diff options
Diffstat (limited to 'src/derivs2.F90')
| -rw-r--r-- | src/derivs2.F90 | 109 |
1 files changed, 90 insertions, 19 deletions
diff --git a/src/derivs2.F90 b/src/derivs2.F90 index 4ca51bf..5b7e98a 100644 --- a/src/derivs2.F90 +++ b/src/derivs2.F90 @@ -10,31 +10,102 @@ module derivs2 private public get_2derivs public get_2derivs2 + public get_2derivs3 contains #endif - subroutine get_2derivs (a, f, pos, off, dx) - CCTK_REAL, intent(in) :: a(*) - CCTK_REAL, intent(out) :: f(2) - integer, intent(in) :: pos, off(2) - CCTK_REAL, intent(in) :: dx(2) + subroutine get_2derivs (a, f, pos, off, dx, order) + CCTK_REAL, intent(in) :: a(*) + CCTK_REAL, intent(out) :: f(2) + integer, intent(in) :: pos, off(2) + CCTK_REAL, intent(in) :: dx(2) + integer, intent(in), optional :: order + integer :: order1 integer :: i - do i=1,2 - f(i) = (a(pos+off(i)) - a(pos-off(i))) / (2*dx(i)) - end do + order1 = 2 + if (present(order)) order1 = order + select case (order1) + case (2) + do i=1,2 + f(i) = (a(pos+off(i)) - a(pos-off(i))) / (2*dx(i)) + end do + case (4) + do i=1,2 + f(i) = (- a(pos+2*off(i)) + 8*a(pos+off(i)) - 8*a(pos-off(i)) + a(pos-2*off(i))) / (12*dx(i)) + end do + case default + call CCTK_WARN (0, "Unsupported finite differencing order") + end select end subroutine get_2derivs - subroutine get_2derivs2 (a, f, pos, off, dx) - CCTK_REAL, intent(in) :: a(*) - CCTK_REAL, intent(out) :: f(2,2) - integer, intent(in) :: pos, off(2) - CCTK_REAL, intent(in) :: dx(2) + subroutine get_2derivs2 (a, f, pos, off, dx, order) + CCTK_REAL, intent(in) :: a(*) + CCTK_REAL, intent(out) :: f(2,2) + integer, intent(in) :: pos, off(2) + CCTK_REAL, intent(in) :: dx(2) + integer, intent(in), optional :: order + integer :: order1 integer :: i - do i=1,2 - f(i,i) = (a(pos+off(i)) - 2*a(pos) + a(pos-off(i))) / dx(i)**2 - end do - f(1,2) = ( a(pos-off(1)-off(2)) - a(pos+off(1)-off(2)) & - & - a(pos-off(1)+off(2)) + a(pos+off(1)+off(2))) / (4*dx(1)*dx(2)) - f(2,1) = f(1,2) + order1 = 2 + if (present(order)) order1 = order + select case (order1) + case (2) + do i=1,2 + f(i,i) = (a(pos+off(i)) - 2*a(pos) + a(pos-off(i))) / dx(i)**2 + end do + f(1,2) = ( a(pos-off(1)-off(2)) - a(pos+off(1)-off(2)) & + & - a(pos-off(1)+off(2)) + a(pos+off(1)+off(2))) / (4*dx(1)*dx(2)) + f(2,1) = f(1,2) + case (4) + do i=1,2 + f(i,i) = (- a(pos-2*off(i)) + 16*a(pos-off(i)) - 30*a(pos) + 16*a(pos+off(i)) - a(pos+2*off(i))) / (12*dx(i)**2) + end do + f(1,2) = ( a(pos+2*off(1)+2*off(2)) - 8*a(pos+off(1)+2*off(2)) + 8*a(pos-off(1)+2*off(2)) - a(pos-2*off(1)+2*off(2)) & + & - 8*a(pos+2*off(1)+ off(2)) + 64*a(pos+off(1)+ off(2)) - 64*a(pos-off(1)+ off(2)) + 8*a(pos-2*off(1)+ off(2)) & + & + 8*a(pos+2*off(1)- off(2)) - 64*a(pos+off(1)- off(2)) + 64*a(pos-off(1)- off(2)) - 8*a(pos-2*off(1)- off(2)) & + & - a(pos+2*off(1)-2*off(2)) + 8*a(pos+off(1)-2*off(2)) - 8*a(pos-off(1)-2*off(2)) + a(pos-2*off(1)-2*off(2))) / (144*dx(1)*dx(2)) + f(2,1) = f(1,2) + case default + call CCTK_WARN (0, "Unsupported finite differencing order") + end select end subroutine get_2derivs2 + subroutine get_2derivs3 (a, f, pos, off, dx, order) + CCTK_REAL, intent(in) :: a(*) + CCTK_REAL, intent(out) :: f(2,2,2) + integer, intent(in) :: pos, off(2) + CCTK_REAL, intent(in) :: dx(2) + integer, intent(in), optional :: order + integer :: order1 + order1 = 2 + if (present(order)) order1 = order + select case (order1) + case (2) + f(1,1,1) = (a(pos+2*off(1)) - 2*a(pos+off(1)) + 2*a(pos-off(1)) - a(pos-2*off(1))) / (2*dx(1)**3) + f(2,1,1) = (a(pos+off(1)+off(2)) - 2*a(pos+off(2)) + a(pos-off(1)+off(2)) - a(pos+off(1)-off(2)) + 2*a(pos-off(2)) - a(pos-off(1)-off(2))) / (2*dx(1)*dx(1)*dx(2)) + f(1,2,1) = f(2,1,1) + f(2,2,1) = (a(pos+off(1)+off(2)) - 2*a(pos+off(1)) + a(pos+off(1)-off(2)) - a(pos-off(1)+off(2)) + 2*a(pos-off(1)) - a(pos-off(1)-off(2))) / (2*dx(1)*dx(2)*dx(2)) + f(:,1,2) = f(:,2,1) + f(1,2,2) = f(2,2,1) + f(2,2,2) = (a(pos+2*off(2)) - 2*a(pos+off(2)) + 2*a(pos-off(2)) - a(pos-2*off(2))) / (2*dx(2)**3) + case (4) + ! [+1 -8 +13 0 -13 +8 -1] / 8 + f(1,1,1) = (a(pos-3*off(1)) - 8*a(pos-2*off(1)) + 13*a(pos-off(1)) - 13*a(pos+off(1)) + 8*a(pos+2*off(1)) - a(pos+3*off(1))) / (8*dx(1)**3) + ! [-1 +8 0 -8 +1] / 12 + ! [-1 +16 -30 +16 -1] / 12 + f(2,1,1) = (+ a(pos-2*off(1)-2*off(2)) - 16*a(pos-off(1)-2*off(2)) + 30*a(pos-2*off(2)) - 16*a(pos+off(1)-2*off(2)) + a(pos+2*off(1)-2*off(2)) & + & - 8*a(pos-2*off(1)- off(2)) + 128*a(pos-off(1)- off(2)) - 240*a(pos- off(2)) + 128*a(pos+off(1)- off(2)) - 8*a(pos+2*off(1)- off(2)) & + & + 8*a(pos-2*off(1)+ off(2)) - 128*a(pos-off(1)+ off(2)) + 240*a(pos+ off(2)) - 128*a(pos+off(1)+ off(2)) + 8*a(pos+2*off(1)+ off(2)) & + & - a(pos-2*off(1)+2*off(2)) + 16*a(pos-off(1)+2*off(2)) - 30*a(pos+2*off(2)) + 16*a(pos+off(1)+2*off(2)) - a(pos+2*off(1)+2*off(2))) / (144*dx(1)**2*dx(2)) + f(1,2,1) = f(2,1,1) + f(2,2,1) = (+ a(pos-2*off(2)-2*off(1)) - 16*a(pos-off(2)-2*off(1)) + 30*a(pos-2*off(1)) - 16*a(pos+off(2)-2*off(1)) + a(pos+2*off(2)-2*off(1)) & + & - 8*a(pos-2*off(2)- off(1)) + 128*a(pos-off(2)- off(1)) - 240*a(pos- off(1)) + 128*a(pos+off(2)- off(1)) - 8*a(pos+2*off(2)- off(1)) & + & + 8*a(pos-2*off(2)+ off(1)) - 128*a(pos-off(2)+ off(1)) + 240*a(pos+ off(1)) - 128*a(pos+off(2)+ off(1)) + 8*a(pos+2*off(2)+ off(1)) & + & - a(pos-2*off(2)+2*off(1)) + 16*a(pos-off(2)+2*off(1)) - 30*a(pos+2*off(1)) + 16*a(pos+off(2)+2*off(1)) - a(pos+2*off(2)+2*off(1))) / (144*dx(2)**2*dx(1)) + f(:,1,2) = f(:,2,1) + f(1,2,2) = f(2,2,1) + f(2,2,2) = (a(pos-3*off(2)) - 8*a(pos-2*off(2)) + 13*a(pos-off(2)) - 13*a(pos+off(2)) + 8*a(pos+2*off(2)) - a(pos+3*off(2))) / (8*dx(2)**3) + case default + call CCTK_WARN (0, "Unsupported finite differencing order") + end select + end subroutine get_2derivs3 #ifndef TGR_INCLUDED end module derivs2 #endif |