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! $Header$
#ifndef TGR_INCLUDED
#include "cctk.h"
#include "cctk_Parameters.h"
module derivs2
implicit none
private
public get_2derivs
public get_2derivs2
public get_2derivs3
contains
#endif
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
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, 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
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
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