! $Header$ #include "cctk.h" #include "cctk_Parameters.h" #include "cctk_Functions.h" subroutine dissipation_6_5_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, 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, 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), tmp(nii,nii) ) atmp = zero; d = zero; b = zero; h = zero; tmp = zero 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) ) 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)-offset(1)-offset(2)) / 2 ir = center + max(gsize(1),3) call set_dmatrix_half ( d(1:ir,1:ir), 1 ) tmp(1:ir,1:ir) = matmul ( b(1:ir,1:ir), d(1:ir,1:ir) ) tmp(1:ir,1:ir) = matmul ( transpose ( d(1:ir,1:ir) ), tmp(1:ir,1:ir) ) tmp(1:ir,1:ir) = matmul ( h(1:ir,1:ir), tmp(1:ir,1:ir) ) tmp(1:ir,1:ir) = -transpose ( tmp(1:ir,1:ir) ) atmp(1:ir,1:center) = tmp(1:ir,1:center) il = center + 1 - max(gsize(1),3) d = zero call set_dmatrix_half ( d(il:nii,il:nii), 2 ) tmp(il:nii,il:nii) = matmul ( b(il:nii,il:nii), d(il:nii,il:nii) ) tmp(il:nii,il:nii) = matmul ( transpose ( d(il:nii,il:nii) ), tmp(il:nii,il:nii) ) tmp(il:nii,il:nii) = matmul ( h(il:nii,il:nii), tmp(il:nii,il:nii) ) tmp(il:nii,il:nii) = -transpose ( tmp(il:nii,il:nii) ) atmp(il:nii,center+1:nii) = tmp(il:nii,center+1:nii) end if allocate ( xcoeff(patch)%coeff(nii,nii) ) xcoeff(patch)%coeff = atmp savedx(patch) = .true. deallocate ( atmp, d, b, h, tmp ) end if a => xcoeff(patch)%coeff if ( scale_with_h > 0 ) then idel = epsilon / ( 64 * delta(1) ) else idel = epsilon / 64 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,:,:) + a(4,1) * var(4+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,:,:) + a(8,2) * var(8+ol,:,:) + & a(9,2) * var(9+ol,:,:) + a(10,2) * var(10+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,:,:) + a(8,3) * var(8+ol,:,:) + & a(9,3) * var(9+ol,:,:) + a(10,3) * var(10+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,:,:) + a(8,4) * var(8+ol,:,:) + & a(9,4) * var(9+ol,:,:) + a(10,4) * var(10+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,:,:) + a(8,5) * var(8+ol,:,:) + & a(9,5) * var(9+ol,:,:) + a(10,5) * var(10+ol,:,:) ) * idel rhs(6+ol,:,:) = rhs(6+ol,:,:) + & ( a(1,6) * var(1+ol,:,:) + a(2,6) * var(2+ol,:,:) + & a(3,6) * var(3+ol,:,:) + a(4,6) * var(4+ol,:,:) + & a(5,6) * var(5+ol,:,:) + a(6,6) * var(6+ol,:,:) + & a(7,6) * var(7+ol,:,:) + a(8,6) * var(8+ol,:,:) + & a(9,6) * var(9+ol,:,:) + a(10,6) * var(10+ol,:,:) ) * idel rhs(7+ol,:,:) = rhs(7+ol,:,:) + & ( a(1,7) * var(1+ol,:,:) + a(2,7) * var(2+ol,:,:) + & a(3,7) * var(3+ol,:,:) + a(4,7) * var(4+ol,:,:) + & a(5,7) * var(5+ol,:,:) + a(6,7) * var(6+ol,:,:) + & a(7,7) * var(7+ol,:,:) + a(8,7) * var(8+ol,:,:) + & a(9,7) * var(9+ol,:,:) + a(10,7) * var(10+ol,:,:) ) * idel il = 8 + ol end if if ( bb(2) == 0 ) then ir = ni - gsize(1) else or = ni - offset(2) rhs(or-6,:,:) = rhs(or-6,:,:) + & ( a(nii-9,nii-6) * var(or-9,:,:) + & a(nii-8,nii-6) * var(or-8,:,:) + & a(nii-7,nii-6) * var(or-7,:,:) + & a(nii-6,nii-6) * var(or-6,:,:) + & a(nii-5,nii-6) * var(or-5,:,:) + & a(nii-4,nii-6) * var(or-4,:,:) + & a(nii-3,nii-6) * var(or-3,:,:) + & a(nii-2,nii-6) * var(or-2,:,:) + & a(nii-1,nii-6) * var(or-1,:,:) + & a(nii,nii-6) * var(or,:,:) ) * idel rhs(or-5,:,:) = rhs(or-5,:,:) + & ( a(nii-9,nii-5) * var(or-9,:,:) + & a(nii-8,nii-5) * var(or-8,:,:) + & a(nii-7,nii-5) * var(or-7,:,:) + & a(nii-6,nii-5) * var(or-6,:,:) + & a(nii-5,nii-5) * var(or-5,:,:) + & a(nii-4,nii-5) * var(or-4,:,:) + & a(nii-3,nii-5) * var(or-3,:,:) + & a(nii-2,nii-5) * var(or-2,:,:) + & a(nii-1,nii-5) * var(or-1,:,:) + & a(nii,nii-5) * var(or,:,:) ) * idel rhs(or-4,:,:) = rhs(or-4,:,:) + & ( a(nii-9,nii-4) * var(or-9,:,:) + & a(nii-8,nii-4) * var(or-8,:,:) + & a(nii-7,nii-4) * var(or-7,:,:) + & 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-9,nii-3) * var(or-9,:,:) + & a(nii-8,nii-3) * var(or-8,:,:) + & a(nii-7,nii-3) * var(or-7,:,:) + & 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-9,nii-2) * var(or-9,:,:) + & a(nii-8,nii-2) * var(or-8,:,:) + & a(nii-7,nii-2) * var(or-7,:,:) + & 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-9,nii-1) * var(or-9,:,:) + & a(nii-8,nii-1) * var(or-8,:,:) + & a(nii-7,nii-1) * var(or-7,:,:) + & 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-3,nii) * var(or-3,:,:) + & a(nii-2,nii) * var(or-2,:,:) + & a(nii-1,nii) * var(or-1,:,:) + & a(nii,nii) * var(or,:,:) ) * idel ir = or - 7 end if if ( bb(1) /= 0) then do i = il, ir rhs(i,:,:) = rhs(i,:,:) + & ( a(i-ol-3,i-ol) * var(i-3,:,:) + & 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,:,:) + & a(i-ol+3,i-ol) * var(i+3,:,:) ) * idel end do else 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 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), tmp(njj,njj) ) atmp = zero; d = zero; b = zero; h = zero; tmp = zero 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) ) 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)-offset(3)-offset(4)) / 2 jr = center + max(gsize(2),3) call set_dmatrix_half ( d(1:jr,1:jr), 1 ) tmp(1:jr,1:jr) = matmul ( b(1:jr,1:jr), d(1:jr,1:jr) ) tmp(1:jr,1:jr) = matmul ( transpose ( d(1:jr,1:jr) ), tmp(1:jr,1:jr) ) tmp(1:jr,1:jr) = matmul ( h(1:jr,1:jr), tmp(1:jr,1:jr) ) tmp(1:jr,1:jr) = -transpose ( tmp(1:jr,1:jr) ) atmp(1:jr,1:center) = tmp(1:jr,1:center) jl = center + 1 - max(gsize(2),3) d = zero call set_dmatrix_half ( d(jl:njj,jl:njj), 2 ) tmp(jl:njj,jl:njj) = -transpose ( & matmul ( h(jl:njj,jl:njj), & matmul ( & transpose ( d(jl:njj,jl:njj) ), & matmul ( b(jl:njj,jl:njj), & d(jl:njj,jl:njj) ) ) ) ) atmp(jl:njj,center+1:njj) = tmp(jl:njj,center+1:njj) end if allocate ( ycoeff(patch)%coeff(njj,njj) ) ycoeff(patch)%coeff = atmp savedy(patch) = .true. deallocate ( atmp, d, b, h, tmp ) end if a => ycoeff(patch)%coeff if ( scale_with_h > 0 ) then idel = epsilon / ( 64 * delta(2) ) else idel = epsilon / 64 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,:) + a(4,1) * var(:,4+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,:) + a(8,2) * var(:,8+ol,:) + & a(9,2) * var(:,9+ol,:) + a(10,2) * var(:,10+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,:) + a(8,3) * var(:,8+ol,:) + & a(9,3) * var(:,9+ol,:) + a(10,3) * var(:,10+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,:) + a(8,4) * var(:,8+ol,:) + & a(9,4) * var(:,9+ol,:) + a(10,4) * var(:,10+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,:) + a(8,5) * var(:,8+ol,:) + & a(9,5) * var(:,9+ol,:) + a(10,5) * var(:,10+ol,:) ) * idel rhs(:,6+ol,:) = rhs(:,6+ol,:) + & ( a(1,6) * var(:,1+ol,:) + a(2,6) * var(:,2+ol,:) + & a(3,6) * var(:,3+ol,:) + a(4,6) * var(:,4+ol,:) + & a(5,6) * var(:,5+ol,:) + a(6,6) * var(:,6+ol,:) + & a(7,6) * var(:,7+ol,:) + a(8,6) * var(:,8+ol,:) + & a(9,6) * var(:,9+ol,:) + a(10,6) * var(:,10+ol,:) ) * idel rhs(:,7+ol,:) = rhs(:,7+ol,:) + & ( a(1,7) * var(:,1+ol,:) + a(2,7) * var(:,2+ol,:) + & a(3,7) * var(:,3+ol,:) + a(4,7) * var(:,4+ol,:) + & a(5,7) * var(:,5+ol,:) + a(6,7) * var(:,6+ol,:) + & a(7,7) * var(:,7+ol,:) + a(8,7) * var(:,8+ol,:) + & a(9,7) * var(:,9+ol,:) + a(10,7) * var(:,10+ol,:) ) * idel jl = 8 + ol end if if ( bb(4) == 0 ) then jr = nj - gsize(2) else or = nj - offset(4) rhs(:,or-6,:) = rhs(:,or-6,:) + & ( a(njj-9,njj-6) * var(:,or-9,:) + & a(njj-8,njj-6) * var(:,or-8,:) + & a(njj-7,njj-6) * var(:,or-7,:) + & a(njj-6,njj-6) * var(:,or-6,:) + & a(njj-5,njj-6) * var(:,or-5,:) + & a(njj-4,njj-6) * var(:,or-4,:) + & a(njj-3,njj-6) * var(:,or-3,:) + & a(njj-2,njj-6) * var(:,or-2,:) + & a(njj-1,njj-6) * var(:,or-1,:) + & a(njj,njj-6) * var(:,or,:) ) * idel rhs(:,or-5,:) = rhs(:,or-5,:) + & ( a(njj-9,njj-5) * var(:,or-9,:) + & a(njj-8,njj-5) * var(:,or-8,:) + & a(njj-7,njj-5) * var(:,or-7,:) + & a(njj-6,njj-5) * var(:,or-6,:) + & a(njj-5,njj-5) * var(:,or-5,:) + & a(njj-4,njj-5) * var(:,or-4,:) + & a(njj-3,njj-5) * var(:,or-3,:) + & a(njj-2,njj-5) * var(:,or-2,:) + & a(njj-1,njj-5) * var(:,or-1,:) + & a(njj,njj-5) * var(:,or,:) ) * idel rhs(:,or-4,:) = rhs(:,or-4,:) + & ( a(njj-9,njj-4) * var(:,or-9,:) + & a(njj-8,njj-4) * var(:,or-8,:) + & a(njj-7,njj-4) * var(:,or-7,:) + & 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-9,njj-3) * var(:,or-9,:) + & a(njj-8,njj-3) * var(:,or-8,:) + & a(njj-7,njj-3) * var(:,or-7,:) + & 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-9,njj-2) * var(:,or-9,:) + & a(njj-8,njj-2) * var(:,or-8,:) + & a(njj-7,njj-2) * var(:,or-7,:) + & 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-9,njj-1) * var(:,or-9,:) + & a(njj-8,njj-1) * var(:,or-8,:) + & a(njj-7,njj-1) * var(:,or-7,:) + & 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-3,njj) * var(:,or-3,:) + & a(njj-2,njj) * var(:,or-2,:) + & a(njj-1,njj) * var(:,or-1,:) + & a(njj,njj) * var(:,or,:) ) * idel jr = or - 7 end if if ( bb(3) /= 0 ) then do j = jl, jr rhs(:,j,:) = rhs(:,j,:) + & ( a(j-ol-3,j-ol) * var(:,j-3,:) + & 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,:) + & a(j-ol+3,j-ol) * var(:,j+3,:) ) * idel end do else 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 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), tmp(nkk,nkk) ) atmp = zero; d = zero; b = zero; h = zero; tmp = zero 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) ) 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)-offset(5)-offset(6)) / 2 kr = center + max(gsize(3),3) call set_dmatrix_half ( d(1:kr,1:kr), 1 ) tmp(1:kr,1:kr) = -transpose ( & matmul ( h(1:kr,1:kr), & matmul ( & transpose ( d(1:kr,1:kr) ), & matmul ( b(1:kr,1:kr), & d(1:kr,1:kr) ) ) ) ) atmp(1:kr,1:center) = tmp(1:kr,1:center) kl = center + 1 - max(gsize(3),3) d = zero call set_dmatrix_half ( d(kl:nkk,kl:nkk), 2 ) tmp(kl:nkk,kl:nkk) = -transpose ( & matmul ( h(kl:nkk,kl:nkk), & matmul ( & transpose ( d(kl:nkk,kl:nkk) ), & matmul ( b(kl:nkk,kl:nkk), & d(kl:nkk,kl:nkk) ) ) ) ) atmp(kl:nkk,center+1:nkk) = tmp(kl:nkk,center+1:nkk) end if allocate ( zcoeff(patch)%coeff(nkk,nkk) ) zcoeff(patch)%coeff = atmp savedz(patch) = .true. deallocate ( atmp, d, b, h, tmp ) end if a => zcoeff(patch)%coeff if ( scale_with_h > 0 ) then idel = epsilon / ( 64 * delta(3) ) else idel = epsilon / 64 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) + a(4,1) * var(:,:,4+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) + a(8,2) * var(:,:,8+ol) + & a(9,2) * var(:,:,9+ol) + a(10,2) * var(:,:,10+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) + a(8,3) * var(:,:,8+ol) + & a(9,3) * var(:,:,9+ol) + a(10,3) * var(:,:,10+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) + a(8,4) * var(:,:,8+ol) + & a(9,4) * var(:,:,9+ol) + a(10,4) * var(:,:,10+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) + a(8,5) * var(:,:,8+ol) + & a(9,5) * var(:,:,9+ol) + a(10,5) * var(:,:,10+ol) ) * idel rhs(:,:,6+ol) = rhs(:,:,6+ol) + & ( a(1,6) * var(:,:,1+ol) + a(2,6) * var(:,:,2+ol) + & a(3,6) * var(:,:,3+ol) + a(4,6) * var(:,:,4+ol) + & a(5,6) * var(:,:,5+ol) + a(6,6) * var(:,:,6+ol) + & a(7,6) * var(:,:,7+ol) + a(8,6) * var(:,:,8+ol) + & a(9,6) * var(:,:,9+ol) + a(10,6) * var(:,:,10+ol) ) * idel rhs(:,:,7+ol) = rhs(:,:,7+ol) + & ( a(1,7) * var(:,:,1+ol) + a(2,7) * var(:,:,2+ol) + & a(3,7) * var(:,:,3+ol) + a(4,7) * var(:,:,4+ol) + & a(5,7) * var(:,:,5+ol) + a(6,7) * var(:,:,6+ol) + & a(7,7) * var(:,:,7+ol) + a(8,7) * var(:,:,8+ol) + & a(9,7) * var(:,:,9+ol) + a(10,7) * var(:,:,10+ol) ) * idel kl = 8 + ol end if if ( bb(6) == 0 ) then kr = nk - gsize(3) else or = nk - offset(6) rhs(:,:,or-6) = rhs(:,:,or-6) + & ( a(nkk-9,nkk-6) * var(:,:,or-9) + & a(nkk-8,nkk-6) * var(:,:,or-8) + & a(nkk-7,nkk-6) * var(:,:,or-7) + & a(nkk-6,nkk-6) * var(:,:,or-6) + & a(nkk-5,nkk-6) * var(:,:,or-5) + & a(nkk-4,nkk-6) * var(:,:,or-4) + & a(nkk-3,nkk-6) * var(:,:,or-3) + & a(nkk-2,nkk-6) * var(:,:,or-2) + & a(nkk-1,nkk-6) * var(:,:,or-1) + & a(nkk,nkk-6) * var(:,:,or) ) * idel rhs(:,:,or-5) = rhs(:,:,or-5) + & ( a(nkk-9,nkk-5) * var(:,:,or-9) + & a(nkk-8,nkk-5) * var(:,:,or-8) + & a(nkk-7,nkk-5) * var(:,:,or-7) + & a(nkk-6,nkk-5) * var(:,:,or-6) + & a(nkk-5,nkk-5) * var(:,:,or-5) + & a(nkk-4,nkk-5) * var(:,:,or-4) + & a(nkk-3,nkk-5) * var(:,:,or-3) + & a(nkk-2,nkk-5) * var(:,:,or-2) + & a(nkk-1,nkk-5) * var(:,:,or-1) + & a(nkk,nkk-5) * var(:,:,or) ) * idel rhs(:,:,or-4) = rhs(:,:,or-4) + & ( a(nkk-9,nkk-4) * var(:,:,or-9) + & a(nkk-8,nkk-4) * var(:,:,or-8) + & a(nkk-7,nkk-4) * var(:,:,or-7) + & 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-9,nkk-3) * var(:,:,or-9) + & a(nkk-8,nkk-3) * var(:,:,or-8) + & a(nkk-7,nkk-3) * var(:,:,or-7) + & 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-9,nkk-2) * var(:,:,or-9) + & a(nkk-8,nkk-2) * var(:,:,or-8) + & a(nkk-7,nkk-2) * var(:,:,or-7) + & 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-9,nkk-1) * var(:,:,or-9) + & a(nkk-8,nkk-1) * var(:,:,or-8) + & a(nkk-7,nkk-1) * var(:,:,or-7) + & 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-3,nkk) * var(:,:,or-3) + & a(nkk-2,nkk) * var(:,:,or-2) + & a(nkk-1,nkk) * var(:,:,or-1) + & a(nkk,nkk) * var(:,:,or) ) * idel kr = or - 7 end if if ( bb(5) /= 0 ) then do k = kl, kr rhs(:,:,k) = rhs(:,:,k) + & ( a(k-ol-3,k-ol) * var(:,:,k-3) + & 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) + & a(k-ol+3,k-ol) * var(:,:,k+3) ) * idel end do else 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 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(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(1:7,1:7) = sigma ( ) end if if ( bb(2) /= 0 ) then h(n:n-6:-1,n:n-6:-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 :: h2, h21, xp2, xp3 CCTK_REAL :: zero = 0.0 integer, parameter :: wp = kind(zero) if ( x < xp ) then h2 = h**2 h21 = 1.0_wp - h2 xp2 = 1.0_wp / xp**2 xp3 = xp2 / xp bf = ( -2.0_wp * h21 * xp3 * x + 3.0_wp * h21 * xp2 ) * x**2 + h2 else if ( x > xmax - xp ) then h2 = h**2 h21 = 1.0_wp - h2 xp2 = 1.0_wp / xp**2 xp3 = xp2 / xp bf = ( 2.0_wp * h21 * xp3 * ( x - xmax ) + & 3.0_wp * h21 * xp2 ) * ( x - xmax )**2 + h2 else bf = 1.0_wp end if end function bf function sigma ( ) implicit none CCTK_REAL, dimension(7,7) :: sigma CCTK_REAL :: zero = 0.0 integer, parameter :: wp = kind(zero) sigma(1,1) = 4.930709842221048047321555312222552006914_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(6,1) = 0.0_wp sigma(7,1) = 0.0_wp sigma(1,2) = 0.0_wp sigma(2,2) = 1.499128158967098993672808967791430710830_wp sigma(3,2) = 0.8363320637711490458766332755492551638364_wp sigma(4,2) = -0.2634194189384563273844251938374368097488_wp sigma(5,2) = -0.1281142262970477369698649073120970227895_wp sigma(6,2) = -0.1830121923043950334684235233648902467425_wp sigma(7,2) = 0.01275879120879511857581469566228951245742_wp sigma(1,3) = 0.0_wp sigma(2,3) = 0.8363320637711490458766332755492551638364_wp sigma(3,3) = 0.8785380112113613457715293301885586949116_wp sigma(4,3) = 0.1454039706555408804118493444561963110723_wp sigma(5,3) = -0.03346859376328961536059718572568704595897_wp sigma(6,3) = -0.1759548942026651677201193466207997400242_wp sigma(7,3) = 0.02020404709761823823384626194775259449799_wp sigma(1,4) = 0.0_wp sigma(2,4) = -0.2634194189384563273844251938374368097488_wp sigma(3,4) = 0.1454039706555408804118493444561963110723_wp sigma(4,4) = 0.5690707861055695191099807759535994201984_wp sigma(5,4) = 0.3374169937858825026860519890688362591356_wp sigma(6,4) = -0.03076801586199402080957339555604653302670_wp sigma(7,4) = 0.004077760901760668929595481886645691229036_wp sigma(1,5) = 0.0_wp sigma(2,5) = -0.1281142262970477369698649073120970227895_wp sigma(3,5) = -0.03346859376328961536059718572568704595897_wp sigma(4,5) = 0.3374169937858825026860519890688362591356_wp sigma(5,5) = 0.5001980842834785426891480539161939116986_wp sigma(6,5) = 0.2904403943485980286998891564955850119600_wp sigma(7,5) = -0.05655813410599246578174268632557910837116_wp sigma(1,6) = 0.0_wp sigma(2,6) = -0.1830121923043950334684235233648902467425_wp sigma(3,6) = -0.1759548942026651677201193466207997400242_wp sigma(4,6) = -0.03076801586199402080957339555604653302670_wp sigma(5,6) = 0.2904403943485980286998891564955850119600_wp sigma(6,6) = 0.8640467497799918355533313312208192675134_wp sigma(7,6) = 0.03704582714017916999084939064121697271831_wp sigma(1,7) = 0.0_wp sigma(2,7) = 0.01275879120879511857581469566228951245742_wp sigma(3,7) = 0.02020404709761823823384626194775259449799_wp sigma(4,7) = 0.004077760901760668929595481886645691229036_wp sigma(5,7) = -0.05655813410599246578174268632557910837116_wp sigma(6,7) = 0.03704582714017916999084939064121697271831_wp sigma(7,7) = 0.9909401061257062767072573096147576992963_wp end function sigma end subroutine dissipation_6_5_opt