=(k(i)-omega(i-1)*beta(i))/mu(i)
omega(i)=l(i)/mu(i)
gamma(i)=(S(i)-a(i)*gamma(i-4)-zeta(i)*gamma(i-3)-alpha(i)*gamma(i-2)-beta(i)*gamma(i-1))/mu(i)
END DO
Hm(N)=gamma(N)
Hm(N-1)=gamma(N-1)-xi(N-1)*Hm(N)
Hm(N-2)=gamma(N-2)-lambda(N-2)*Hm(N)-xi(N-2)*Hm(N-1)
Hm(N-3)=gamma(N-3)-eta(N-3)*Hm(N)-lambda(N-3)*Hm(N-1)-xi(N-3)*Hm(N-2)
DO i=N-4,1,-1
Hm(i)=gamma(i)-xi(i)*Hm(i+1)-lambda(i)*Hm(i+2)-eta(i)*Hm(i+3)-omega(i)*Hm(i+4)
END DO
DEALLOCATE(zeta,alpha,beta,mu,xi,lambda,eta,omega,gamma)
END SUBROUTINE NONA_DIAGO
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!-------------------------------------------------------------------------------------
! SUBROUTINE TRIDIAG
!-------------------------------------------------------------------------------------
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
SUBROUTINE TRIDIAG(A,B,C,S,N,U,CODE)
!*****************************************************************
! Solves for a vector U of length N the tridiagonal linear set
! M U = R, where A, B and C are the three main diagonals of matrix
! M(N,N), the other terms are 0. R is the right side vector.
!*****************************************************************
IMPLICIT NONE
DOUBLE PRECISION, DIMENSION(N), INTENT(IN) :: A,B,C,S
DOUBLE PRECISION, DIMENSION(N), INTENT(OUT) :: U
INTEGER, INTENT(IN) :: N
INTEGER, INTENT(OUT) :: CODE
DOUBLE PRECISION, DIMENSION(N) :: GAM
DOUBLE PRECISION :: BET
INTEGER :: j
IF(B(1).EQ.0.D0) THEN
CODE=1
RETURN
END IF
BET = B(1)
U(1) = S(1)/BET
DO J=2,N !Decomposition and forward substitution
GAM(j)=C(j-1)/BET
BET=B(j)-A(j)*GAM(j)
IF(BET.EQ.0.D0) THEN !Algorithm fails
CODE=2
RETURN
END IF
U(j)=(S(j)-A(j)*U(j-1))/BET
END DO
DO J=N-1,1,-1 !Back substitution
U(J)=U(J)-GAM(J+1)*U(J+1)
END DO
CODE=0
RETURN
END SUBROUTINE TRIDIAG
END MODULE MODULE_THICKNESS_SKIN_NEWTON_ARRHENIUS