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/*@@
@file setupbrilldata2D.F
@date
@author Carsten Gundlach (Cactus 4, Miguel Alcubierre)
@desc
Set up axisymmetric Brill data for elliptic solve.
@enddesc
@version $Header$
@@*/
#include "cctk.h"
#include "cctk_Parameters.h"
#include "cctk_Arguments.h"
#include "CactusEinstein/Einstein/src/Einstein.h"
subroutine setupbrilldata2D(CCTK_ARGUMENTS)
c Set up axisymmetric Brill data for elliptic solve. The elliptic
c equation we need to solve is:
c
c __ 2 2
c \/ psi + psi ( d q + d q ) / 4 = 0
c f z rho
c
c where:
c
c __
c \/ = Flat space Laplacian.
c f
implicit none
DECLARE_CCTK_ARGUMENTS
DECLARE_CCTK_PARAMETERS
integer i,j,k
integer nx,ny,nz
integer ierr
integer, dimension(3) :: sym
CCTK_REAL x1,y1,z1,rho1
CCTK_REAL brillq,eps
CCTK_REAL zp,zm,rhop,rhom
CCTK_REAL zero,one
external brillq
c Numbers.
zero = 0.0D0
one = 1.0D0
c Set up grid size.
nx = cctk_lsh(1)
ny = cctk_lsh(2)
nz = cctk_lsh(3)
c Epsilon for finite differencing.
eps = cctk_delta_space(1)
c Initialize psi.
brillpsi = one
c Initialize metric.
psi = one
gxx = one
gyy = one
gzz = one
gxy = zero
gxz = zero
gyz = zero
c Define the symmetries for the brill GFs.
sym(1) = 1
sym(2) = 1
sym(3) = 1
call SetCartSymVN(ierr,cctkGH,sym,'idbrilldata::brillMlinear')
call SetCartSymVN(ierr,cctkGH,sym,'idbrilldata::brillNsource')
c Set up coefficient arrays for elliptic solve.
c Notice that the Cactus conventions are:
c __
c \/ psi + Mlinear*psi + Nsource = 0
do k=1,nz
do j=1,ny
do i=1,nx
x1 = x(i,j,k)
y1 = y(i,j,k)
z1 = z(i,j,k)
rho1 = dsqrt(x1**2 + y1**2)
c Centered derivatives. Note that here we may be calling brillq
c with a small negative rho, but that should be ok as long as
c brillq is even in rho - physically it must be, or the data
c will not be regular on the axis.
zp = z1 + eps
zm = z1 - eps
rhop = rho1 + eps
rhom = rho1 - eps
brillMlinear(i,j,k) = 0.25D0
. *(brillq(rho1,zp,zero)
. + brillq(rho1,zm,zero)
. + brillq(rhop,z1,zero)
. + brillq(rhom,z1,zero)
. - 4.0D0*brillq(rho1,z1,zero))/eps**2
end do
end do
end do
c Set coefficient Nsource = 0.
brillNsource = zero
c Synchronization and boundaries.
call CCTK_SyncGroup(ierr,cctkGH,'idbrilldata::brillelliptic')
call CartSymGN(ierr,cctkGH,'idbrilldata::brillelliptic')
return
end
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