! $Header$ #include "cctk.h" #include "cctk_Parameters.h" #include "cctk_Functions.h" subroutine dissipation_4_3_opt (var, lsh, gsh, lbnd, bb, gsize, offset, & 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_INT, dimension(6), intent(in) :: offset 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, ol, or CCTK_INT :: nii, njj, nkk 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 nii = ni if ( bb(1) /= 0 ) then nii = nii - offset(1) endif if ( bb(2) /= 0 ) then nii = nii - offset(2) endif allocate ( atmp(nii,nii), d(nii,nii), b(nii,nii), h(nii,nii) ) 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)-offset(1)-offset(2), 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(nii,nii) ) 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 ol = offset(1) rhs(1+ol,:,:) = rhs(1+ol,:,:) + & ( a(1,1) * var(1+ol,:,:) + a(2,1) * var(2+ol,:,:) + & a(3,1) * var(3+ol,:,:) ) * idel rhs(2+ol,:,:) = rhs(2+ol,:,:) + & ( a(1,2) * var(1+ol,:,:) + a(2,2) * var(2+ol,:,:) + & a(3,2) * var(3+ol,:,:) + a(4,2) * var(4+ol,:,:) + & a(5,2) * var(5+ol,:,:) + a(6,2) * var(6+ol,:,:) + & a(7,2) * var(7+ol,:,:) ) * idel rhs(3+ol,:,:) = rhs(3+ol,:,:) + & ( a(1,3) * var(1+ol,:,:) + a(2,3) * var(2+ol,:,:) + & a(3,3) * var(3+ol,:,:) + a(4,3) * var(4+ol,:,:) + & a(5,3) * var(5+ol,:,:) + a(6,3) * var(6+ol,:,:) + & a(7,3) * var(7+ol,:,:) ) * idel rhs(4+ol,:,:) = rhs(4+ol,:,:) + & ( a(1,4) * var(1+ol,:,:) + a(2,4) * var(2+ol,:,:) + & a(3,4) * var(3+ol,:,:) + a(4,4) * var(4+ol,:,:) + & a(5,4) * var(5+ol,:,:) + a(6,4) * var(6+ol,:,:) + & a(7,4) * var(7+ol,:,:) ) * idel rhs(5+ol,:,:) = rhs(5+ol,:,:) + & ( a(1,5) * var(1+ol,:,:) + a(2,5) * var(2+ol,:,:) + & a(3,5) * var(3+ol,:,:) + a(4,5) * var(4+ol,:,:) + & a(5,5) * var(5+ol,:,:) + a(6,5) * var(6+ol,:,:) + & a(7,5) * var(7+ol,:,:) ) * idel il = 6 + ol end if if ( bb(2) == 0 ) then ir = ni - gsize(1) else or = ni - offset(2) rhs(or-4,:,:) = rhs(or-4,:,:) + & ( a(nii-6,nii-4) * var(or-6,:,:) + & a(nii-5,nii-4) * var(or-5,:,:) + & a(nii-4,nii-4) * var(or-4,:,:) + & a(nii-3,nii-4) * var(or-3,:,:) + & a(nii-2,nii-4) * var(or-2,:,:) + & a(nii-1,nii-4) * var(or-1,:,:) + & a(nii,nii-4) * var(or,:,:) ) * idel rhs(or-3,:,:) = rhs(or-3,:,:) + & ( a(nii-6,nii-3) * var(or-6,:,:) + & a(nii-5,nii-3) * var(or-5,:,:) + & a(nii-4,nii-3) * var(or-4,:,:) + & a(nii-3,nii-3) * var(or-3,:,:) + & a(nii-2,nii-3) * var(or-2,:,:) + & a(nii-1,nii-3) * var(or-1,:,:) + & a(nii,nii-3) * var(or,:,:) ) * idel rhs(or-2,:,:) = rhs(or-2,:,:) + & ( a(nii-6,nii-2) * var(or-6,:,:) + & a(nii-5,nii-2) * var(or-5,:,:) + & a(nii-4,nii-2) * var(or-4,:,:) + & a(nii-3,nii-2) * var(or-3,:,:) + & a(nii-2,nii-2) * var(or-2,:,:) + & a(nii-1,nii-2) * var(or-1,:,:) + & a(nii,nii-2) * var(or,:,:) ) * idel rhs(or-1,:,:) = rhs(or-1,:,:) + & ( a(nii-6,nii-1) * var(or-6,:,:) + & a(nii-5,nii-1) * var(or-5,:,:) + & a(nii-4,nii-1) * var(or-4,:,:) + & a(nii-3,nii-1) * var(or-3,:,:) + & a(nii-2,nii-1) * var(or-2,:,:) + & a(nii-1,nii-1) * var(or-1,:,:) + & a(nii,nii-1) * var(or,:,:) ) * idel rhs(or,:,:) = rhs(or,:,:) + & ( a(nii-2,nii) * var(or-2,:,:) + & a(nii-1,nii) * var(or-1,:,:) + & a(nii,nii) * var(or,:,:) ) * idel ir = or - 5 end if if (bb(1) /= 0) then do i = il, ir rhs(i,:,:) = rhs(i,:,:) + & ( a(i-ol-2,i-ol) * var(i-2,:,:) + & a(i-ol-1,i-ol) * var(i-1,:,:) + & a(i-ol,i-ol) * var(i,:,:) + & a(i-ol+1,i-ol) * var(i+1,:,:) + & a(i-ol+2,i-ol) * var(i+2,:,:) ) * idel end do else 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 endif if ( zero_derivs_y == 0 ) then if ( .not. savedy(patch) ) then njj = nj if ( bb(3) /= 0 ) then njj = njj - offset(3) endif if ( bb(4) /= 0 ) then njj = njj - offset(4) endif allocate ( atmp(njj,njj), d(njj,njj), b(njj,njj), h(njj,njj) ) 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)-offset(3)-offset(4), 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(njj,njj) ) 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 ol = offset(3) rhs(:,1+ol,:) = rhs(:,1+ol,:) + & ( a(1,1) * var(:,1+ol,:) + a(2,1) * var(:,2+ol,:) + & a(3,1) * var(:,3+ol,:) ) * idel rhs(:,2+ol,:) = rhs(:,2+ol,:) + & ( a(1,2) * var(:,1+ol,:) + a(2,2) * var(:,2+ol,:) + & a(3,2) * var(:,3+ol,:) + a(4,2) * var(:,4+ol,:) + & a(5,2) * var(:,5+ol,:) + a(6,2) * var(:,6+ol,:) + & a(7,2) * var(:,7+ol,:) ) * idel rhs(:,3+ol,:) = rhs(:,3+ol,:) + & ( a(1,3) * var(:,1+ol,:) + a(2,3) * var(:,2+ol,:) + & a(3,3) * var(:,3+ol,:) + a(4,3) * var(:,4+ol,:) + & a(5,3) * var(:,5+ol,:) + a(6,3) * var(:,6+ol,:) + & a(7,3) * var(:,7+ol,:) ) * idel rhs(:,4+ol,:) = rhs(:,4+ol,:) + & ( a(1,4) * var(:,1+ol,:) + a(2,4) * var(:,2+ol,:) + & a(3,4) * var(:,3+ol,:) + a(4,4) * var(:,4+ol,:) + & a(5,4) * var(:,5+ol,:) + a(6,4) * var(:,6+ol,:) + & a(7,4) * var(:,7+ol,:) ) * idel rhs(:,5+ol,:) = rhs(:,5+ol,:) + & ( a(1,5) * var(:,1+ol,:) + a(2,5) * var(:,2+ol,:) + & a(3,5) * var(:,3+ol,:) + a(4,5) * var(:,4+ol,:) + & a(5,5) * var(:,5+ol,:) + a(6,5) * var(:,6+ol,:) + & a(7,5) * var(:,7+ol,:) ) * idel jl = 6 + ol end if if ( bb(4) == 0 ) then jr = nj - gsize(2) else or = nj - offset(4) rhs(:,or-4,:) = rhs(:,or-4,:) + & ( a(njj-6,njj-4) * var(:,or-6,:) + & a(njj-5,njj-4) * var(:,or-5,:) + & a(njj-4,njj-4) * var(:,or-4,:) + & a(njj-3,njj-4) * var(:,or-3,:) + & a(njj-2,njj-4) * var(:,or-2,:) + & a(njj-1,njj-4) * var(:,or-1,:) + & a(njj,njj-4) * var(:,or,:) ) * idel rhs(:,or-3,:) = rhs(:,or-3,:) + & ( a(njj-6,njj-3) * var(:,or-6,:) + & a(njj-5,njj-3) * var(:,or-5,:) + & a(njj-4,njj-3) * var(:,or-4,:) + & a(njj-3,njj-3) * var(:,or-3,:) + & a(njj-2,njj-3) * var(:,or-2,:) + & a(njj-1,njj-3) * var(:,or-1,:) + & a(njj,njj-3) * var(:,or,:) ) * idel rhs(:,or-2,:) = rhs(:,or-2,:) + & ( a(njj-6,njj-2) * var(:,or-6,:) + & a(njj-5,njj-2) * var(:,or-5,:) + & a(njj-4,njj-2) * var(:,or-4,:) + & a(njj-3,njj-2) * var(:,or-3,:) + & a(njj-2,njj-2) * var(:,or-2,:) + & a(njj-1,njj-2) * var(:,or-1,:) + & a(njj,njj-2) * var(:,or,:) ) * idel rhs(:,or-1,:) = rhs(:,or-1,:) + & ( a(njj-6,njj-1) * var(:,or-6,:) + & a(njj-5,njj-1) * var(:,or-5,:) + & a(njj-4,njj-1) * var(:,or-4,:) + & a(njj-3,njj-1) * var(:,or-3,:) + & a(njj-2,njj-1) * var(:,or-2,:) + & a(njj-1,njj-1) * var(:,or-1,:) + & a(njj,njj-1) * var(:,or,:) ) * idel rhs(:,or,:) = rhs(:,or,:) + & ( a(njj-2,njj) * var(:,or-2,:) + & a(njj-1,njj) * var(:,or-1,:) + & a(njj,njj) * var(:,or,:) ) * idel jr = or - 5 end if if ( bb(3) /= 0 ) then do j = jl, jr rhs(:,j,:) = rhs(:,j,:) + & ( a(j-ol-2,j-ol) * var(:,j-2,:) + & a(j-ol-1,j-ol) * var(:,j-1,:) + & a(j-ol,j-ol) * var(:,j,:) + & a(j-ol+1,j-ol) * var(:,j+1,:) + & a(j-ol+2,j-ol) * var(:,j+2,:) ) * idel end do else 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 endif end if if ( zero_derivs_z == 0 ) then if ( .not. savedz(patch) ) then nkk = nk if ( bb(5) /= 0 ) then nkk = nkk - offset(5) endif if ( bb(6) /= 0 ) then nkk = nkk - offset(6) endif allocate ( atmp(nkk,nkk), d(nkk,nkk), b(nkk,nkk), h(nkk,nkk) ) 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)-offset(5)-offset(6), 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(nkk,nkk) ) 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 ol = offset(5) rhs(:,:,1+ol) = rhs(:,:,1+ol) + & ( a(1,1) * var(:,:,1+ol) + a(2,1) * var(:,:,2+ol) + & a(3,1) * var(:,:,3+ol) ) * idel rhs(:,:,2+ol) = rhs(:,:,2+ol) + & ( a(1,2) * var(:,:,1+ol) + a(2,2) * var(:,:,2+ol) + & a(3,2) * var(:,:,3+ol) + a(4,2) * var(:,:,4+ol) + & a(5,2) * var(:,:,5+ol) + a(6,2) * var(:,:,6+ol) + & a(7,2) * var(:,:,7+ol) ) * idel rhs(:,:,3+ol) = rhs(:,:,3+ol) + & ( a(1,3) * var(:,:,1+ol) + a(2,3) * var(:,:,2+ol) + & a(3,3) * var(:,:,3+ol) + a(4,3) * var(:,:,4+ol) + & a(5,3) * var(:,:,5+ol) + a(6,3) * var(:,:,6+ol) + & a(7,3) * var(:,:,7+ol) ) * idel rhs(:,:,4+ol) = rhs(:,:,4+ol) + & ( a(1,4) * var(:,:,1+ol) + a(2,4) * var(:,:,2+ol) + & a(3,4) * var(:,:,3+ol) + a(4,4) * var(:,:,4+ol) + & a(5,4) * var(:,:,5+ol) + a(6,4) * var(:,:,6+ol) + & a(7,4) * var(:,:,7+ol) ) * idel rhs(:,:,5+ol) = rhs(:,:,5+ol) + & ( a(1,5) * var(:,:,1+ol) + a(2,5) * var(:,:,2+ol) + & a(3,5) * var(:,:,3+ol) + a(4,5) * var(:,:,4+ol) + & a(5,5) * var(:,:,5+ol) + a(6,5) * var(:,:,6+ol) + & a(7,5) * var(:,:,7+ol) ) * idel kl = 6 + ol end if if ( bb(6) == 0 ) then kr = nk - gsize(3) else or = nk - offset(6) rhs(:,:,or-4) = rhs(:,:,or-4) + & ( a(nkk-6,nkk-4) * var(:,:,or-6) + & a(nkk-5,nkk-4) * var(:,:,or-5) + & a(nkk-4,nkk-4) * var(:,:,or-4) + & a(nkk-3,nkk-4) * var(:,:,or-3) + & a(nkk-2,nkk-4) * var(:,:,or-2) + & a(nkk-1,nkk-4) * var(:,:,or-1) + & a(nkk,nkk-4) * var(:,:,or) ) * idel rhs(:,:,or-3) = rhs(:,:,or-3) + & ( a(nkk-6,nkk-3) * var(:,:,or-6) + & a(nkk-5,nkk-3) * var(:,:,or-5) + & a(nkk-4,nkk-3) * var(:,:,or-4) + & a(nkk-3,nkk-3) * var(:,:,or-3) + & a(nkk-2,nkk-3) * var(:,:,or-2) + & a(nkk-1,nkk-3) * var(:,:,or-1) + & a(nkk,nkk-3) * var(:,:,or) ) * idel rhs(:,:,or-2) = rhs(:,:,or-2) + & ( a(nkk-6,nkk-2) * var(:,:,or-6) + & a(nkk-5,nkk-2) * var(:,:,or-5) + & a(nkk-4,nkk-2) * var(:,:,or-4) + & a(nkk-3,nkk-2) * var(:,:,or-3) + & a(nkk-2,nkk-2) * var(:,:,or-2) + & a(nkk-1,nkk-2) * var(:,:,or-1) + & a(nkk,nkk-2) * var(:,:,or) ) * idel rhs(:,:,or-1) = rhs(:,:,or-1) + & ( a(nkk-6,nkk-1) * var(:,:,or-6) + & a(nkk-5,nkk-1) * var(:,:,or-5) + & a(nkk-4,nkk-1) * var(:,:,or-4) + & a(nkk-3,nkk-1) * var(:,:,or-3) + & a(nkk-2,nkk-1) * var(:,:,or-2) + & a(nkk-1,nkk-1) * var(:,:,or-1) + & a(nkk,nkk-1) * var(:,:,or) ) * idel rhs(:,:,or) = rhs(:,:,or) + & ( a(nkk-2,nkk) * var(:,:,or-2) + & a(nkk-1,nkk) * var(:,:,or-1) + & a(nkk,nkk) * var(:,:,or) ) * idel kr = or - 5 end if if ( bb(5) /= 0) then do k = kl, kr rhs(:,:,k) = rhs(:,:,k) + & ( a(k-ol-2,k-ol) * var(:,:,k-2) + & a(k-ol-1,k-ol) * var(:,:,k-1) + & a(k-ol,k-ol) * var(:,:,k) + & a(k-ol+1,k-ol) * var(:,:,k+1) + & a(k-ol+2,k-ol) * var(:,:,k+2) ) * idel end do else 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 endif 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