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! $Header$
#include "cctk.h"
#include "cctk_Parameters.h"
#include "cctk_Functions.h"
subroutine dissipation_4_3_alt (var, lsh, gsh, lbnd, bb, gsize, &
delta, epsilon, dfl, npatches, patch, rhs)
use dissipation_coeff
implicit none
DECLARE_CCTK_PARAMETERS
DECLARE_CCTK_FUNCTIONS
CCTK_INT, dimension(3), intent(in) :: lsh, gsh, lbnd
CCTK_INT :: ni, nj, nk
CCTK_REAL, dimension(lsh(1),lsh(2),lsh(3)), intent(in) :: var
CCTK_REAL, dimension(lsh(1),lsh(2),lsh(3)), intent(inout) :: rhs
CCTK_INT, dimension(6), intent(in) :: bb
CCTK_INT, dimension(3), intent(in) :: gsize
CCTK_REAL, dimension(3), intent(in) :: delta
CCTK_REAL, intent(in) :: epsilon
CCTK_REAL, dimension(3), intent(in) :: dfl
CCTK_INT, intent(in) :: npatches, patch
CCTK_REAL :: zero = 0.0
integer, parameter :: wp = kind(zero)
integer :: i, j, k, center
CCTK_REAL, dimension(:,:), allocatable :: atmp, d, b, h, tmp
CCTK_REAL, dimension(:,:), pointer :: a
CCTK_REAL :: idel
CCTK_INT :: il, ir, jl, jr, kl, kr
ni = lsh(1); nj = lsh(2); nk = lsh(3)
if ( first ) then
allocate ( savedx(npatches), savedy(npatches), savedz(npatches) )
savedx = .false.; savedy = .false.; savedz = .false.
allocate ( xcoeff(npatches), ycoeff(npatches), zcoeff(npatches) )
first = .false.
end if
if ( .not. savedx(patch) ) then
allocate ( atmp(ni,ni), d(ni,ni), b(ni,ni), h(ni,ni), tmp(ni,ni) )
atmp = zero; d = zero; b = zero; h = zero; tmp = zero
call set_bmatrix ( b, bb(1:2), lsh(1), gsh(1), lbnd(1), delta(1), dfl(1) )
call set_hmatrix ( h, bb(1:2) )
if ( any ( bb(1:2) == 0 ) ) then
call set_dmatrix ( d, bb(1:2) )
atmp = -transpose ( matmul ( h, matmul ( transpose(d), matmul ( b, d ) ) ) )
else
if ( lsh(1) /= gsh(1) ) then
call CCTK_WARN(0, 'Internal error. Bounding box inconsistent with grid' )
end if
center = gsh(1) / 2
ir = center + max(3,gsize(1))
call set_dmatrix_half ( d(1:ir,1:ir), 1 )
tmp(1:ir,1:ir) = -transpose ( &
matmul ( h(1:ir,1:ir), &
matmul ( &
transpose ( d(1:ir,1:ir) ), &
matmul ( b(1:ir,1:ir), &
d(1:ir,1:ir) ) ) ) )
atmp(1:ir,1:center) = tmp(1:ir,1:center)
il = center + 1 - max(3,gsize(1))
d = zero
call set_dmatrix_half ( d(il:ni,il:ni), 2 )
tmp(il:ni,il:ni) = matmul ( b(il:ni,il:ni), d(il:ni,il:ni) )
tmp(il:ni,il:ni) = matmul ( transpose ( d(il:ni,il:ni) ), tmp(il:ni,il:ni) )
tmp(il:ni,il:ni) = matmul ( h(il:ni,il:ni), tmp(il:ni,il:ni) )
tmp(il:ni,il:ni) = -transpose ( tmp(il:ni,il:ni) )
atmp(il:ni,center+1:ni) = tmp(il:ni,center+1:ni)
end if
allocate ( xcoeff(patch)%coeff(ni,ni) )
xcoeff(patch)%coeff = atmp
savedx(patch) = .true.
deallocate ( atmp, d, b, h, tmp )
end if
a => xcoeff(patch)%coeff
idel = epsilon / ( 64 * delta(1) )
if ( bb(1) == 0 ) then
il = 1 + gsize(1)
else
rhs(1,:,:) = rhs(1,:,:) + &
( a(1,1) * var(1,:,:) + a(2,1) * var(2,:,:) + &
a(3,1) * var(3,:,:) + a(4,1) * var(4,:,:) ) * idel
rhs(2,:,:) = rhs(2,:,:) + &
( a(1,2) * var(1,:,:) + a(2,2) * var(2,:,:) + &
a(3,2) * var(3,:,:) + a(4,2) * var(4,:,:) + &
a(5,2) * var(5,:,:) + a(6,2) * var(6,:,:) + &
a(7,2) * var(7,:,:) + a(8,2) * var(8,:,:) ) * idel
rhs(3,:,:) = rhs(3,:,:) + &
( a(1,3) * var(1,:,:) + a(2,3) * var(2,:,:) + &
a(3,3) * var(3,:,:) + a(4,3) * var(4,:,:) + &
a(5,3) * var(5,:,:) + a(6,3) * var(6,:,:) + &
a(7,3) * var(7,:,:) + a(8,3) * var(8,:,:) ) * idel
rhs(4,:,:) = rhs(4,:,:) + &
( a(1,4) * var(1,:,:) + a(2,4) * var(2,:,:) + &
a(3,4) * var(3,:,:) + a(4,4) * var(4,:,:) + &
a(5,4) * var(5,:,:) + a(6,4) * var(6,:,:) + &
a(7,4) * var(7,:,:) + a(8,4) * var(8,:,:) ) * idel
rhs(5,:,:) = rhs(5,:,:) + &
( a(1,5) * var(1,:,:) + a(2,5) * var(2,:,:) + &
a(3,5) * var(3,:,:) + a(4,5) * var(4,:,:) + &
a(5,5) * var(5,:,:) + a(6,5) * var(6,:,:) + &
a(7,5) * var(7,:,:) + a(8,5) * var(8,:,:) ) * idel
il = 6
end if
if ( bb(2) == 0 ) then
ir = ni - gsize(1)
else
rhs(ni-4,:,:) = rhs(ni-4,:,:) + &
( a(ni-7,ni-4) * var(ni-7,:,:) + &
a(ni-6,ni-4) * var(ni-6,:,:) + &
a(ni-5,ni-4) * var(ni-5,:,:) + &
a(ni-4,ni-4) * var(ni-4,:,:) + &
a(ni-3,ni-4) * var(ni-3,:,:) + &
a(ni-2,ni-4) * var(ni-2,:,:) + &
a(ni-1,ni-4) * var(ni-1,:,:) + &
a(ni,ni-4) * var(ni,:,:) ) * idel
rhs(ni-3,:,:) = rhs(ni-3,:,:) + &
( a(ni-7,ni-3) * var(ni-7,:,:) + &
a(ni-6,ni-3) * var(ni-6,:,:) + &
a(ni-5,ni-3) * var(ni-5,:,:) + &
a(ni-4,ni-3) * var(ni-4,:,:) + &
a(ni-3,ni-3) * var(ni-3,:,:) + &
a(ni-2,ni-3) * var(ni-2,:,:) + &
a(ni-1,ni-3) * var(ni-1,:,:) + &
a(ni,ni-3) * var(ni,:,:) ) * idel
rhs(ni-2,:,:) = rhs(ni-2,:,:) + &
( a(ni-7,ni-2) * var(ni-7,:,:) + &
a(ni-6,ni-2) * var(ni-6,:,:) + &
a(ni-5,ni-2) * var(ni-5,:,:) + &
a(ni-4,ni-2) * var(ni-4,:,:) + &
a(ni-3,ni-2) * var(ni-3,:,:) + &
a(ni-2,ni-2) * var(ni-2,:,:) + &
a(ni-1,ni-2) * var(ni-1,:,:) + &
a(ni,ni-2) * var(ni,:,:) ) * idel
rhs(ni-1,:,:) = rhs(ni-1,:,:) + &
( a(ni-7,ni-1) * var(ni-7,:,:) + &
a(ni-6,ni-1) * var(ni-6,:,:) + &
a(ni-5,ni-1) * var(ni-5,:,:) + &
a(ni-4,ni-1) * var(ni-4,:,:) + &
a(ni-3,ni-1) * var(ni-3,:,:) + &
a(ni-2,ni-1) * var(ni-2,:,:) + &
a(ni-1,ni-1) * var(ni-1,:,:) + &
a(ni,ni-1) * var(ni,:,:) ) * idel
rhs(ni,:,:) = rhs(ni,:,:) + &
( a(ni-3,ni) * var(ni-3,:,:) + &
a(ni-2,ni) * var(ni-2,:,:) + &
a(ni-1,ni) * var(ni-1,:,:) + &
a(ni,ni) * var(ni,:,:) ) * idel
ir = ni - 5
end if
do i = il, ir
rhs(i,:,:) = rhs(i,:,:) + &
( a(i-3,i) * var(i-3,:,:) + &
a(i-2,i) * var(i-2,:,:) + &
a(i-1,i) * var(i-1,:,:) + &
a(i,i) * var(i,:,:) + &
a(i+1,i) * var(i+1,:,:) + &
a(i+2,i) * var(i+2,:,:) + &
a(i+3,i) * var(i+3,:,:) ) * idel
end do
if ( zero_derivs_y == 0 ) then
if ( .not. savedy(patch) ) then
allocate ( atmp(nj,nj), d(nj,nj), b(nj,nj), h(nj,nj), tmp(nj,nj) )
atmp = zero; d = zero; b = zero; h = zero; tmp = zero
call set_bmatrix ( b, bb(3:4), lsh(2), gsh(2), lbnd(2), delta(2), dfl(2) )
call set_hmatrix ( h, bb(3:4) )
if ( any ( bb(3:4) == 0 ) ) then
call set_dmatrix ( d, bb(3:4) )
atmp = -transpose ( matmul ( h, matmul ( transpose(d), matmul ( b, d ) ) ) )
else
if ( lsh(2) /= gsh(2) ) then
call CCTK_WARN(0, 'Internal error. Bounding box inconsistent with grid' )
end if
center = gsh(2) / 2
jr = center + max(3,gsize(2))
call set_dmatrix_half ( d(1:jr,1:jr), 1 )
tmp(1:jr,1:jr) = -transpose ( &
matmul ( h(1:jr,1:jr), &
matmul ( &
transpose ( d(1:jr,1:jr) ), &
matmul ( b(1:jr,1:jr), &
d(1:jr,1:jr) ) ) ) )
atmp(1:jr,1:center) = tmp(1:jr,1:center)
jl = center + 1 - max(3,gsize(2))
d = zero
call set_dmatrix_half ( d(jl:nj,jl:nj), 2 )
tmp(jl:nj,jl:nj) = -transpose ( &
matmul ( h(jl:nj,jl:nj), &
matmul ( &
transpose ( d(jl:nj,jl:nj) ), &
matmul ( b(jl:nj,jl:nj), &
d(jl:nj,jl:nj) ) ) ) )
atmp(jl:nj,center+1:nj) = tmp(jl:nj,center+1:nj)
end if
allocate ( ycoeff(patch)%coeff(nj,nj) )
ycoeff(patch)%coeff = atmp
savedy(patch) = .true.
deallocate ( atmp, d, b, h, tmp )
end if
a => ycoeff(patch)%coeff
idel = epsilon / ( 64 * delta(2) )
if ( bb(3) == 0 ) then
jl = 1 + gsize(2)
else
rhs(:,1,:) = rhs(:,1,:) + &
( a(1,1) * var(:,1,:) + a(2,1) * var(:,2,:) + &
a(3,1) * var(:,3,:) + a(4,1) * var(:,4,:) ) * idel
rhs(:,2,:) = rhs(:,2,:) + &
( a(1,2) * var(:,1,:) + a(2,2) * var(:,2,:) + &
a(3,2) * var(:,3,:) + a(4,2) * var(:,4,:) + &
a(5,2) * var(:,5,:) + a(6,2) * var(:,6,:) + &
a(7,2) * var(:,7,:) + a(8,2) * var(:,8,:) ) * idel
rhs(:,3,:) = rhs(:,3,:) + &
( a(1,3) * var(:,1,:) + a(2,3) * var(:,2,:) + &
a(3,3) * var(:,3,:) + a(4,3) * var(:,4,:) + &
a(5,3) * var(:,5,:) + a(6,3) * var(:,6,:) + &
a(7,3) * var(:,7,:) + a(8,3) * var(:,8,:) ) * idel
rhs(:,4,:) = rhs(:,4,:) + &
( a(1,4) * var(:,1,:) + a(2,4) * var(:,2,:) + &
a(3,4) * var(:,3,:) + a(4,4) * var(:,4,:) + &
a(5,4) * var(:,5,:) + a(6,4) * var(:,6,:) + &
a(7,4) * var(:,7,:) + a(8,4) * var(:,8,:) ) * idel
rhs(:,5,:) = rhs(:,5,:) + &
( a(1,5) * var(:,1,:) + a(2,5) * var(:,2,:) + &
a(3,5) * var(:,3,:) + a(4,5) * var(:,4,:) + &
a(5,5) * var(:,5,:) + a(6,5) * var(:,6,:) + &
a(7,5) * var(:,7,:) + a(8,5) * var(:,8,:) ) * idel
jl = 6
end if
if ( bb(4) == 0 ) then
jr = nj - gsize(2)
else
rhs(:,nj-4,:) = rhs(:,nj-4,:) + &
( a(nj-7,nj-4) * var(:,nj-7,:) + &
a(nj-6,nj-4) * var(:,nj-6,:) + &
a(nj-5,nj-4) * var(:,nj-5,:) + &
a(nj-4,nj-4) * var(:,nj-4,:) + &
a(nj-3,nj-4) * var(:,nj-3,:) + &
a(nj-2,nj-4) * var(:,nj-2,:) + &
a(nj-1,nj-4) * var(:,nj-1,:) + &
a(nj,nj-4) * var(:,nj,:) ) * idel
rhs(:,nj-3,:) = rhs(:,nj-3,:) + &
( a(nj-7,nj-3) * var(:,nj-7,:) + &
a(nj-6,nj-3) * var(:,nj-6,:) + &
a(nj-5,nj-3) * var(:,nj-5,:) + &
a(nj-4,nj-3) * var(:,nj-4,:) + &
a(nj-3,nj-3) * var(:,nj-3,:) + &
a(nj-2,nj-3) * var(:,nj-2,:) + &
a(nj-1,nj-3) * var(:,nj-1,:) + &
a(nj,nj-3) * var(:,nj,:) ) * idel
rhs(:,nj-2,:) = rhs(:,nj-2,:) + &
( a(nj-7,nj-2) * var(:,nj-7,:) + &
a(nj-6,nj-2) * var(:,nj-6,:) + &
a(nj-5,nj-2) * var(:,nj-5,:) + &
a(nj-4,nj-2) * var(:,nj-4,:) + &
a(nj-3,nj-2) * var(:,nj-3,:) + &
a(nj-2,nj-2) * var(:,nj-2,:) + &
a(nj-1,nj-2) * var(:,nj-1,:) + &
a(nj,nj-2) * var(:,nj,:) ) * idel
rhs(:,nj-1,:) = rhs(:,nj-1,:) + &
( a(nj-7,nj-1) * var(:,nj-7,:) + &
a(nj-6,nj-1) * var(:,nj-6,:) + &
a(nj-5,nj-1) * var(:,nj-5,:) + &
a(nj-4,nj-1) * var(:,nj-4,:) + &
a(nj-3,nj-1) * var(:,nj-3,:) + &
a(nj-2,nj-1) * var(:,nj-2,:) + &
a(nj-1,nj-1) * var(:,nj-1,:) + &
a(nj,nj-1) * var(:,nj,:) ) * idel
rhs(:,nj,:) = rhs(:,nj,:) + &
( a(nj-3,nj) * var(:,nj-3,:) + &
a(nj-2,nj) * var(:,nj-2,:) + &
a(nj-1,nj) * var(:,nj-1,:) + &
a(nj,nj) * var(:,nj,:) ) * idel
jr = nj - 5
end if
do j = jl, jr
rhs(:,j,:) = rhs(:,j,:) + &
( a(j-3,j) * var(:,j-3,:) + &
a(j-2,j) * var(:,j-2,:) + &
a(j-1,j) * var(:,j-1,:) + &
a(j,j) * var(:,j,:) + &
a(j+1,j) * var(:,j+1,:) + &
a(j+2,j) * var(:,j+2,:) + &
a(j+3,j) * var(:,j+3,:) ) * idel
end do
end if
if ( zero_derivs_z == 0 ) then
if ( .not. savedz(patch) ) then
allocate ( atmp(nk,nk), d(nk,nk), b(nk,nk), h(nk,nk), tmp(nk,nk) )
atmp = zero; d = zero; b = zero; h = zero; tmp = zero
call set_bmatrix ( b, bb(5:6), lsh(3), gsh(3), lbnd(3), delta(3), dfl(3) )
call set_hmatrix ( h, bb(5:6) )
if ( any ( bb(5:6) == 0 ) ) then
call set_dmatrix ( d, bb(5:6) )
atmp = -transpose ( matmul ( h, matmul ( transpose(d), matmul ( b, d ) ) ) )
else
if ( lsh(3) /= gsh(3) ) then
call CCTK_WARN(0, 'Internal error. Bounding box inconsistent with grid' )
end if
center = gsh(3) / 2
kr = center + max(3,gsize(3))
call set_dmatrix_half ( d(1:kr,1:kr), 1 )
tmp(1:kr,1:kr) = matmul ( b(1:kr,1:kr), d(1:kr,1:kr) )
tmp(1:kr,1:kr) = matmul ( transpose ( d(1:kr,1:kr) ), tmp(1:kr,1:kr) )
tmp(1:kr,1:kr) = matmul ( h(1:kr,1:kr), tmp(1:kr,1:kr) )
tmp(1:kr,1:kr) = -transpose ( tmp(1:kr,1:kr) )
atmp(1:kr,1:center) = tmp(1:kr,1:center)
kl = center + 1 - max(3,gsize(3))
d = zero
call set_dmatrix_half ( d(kl:nk,kl:nk), 2 )
tmp(kl:nk,kl:nk) = -transpose ( &
matmul ( h(kl:nk,kl:nk), &
matmul ( &
transpose ( d(kl:nk,kl:nk) ), &
matmul ( b(kl:nk,kl:nk), &
d(kl:nk,kl:nk) ) ) ) )
atmp(kl:nk,center+1:nk) = tmp(kl:nk,center+1:nk)
end if
allocate ( zcoeff(patch)%coeff(nk,nk) )
zcoeff(patch)%coeff = atmp
savedz(patch) = .true.
deallocate ( atmp, d, b, h, tmp )
end if
a => zcoeff(patch)%coeff
idel = epsilon / ( 64 * delta(3) )
if ( bb(5) == 0 ) then
kl = 1 + gsize(3)
else
rhs(:,:,1) = rhs(:,:,1) + &
( a(1,1) * var(:,:,1) + a(2,1) * var(:,:,2) + &
a(3,1) * var(:,:,3) + a(4,1) * var(:,:,4) ) * idel
rhs(:,:,2) = rhs(:,:,2) + &
( a(1,2) * var(:,:,1) + a(2,2) * var(:,:,2) + &
a(3,2) * var(:,:,3) + a(4,2) * var(:,:,4) + &
a(5,2) * var(:,:,5) + a(6,2) * var(:,:,6) + &
a(7,2) * var(:,:,7) + a(8,2) * var(:,:,8) ) * idel
rhs(:,:,3) = rhs(:,:,3) + &
( a(1,3) * var(:,:,1) + a(2,3) * var(:,:,2) + &
a(3,3) * var(:,:,3) + a(4,3) * var(:,:,4) + &
a(5,3) * var(:,:,5) + a(6,3) * var(:,:,6) + &
a(7,3) * var(:,:,7) + a(8,3) * var(:,:,8) ) * idel
rhs(:,:,4) = rhs(:,:,4) + &
( a(1,4) * var(:,:,1) + a(2,4) * var(:,:,2) + &
a(3,4) * var(:,:,3) + a(4,4) * var(:,:,4) + &
a(5,4) * var(:,:,5) + a(6,4) * var(:,:,6) + &
a(7,4) * var(:,:,7) + a(8,4) * var(:,:,8) ) * idel
rhs(:,:,5) = rhs(:,:,5) + &
( a(1,5) * var(:,:,1) + a(2,5) * var(:,:,2) + &
a(3,5) * var(:,:,3) + a(4,5) * var(:,:,4) + &
a(5,5) * var(:,:,5) + a(6,5) * var(:,:,6) + &
a(7,5) * var(:,:,7) + a(8,5) * var(:,:,8) ) * idel
kl = 6
end if
if ( bb(6) == 0 ) then
kr = nk - gsize(3)
else
rhs(:,:,nk-4) = rhs(:,:,nk-4) + &
( a(nk-7,nk-4) * var(:,:,nk-7) + &
a(nk-6,nk-4) * var(:,:,nk-6) + &
a(nk-5,nk-4) * var(:,:,nk-5) + &
a(nk-4,nk-4) * var(:,:,nk-4) + &
a(nk-3,nk-4) * var(:,:,nk-3) + &
a(nk-2,nk-4) * var(:,:,nk-2) + &
a(nk-1,nk-4) * var(:,:,nk-1) + &
a(nk,nk-4) * var(:,:,nk) ) * idel
rhs(:,:,nk-3) = rhs(:,:,nk-3) + &
( a(nk-7,nk-3) * var(:,:,nk-7) + &
a(nk-6,nk-3) * var(:,:,nk-6) + &
a(nk-5,nk-3) * var(:,:,nk-5) + &
a(nk-4,nk-3) * var(:,:,nk-4) + &
a(nk-3,nk-3) * var(:,:,nk-3) + &
a(nk-2,nk-3) * var(:,:,nk-2) + &
a(nk-1,nk-3) * var(:,:,nk-1) + &
a(nk,nk-3) * var(:,:,nk) ) * idel
rhs(:,:,nk-2) = rhs(:,:,nk-2) + &
( a(nk-7,nk-2) * var(:,:,nk-7) + &
a(nk-6,nk-2) * var(:,:,nk-6) + &
a(nk-5,nk-2) * var(:,:,nk-5) + &
a(nk-4,nk-2) * var(:,:,nk-4) + &
a(nk-3,nk-2) * var(:,:,nk-3) + &
a(nk-2,nk-2) * var(:,:,nk-2) + &
a(nk-1,nk-2) * var(:,:,nk-1) + &
a(nk,nk-2) * var(:,:,nk) ) * idel
rhs(:,:,nk-1) = rhs(:,:,nk-1) + &
( a(nk-7,nk-1) * var(:,:,nk-7) + &
a(nk-6,nk-1) * var(:,:,nk-6) + &
a(nk-5,nk-1) * var(:,:,nk-5) + &
a(nk-4,nk-1) * var(:,:,nk-4) + &
a(nk-3,nk-1) * var(:,:,nk-3) + &
a(nk-2,nk-1) * var(:,:,nk-2) + &
a(nk-1,nk-1) * var(:,:,nk-1) + &
a(nk,nk-1) * var(:,:,nk) ) * idel
rhs(:,:,nk) = rhs(:,:,nk) + &
( a(nk-3,nk) * var(:,:,nk-3) + &
a(nk-2,nk) * var(:,:,nk-2) + &
a(nk-1,nk) * var(:,:,nk-1) + &
a(nk,nk) * var(:,:,nk) ) * idel
kr = nk - 5
end if
do k = kl, kr
rhs(:,:,k) = rhs(:,:,k) + &
( a(k-3,k) * var(:,:,k-3) + &
a(k-2,k) * var(:,:,k-2) + &
a(k-1,k) * var(:,:,k-1) + &
a(k,k) * var(:,:,k) + &
a(k+1,k) * var(:,:,k+1) + &
a(k+2,k) * var(:,:,k+2) + &
a(k+3,k) * var(:,:,k+3) ) * idel
end do
end if
contains
subroutine set_dmatrix ( d, bb )
implicit none
CCTK_REAL, dimension(:,:), intent(out) :: d
CCTK_INT, dimension(2), intent(in) :: bb
CCTK_INT :: n
CCTK_REAL, dimension(4), save :: ac = (/ -1.0_wp, 3.0_wp, -3.0_wp, 1.0_wp /)
CCTK_INT :: i
n = size(d,1)
if ( any(bb /= 0) ) then
if ( bb(1) /= 0 ) then
d(1,1:4) = ac
d(2,1:4) = ac
do i = 3, n-1
d(i,i-2:i+1) = ac
end do
d(n,n-2:n) = ac(1:3)
else
d(1,1:3) = ac(2:4)
do i = 2, n-2
d(i,i-1:i+2) = ac
end do
d(n-1,n-3:n) = ac
d(n,n-3:n) = ac
end if
else
d(1,1:2) = ac(3:4)
d(2,1:3) = ac(2:4)
do i = 3, n-1
d(i,i-2:i+1) = ac
end do
d(n,n-2:n) = ac(1:3)
end if
end subroutine set_dmatrix
subroutine set_dmatrix_half ( d, part )
implicit none
CCTK_REAL, dimension(:,:), intent(out) :: d
integer, intent(in) :: part
CCTK_INT :: n
CCTK_REAL, dimension(4), save :: ac = (/ -1.0_wp, 3.0_wp, -3.0_wp, 1.0_wp /)
CCTK_INT :: i
n = size(d,1)
if ( part == 1 ) then
d(1,1:4) = ac
d(2,1:4) = ac
do i = 3, n-1
d(i,i-2:i+1) = ac
end do
d(n,n-2:n) = ac(1:3)
else if ( part == 2 ) then
d(1,1:3) = ac(2:4)
do i = 2, n-2
d(i,i-1:i+2) = ac
end do
d(n-1,n-3:n) = ac
d(n,n-3:n) = ac
end if
end subroutine set_dmatrix_half
subroutine set_bmatrix ( b, bb, lsh, gsh, lbnd, h, dfl )
implicit none
CCTK_REAL, dimension(:,:), intent(out) :: b
CCTK_INT, dimension(2), intent(in) :: bb
CCTK_INT, intent(in) :: lsh, gsh, lbnd
CCTK_REAL, intent(in) :: h, dfl
CCTK_INT :: n
CCTK_INT :: i
CCTK_REAL :: xp
CCTK_REAL :: zero = 0.0
integer, parameter :: wp = kind(zero)
n = size(b,1)
xp = ( gsh - 1 ) * dfl - 1
do i = 1, n
b(i,i) = bf ( real(i+lbnd-1,wp), xp, real(gsh-1,wp), h )
end do
end subroutine set_bmatrix
subroutine set_hmatrix ( h, bb )
implicit none
CCTK_REAL, dimension(:,:), intent(out) :: h
CCTK_INT, dimension(2), intent(in) :: bb
CCTK_INT :: n, i
CCTK_REAL :: zero = 0.0
integer, parameter :: wp = kind(zero)
n = size(h,1)
do i = 1, n
h(i,i) = 1.0_wp
end do
if ( bb(1) /= 0 ) then
h(1:5,1:5) = sigma ( )
end if
if ( bb(2) /= 0 ) then
h(n:n-4:-1,n:n-4:-1) = sigma ( )
end if
end subroutine set_hmatrix
function bf ( x, xp, xmax, h )
implicit none
CCTK_REAL :: bf
CCTK_REAL, intent(in) :: x, xp, xmax, h
CCTK_REAL :: zero = 0.0
integer, parameter :: wp = kind(zero)
if ( x < xp ) then
bf = ( 1.0_wp - h ) / xp * x + h
else if ( x > xmax - xp ) then
bf = ( h - 1.0_wp ) / xp * ( x + xp - xmax ) + 1
else
bf = 1.0_wp
end if
end function bf
function sigma ( )
implicit none
CCTK_REAL, dimension(5,5) :: sigma
CCTK_REAL :: zero = 0.0
integer, parameter :: wp = kind(zero)
sigma(1,1) = 4.186595370392226897362216859769846226369_wp
sigma(2,1) = 0.0_wp
sigma(3,1) = 0.0_wp
sigma(4,1) = 0.0_wp
sigma(5,1) = 0.0_wp
sigma(1,2) = 0.0_wp
sigma(2,2) = 0.6725191921225620731888714836983116420871_wp
sigma(3,2) = 0.3613418181134949259370502966736306984367_wp
sigma(4,2) = -0.2021316117293899791481674539631879662707_wp
sigma(5,2) = 0.03455320708729270824077678274955265350304_wp
sigma(1,3) = 0.0_wp
sigma(2,3) = 0.3613418181134949259370502966736306984367_wp
sigma(3,3) = 0.7206133711630147057720442098623847362950_wp
sigma(4,3) = 0.1376472340546569368321616389764958792591_wp
sigma(5,3) = -0.04136405531324488624637892257286207044784_wp
sigma(1,4) = 0.0_wp
sigma(2,4) = -0.2021316117293899791481674539631879662707_wp
sigma(3,4) = 0.1376472340546569368321616389764958792591_wp
sigma(4,4) = 0.9578653607931026822074133441449909689509_wp
sigma(5,4) = 0.02069353627247161734563597102894256809696_wp
sigma(1,5) = 0.0_wp
sigma(2,5) = 0.03455320708729270824077678274955265350304_wp
sigma(3,5) = -0.04136405531324488624637892257286207044784_wp
sigma(4,5) = 0.02069353627247161734563597102894256809696_wp
sigma(5,5) = 0.9908272703370861473007798925906968380654_wp
end function sigma
end subroutine dissipation_4_3_alt
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