! $Header$ #include "cctk.h" #include "cctk_Parameters.h" #include "cctk_Functions.h" subroutine dissipation_4_3_opt (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 CCTK_REAL, dimension(:,:), allocatable :: atmp, d, b, h 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) ) atmp = zero; d = zero; b = zero; h = zero call set_dmatrix ( d, bb(1:2) ) call set_bmatrix ( b, bb(1:2), lsh(1), gsh(1), lbnd(1), delta(1), dfl(1) ) call set_hmatrix ( h, bb(1:2) ) atmp = -transpose ( matmul ( h, matmul ( transpose(d), matmul ( b, d ) ) ) ) allocate ( xcoeff(patch)%coeff(ni,ni) ) xcoeff(patch)%coeff = atmp savedx(patch) = .true. deallocate ( atmp, d, b, h ) end if a => xcoeff(patch)%coeff if ( scale_with_h > 0 ) then idel = epsilon / ( 16 * delta(1) ) else idel = epsilon / 16 end if 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,:,:) ) * 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,:,:) ) * 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,:,:) ) * 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,:,:) ) * 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,:,:) ) * idel il = 6 end if if ( bb(2) == 0 ) then ir = ni - gsize(1) else rhs(ni-4,:,:) = rhs(ni-4,:,:) + & ( 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-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-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-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-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-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,:,:) ) * 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) ) atmp = zero; d = zero; b = zero; h = zero call set_dmatrix ( d, bb(3:4) ) call set_bmatrix ( b, bb(3:4), lsh(2), gsh(2), lbnd(2), delta(2), dfl(2) ) call set_hmatrix ( h, bb(3:4) ) atmp = -transpose ( matmul ( h, matmul ( transpose(d), matmul ( b, d ) ) ) ) allocate ( ycoeff(patch)%coeff(nj,nj) ) ycoeff(patch)%coeff = atmp savedy(patch) = .true. deallocate ( atmp, d, b, h ) end if a => ycoeff(patch)%coeff if ( scale_with_h > 0 ) then idel = epsilon / ( 16 * delta(2) ) else idel = epsilon / 16 end if 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,:) ) * 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,:) ) * 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,:) ) * 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,:) ) * 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,:) ) * idel jl = 6 end if if ( bb(4) == 0 ) then jr = nj - gsize(2) else rhs(:,nj-4,:) = rhs(:,nj-4,:) + & ( 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-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-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-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-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-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,:) ) * 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) ) atmp = zero; d = zero; b = zero; h = zero call set_dmatrix ( d, bb(5:6) ) call set_bmatrix ( b, bb(5:6), lsh(3), gsh(3), lbnd(3), delta(3), dfl(3) ) call set_hmatrix ( h, bb(5:6) ) atmp = -transpose ( matmul ( h, matmul ( transpose(d), matmul ( b, d ) ) ) ) allocate ( zcoeff(patch)%coeff(nk,nk) ) zcoeff(patch)%coeff = atmp savedz(patch) = .true. deallocate ( atmp, d, b, h ) end if a => zcoeff(patch)%coeff if ( scale_with_h > 0 ) then idel = epsilon / ( 16 * delta(3) ) else idel = epsilon / 16 end if 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) ) * 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) ) * 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) ) * 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) ) * 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) ) * idel kl = 6 end if if ( bb(6) == 0 ) then kr = nk - gsize(3) else rhs(:,:,nk-4) = rhs(:,:,nk-4) + & ( 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-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-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-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-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-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) ) * 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(3), save :: ac = (/ 1.0_wp, -2.0_wp, 1.0_wp /) CCTK_INT :: i n = size(d,1) if ( bb(1) == 0 ) then d(1,1:2) = ac(2:3) else d(1,1:3) = ac end if if ( bb(2) == 0 ) then d(n,n-1:n) = ac(1:2) else d(n,n-2:n) = ac end if do i = 2, n-1 d(i,i-1:i+1) = ac end do end subroutine set_dmatrix 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, 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_opt