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solver.f90
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solver.f90
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SUBROUTINE ICCG2(coef,jcoef,L,Ldiag,b,x,n,m,eps,p,r,r2,q,s,itmax)
!-----------------------------------------------------------------------!
! !
! CONJUGUATE GRADIENT + PRECONDITIONED LU FILL-IN 2 !
! !
! ATTENTION : coef, jcoef et b are modified in this routine !
! --------- !
! !
!-----------------------------------------------------------------------!
implicit none
!---------------------------------------------------!
! VARIABLES IN CALL !
!---------------------------------------------------!
integer, intent(in) :: n,m,itmax
real*8, intent(in) :: eps
integer, dimension(m), intent(inout) :: jcoef
real*8, dimension(n,m), intent (inout) :: coef
integer, dimension(5), intent(inout) :: Ldiag
real*8, dimension(n,5), intent (inout) :: L
real*8, dimension(n), intent (inout) :: b,x
real*8, dimension(n), intent(inout) :: p,r,r2,q,s
!---------------------------------------------------!
! LOCAL VARIABLES !
!---------------------------------------------------!
real*8 :: alpha,beta,nu,mu,norm0,norm,sum,scal,norm1,norm2
integer :: i,j,col
write(6,*) 'itmax=',itmax
!-----------------------------------------------------------!
! PRECONDITIONING MATRIX CALCULUS + SCALING !
!-----------------------------------------------------------!
do i=1,3; Ldiag(i)=jcoef(i); end do
Ldiag(4)=Ldiag(3)-1
Ldiag(5)=Ldiag(3)-2
L=0.
do i=1,n
L(i,1)=coef(i,1)
do j=2,5
col=Ldiag(j)
if (col<i) L(i,1)=L(i,1)-L(i-col,j)*L(i-col,j)*s(i-col)
end do
s(i)=1./L(i,1) ! Temporary variable to avoid divisions by L(i,1)
L(i,2)=coef(i,2)
do j=4,5
col=Ldiag(j)
if (col<i) L(i,2)=L(i,2)-L(i-col,j)*L(i-col,j-1)*s(i-col)
end do
L(i,3)=coef(i,3)
if (i>1) then
L(i,4)=-L(i-1,3)*L(i-1,2)*s(i-1)
L(i,5)=-L(i-1,4)*L(i-1,2)*s(i-1)
end if
end do
do i=1,n; L(i,1)=sqrt(s(i)); end do
do j=1,3
col=Ldiag(j)
do i=1,n-col
coef(i,j)=coef(i,j)*L(i,1)*L(i+col,1)
end do
end do
do i=1,n
L(i,2)=coef(i,2)
do j=4,5
col=Ldiag(j)
if (col<i) L(i,2)=L(i,2)-L(i-col,j)*L(i-col,j-1)
end do
L(i,3)=coef(i,3)
if (i>1) then
L(i,4)=-L(i-1,3)*L(i-1,2)
L(i,5)=-L(i-1,4)*L(i-1,2)
end if
end do
norm0=norm2(b,n)
do i=1,n; s(i)=1./s(i); end do
do i=1,n; b(i)=b(i)*L(i,1); end do
!---------------------------------------------------!
! CONJUGUATE GRADIENT !
!---------------------------------------------------!
call matmul_ell(p,coef,jcoef,x,n,m)
do i=1,n; r(i)=b(i)-p(i); end do
call resLU_ell5(r2,L,Ldiag,r,n)
p=r2
nu=scal(r,r2,n)
norm=0.
do i=1,n; norm=norm+r(i)*r(i)*s(i); end do
norm=sqrt(norm)/norm0
j=0
do while (norm>eps.and.j.lt.itmax)
j=j+1
call matmul_ell(q,coef,jcoef,p,n,m)
alpha=nu/scal(p,q,n)
do i=1,n; x(i)=x(i)+alpha*p(i); end do
do i=1,n; r(i)=r(i)-alpha*q(i); end do
call resLU_ell5(r2,L,Ldiag,r,n)
mu=scal(r,r2,n)
beta=mu/nu
do i=1,n; p(i)=r2(i)+beta*p(i); end do
nu=mu
norm=0.
do i=1,n; norm=norm+r(i)*r(i)*s(i); end do
norm=sqrt(norm)/norm0
end do
!---------------------------------------------------!
! SOLUTION SCALING !
!---------------------------------------------------!
do i=1,n; x(i)=x(i)*L(i,1); end do
if(j.ge.itmax) then
print*, 'non convergence apres =', j,norm
else
print*, ' Nombre It�rations ICCG2 ( Fill-In 2 ) =', j
endif
return
END SUBROUTINE ICCG2
SUBROUTINE resLU_ell5(x,L,Ldiag,y,n)
implicit none
integer, intent(in) :: n
real*8, dimension(n,5), intent (in) :: L
integer, dimension(5), intent(in) :: Ldiag
real*8, dimension(n), intent(in) :: y
real*8, dimension(n), intent(out) :: x
integer :: i,j,col1,col2,col3,col4,col5,col6
col1=Ldiag(2)
col2=Ldiag(5)
col3=Ldiag(4)
col4=Ldiag(3)
do i=1,col1
x(i)=y(i)
end do
do i=col1+1,col2
x(i)=y(i)-L(i-col1,2)*x(i-col1)
end do
do i=col2+1,col3
x(i)=y(i)-L(i-col1,2)*x(i-col1)-L(i-col2,5)*x(i-col2)
end do
do i=col3+1,col4
x(i)=y(i)-L(i-col1,2)*x(i-col1)-L(i-col2,5)*x(i-col2)&
-L(i-col3,4)*x(i-col3)
end do
do i=col4+1,n
x(i)=y(i)-L(i-col1,2)*x(i-col1)-L(i-col2,5)*x(i-col2)&
-L(i-col3,4)*x(i-col3)-L(i-col4,3)*x(i-col4)
end do
do i=n-col1,n-col2+1,-1
x(i)=x(i)-L(i,2)*x(i+col1)
end do
do i=n-col2,n-col3+1,-1
x(i)=x(i)-L(i,2)*x(i+col1)-L(i,5)*x(i+col2)
end do
do i=n-col3,n-col4+1,-1
x(i)=x(i)-L(i,2)*x(i+col1)-L(i,5)*x(i+col2)-L(i,4)*x(i+col3)
end do
do i=n-col4,1,-1
x(i)=x(i)-L(i,2)*x(i+col1)-L(i,5)*x(i+col2)-L(i,4)*x(i+col3)&
-L(i,3)*x(i+col4)
end do
return
END SUBROUTINE resLU_ell5
SUBROUTINE matmul_ell(x,coef,jcoef,y,n,m)
implicit none
integer, intent(in) :: n,m
real*8, dimension(n,m), intent (in) :: coef
integer, dimension(m), intent(in) :: jcoef
real*8, dimension(n), intent(in) :: y
real*8, dimension(n), intent(out) :: x
integer :: i,j,col
do i=1,n
x(i)=coef(i,1)*y(i)
end do
do j=2,m
col=jcoef(j)
do i=1,n-col
x(i)=x(i)+coef(i,j)*y(i+col)
x(i+col)=x(i+col)+coef(i,j)*y(i)
end do
end do
return
END SUBROUTINE matmul_ell
FUNCTION scal(x,y,n) result(res)
implicit none
integer, intent(in) :: n
real*8, dimension(n), intent(in) :: x,y
integer :: i
real*8 :: res
res=0.
do i=1,n; res=res+x(i)*y(i); end do
END FUNCTION
FUNCTION norm1(x,n) result(res)
implicit none
integer, intent(in) :: n
real*8, dimension(n), intent(in) :: x
integer :: i
real*8 :: res
res=0.
do i=1,n; res=res+x(i)*x(i); end do
END FUNCTION
FUNCTION norm2(x,n) result(res)
implicit none
integer, intent(in) :: n
real*8, dimension(n), intent(in) :: x
integer :: i
real*8 :: res
res=0.
do i=1,n; res=res+x(i)*x(i); end do
res=sqrt(res)
END FUNCTION