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/*@@
@file setupbrilldata3D.F
@date October 1998
@author Miguel Alcubierre
@desc
Set up non-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 setupbrilldata3D(CCTK_ARGUMENTS)
c Set up 3D Brill data for elliptic solve. The elliptic
c equation we need to solve is:
c
c __
c \/ psi - psi R / 8 = 0
c c c
c
c where:
c __
c \/ = Laplacian operator for conformal metric.
c c
c
c R = Ricci scalar for conformal metric.
c c
c
c The Ricci scalar for the conformal metric turns out to be:
c
c / -2q 2 2 -2 2 2 \
c R = - 2 | e ( d q + d q ) + rho ( 3 (d q) + 2 d q ) |
c c \ z rho phi phi /
implicit none
DECLARE_CCTK_ARGUMENTS
DECLARE_CCTK_PARAMETERS
integer CCTK_Equals
integer i,j,k
integer nx,ny,nz
integer ierr
integer, dimension(3) :: sym
CCTK_REAL x1,y1,z1,rho1,rho2
CCTK_REAL phi,phif,e2q
CCTK_REAL brillq,rhofudge,eps
CCTK_REAL zero,one,two,three
c Set up grid size.
nx = cctk_lsh(1)
ny = cctk_lsh(2)
nz = cctk_lsh(3)
c Define numbers
zero = 0.0D0
one = 1.0D0
two = 2.0D0
three = 3.0D0
c Parameters.
rhofudge = brill_rhofudge
c Epsilon for finite differencing.
eps = cctk_delta_space(1)
c Initialize psi.
brillpsi = one
c Set up conformal metric.
psi = one
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)
rho2 = x1**2 + y1**2
rho1 = dsqrt(rho2)
phi = phif(x1,y1)
e2q = dexp(two*brillq(rho1,z1,phi))
if (rho1.gt.rhofudge) then
gxx(i,j,k) = e2q + (one - e2q)*y1**2/rho2
gyy(i,j,k) = e2q + (one - e2q)*x1**2/rho2
gzz(i,j,k) = e2q
gxy(i,j,k) = - (one - e2q)*x1*y1/rho2
else
gxx(i,j,k) = one
gyy(i,j,k) = one
gzz(i,j,k) = one
gxy(i,j,k) = zero
end if
end do
end do
end do
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)
rho2 = x1**2 + y1**2
rho1 = dsqrt(rho2)
phi = phif(x1,y1)
e2q = dexp(two*brillq(rho1,z1,phi))
c Find M using centered differences over a small
c interval.
if (rho1.gt.rhofudge) then
brillMlinear(i,j,k) = 0.25D0/e2q
. *(brillq(rho1,z1+eps,phi)
. + brillq(rho1,z1-eps,phi)
. + brillq(rho1+eps,z1,phi)
. + brillq(rho1-eps,z1,phi)
. - 4.0D0*brillq(rho1,z1,phi))
. / eps**2
else
brillMlinear(i,j,k) = 0.25D0/e2q
. *(brillq(rho1,z1+eps,phi)
. + brillq(rho1,z1-eps,phi)
. + two*brillq(eps,z1,phi)
. - two*brillq(rho1,z1,phi))
. / eps**2
end if
c Here I assume that for very small rho, the
c phi derivatives are essentially zero. This
c must always be true otherwise the function
c is not regular on the axis.
if (rho1.gt.rhofudge) then
brillMlinear(i,j,k) = brillMlinear(i,j,k) + 0.25D0/rho2
. *(three*0.25D0*(brillq(rho1,z1,phi+eps)
. - brillq(rho1,z1,phi-eps))**2
. + two*(brillq(rho1,z1,phi+eps)
. - two*brillq(rho1,z1,phi)
. + brillq(rho1,z1,phi-eps)))/eps**2
end if
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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