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c/*@@
c @file AxiBrillBHIVP.F
c @date
c @author
c @desc
c
c @enddesc
c@@*/
#include "cctk.h"
#include "cctk_Parameters.h"
#include "cctk_Arguments.h"
c/*@@
c @routine AxiBrillBHIVP
c @date
c @author
c @desc
c
c @enddesc
c @calls
c @calledby
c @history
c
c @endhistory
c@@*/
c Need include file from Einstein
#include "CactusEinstein/Einstein/src/Einstein.h"
subroutine AxiBrillBHIVP(CCTK_FARGUMENTS)
implicit none
DECLARE_CCTK_FARGUMENTS
DECLARE_CCTK_PARAMETERS
c Perhaps this and others should go into cctk.h
integer CCTK_Equals
real*8 axibheps, rmax, dq, deta
integer levels,id5,id9,idi,idg,ier
real*8, allocatable :: cc(:,:),ce(:,:),cw(:,:),cn(:,:),cs(:,:),
$ rhs(:,:),psi2d(:,:),detapsi2d(:,:),dqpsi2d(:,:),
$ detaetapsi2d(:,:),detaqpsi2d(:,:),dqqpsi2d(:,:)
real*8, allocatable :: etagrd(:),qgrd(:)
real*8, allocatable :: eta(:,:,:),abseta(:,:,:),sign_eta(:,:,:),
$ q(:,:,:),phi(:,:,:)
real*8, allocatable :: psi2dv(:,:,:),detapsi2dv(:,:,:),
$ dqpsi2dv(:,:,:),detaetapsi2dv(:,:,:),detaqpsi2dv(:,:,:),
$ dqqpsi2dv(:,:,:)
parameter(axibheps = 1.0d-12)
real*8 ep1,ep2
real*8 o1,o2,o3,o4,o5,o6,o7,o8,o9
real*8 o10,o11,o12,o13,o14,o15,o16,o17,o18,o19
real*8 o20,o21,o22,o23,o24,o25,o26,o27,o28,o29
real*8 o30,o31,o32,o33,o34,o35,o36,o37,o38,o39
real*8 o40,o41,o42,o43,o44,o45,o46,o47,o48,o49
real*8 o50,o51,o52,o53,o54,o55,o56,o57,o58,o59
real*8 o60,o61,o62,o63,o64,o65,o66,o67,o68,o69
real*8 o70,o71,o72,o73,o74,o75,o76,o77,o78,o79
real*8 o80,o81,o82,o83,o84,o85,o86,o87,o88,o89
real*8 o90,o91,o92,o93,o94,o95,o96,o97,o98,o99
real*8 pi
real*8 adm
integer :: nx,ny,nz
integer i,j,k,nquads
integer npoints,handle,ierror
pi = 4.0d0*atan(1.0d0)
c Set up the grid spacings
nx = cctk_lsh(1)
ny = cctk_lsh(2)
nz = cctk_lsh(3)
c Brill wave parameters
print *,"Brill wave + BH Axisymmetric solve"
write (*,123)amp,eta0,sigma,n
print *,'etamax=',etamax
123 format(1x,'Pars : Amp',f8.5,' eta0',f8.5,' sigma',f8.5,' n ',i3)
c Solve on this sized cartesian grid
c 2D grid size NE x NQ
c Add 2 zones for boundaries...
ne = ne+2
nq = nq+2
! do I need to call free?
allocate(cc(ne,nq),ce(ne,nq),cw(ne,nq),cn(ne,nq),cs(ne,nq),
$ rhs(ne,nq),psi2d(ne,nq),detapsi2d(ne,nq),dqpsi2d(ne,nq),
$ detaetapsi2d(ne,nq),detaqpsi2d(ne,nq),dqqpsi2d(ne,nq),
$ etagrd(ne),qgrd(nq))
allocate(eta(nx,ny,nz),abseta(nx,ny,nz),sign_eta(nx,ny,nz),
$ q(nx,ny,nz),phi(nx,ny,nz),
$ psi2dv(nx,ny,nz),detapsi2dv(nx,ny,nz),dqpsi2dv(nx,ny,nz),
$ detaetapsi2dv(nx,ny,nz),detaqpsi2dv(nx,ny,nz),
$ dqqpsi2dv(nx,ny,nz))
c Initialize some arrays
psi2d = 1.0d0
detapsi2d = 0.0d0
nquads = 2
dq = nquads*0.5*pi/(nq-2)
deta = etamax/(ne-3)
do j=1,nq
qgrd(j) = (j-1.5)*dq
do i=1,ne
etagrd(i) = (i-2)*deta
#include "Development/IDAxiBrillBH/src/bhbrill.x"
enddo
enddo
c Boundary conditions
do j=1,nq
ce(2,j)=ce(2,j)+cw(2,j)
cw(2,j)=0.0
cw(ne-1,j)=cw(ne-1,j)+ce(ne-1,j)
cc(ne-1,j)=cc(ne-1,j)-deta*ce(ne-1,j)
ce(ne-1,j)=0.0
enddo
do i=1,ne
cc(i,2)=cc(i,2)+cs(i,2)
cs(i,2)=0.0
cc(i,nq-1)=cc(i,nq-1)+cn(i,nq-1)
cn(i,nq-1)=0.0
enddo
c Do the solve
print *, " Calling axisymmetric solver"
call mgparm (levels,5,id5,id9,idi,idg,ne,nq)
call mg5 (ne,2,ne-1,nq,2,nq-1,
$ cc,cn,cs,cw,ce,psi2d,rhs,
$ id5,id9,idi,idg,1,axibheps,rmax,ier)
print *, " Solve complete"
c The solution is now available.
c Debugging is needed, a stop statement should
c be called if the IVP solve is not successful
if(ier .ne. 0) stop 'bad solution to brill wave problem'
print *,'rmax = ',rmax
print *,'axibheps = ',axibheps
print *,'psi2d = ',maxval(psi2d),' ',minval(psi2d)
ep2 = 0.0
do j=2,nq-1
do i=2,ne-1
ep1 = rhs(i,j)-psi2d(i,j)*cc(i,j)-psi2d(i,j+1)*cn(i,j)-psi2d(i,j-1)*cs(i,j)-
& psi2d(i+1,j)*ce(i,j)-psi2d(i-1,j)*cw(i,j)
ep2 = max(abs(ep1),ep2)
enddo
enddo
print *,'Resulting eps =',ep2
! what a pain all this is....
do j=1,nq
psi2d(1,j)=psi2d(3,j)
psi2d(ne,j)=-deta*psi2d(ne-1,j)+psi2d(ne-2,j)
enddo
do i=1,ne
psi2d(i,1)=psi2d(i,2)
psi2d(i,nq)=psi2d(i,nq-1)
enddo
c goto 111
do j=2,nq-1
do i=2,ne-1
dqpsi2d(i,j)=0.5*(psi2d(i,j+1)-psi2d(i,j-1))/dq
dqqpsi2d(i,j)=(psi2d(i,j+1)+psi2d(i,j-1)-2.*psi2d(i,j))/dq**2
detapsi2d(i,j)=sinh(0.5*etagrd(i))+0.5*(psi2d(i+1,j)-psi2d(i-1,j))/deta
detaetapsi2d(i,j)=0.5*cosh(0.5*etagrd(i))+
$ (psi2d(i+1,j)+psi2d(i-1,j)-2.*psi2d(i,j))/deta**2
enddo
enddo
do j=1,nq
detapsi2d(1,j)=-detapsi2d(3,j)
detapsi2d(ne,j)=detapsi2d(ne-2,j) ! simplified
detaetapsi2d(1,j)=detaetapsi2d(3,j)
detaetapsi2d(ne,j)=detaetapsi2d(ne-2,j) ! simplified...
dqqpsi2d(1,j)=dqqpsi2d(3,j)
dqqpsi2d(ne,j)=dqqpsi2d(ne-2,j) ! simplified
dqpsi2d(1,j)=dqpsi2d(3,j)
dqpsi2d(ne,j)=-dq*dqpsi2d(ne-1,j)+dqpsi2d(ne-2,j)
enddo
do i=1,ne
detapsi2d(i,1)=detapsi2d(i,2)
detapsi2d(i,nq)=detapsi2d(i,nq-1)
detaetapsi2d(i,1)=detaetapsi2d(i,2)
detaetapsi2d(i,nq)=detaetapsi2d(i,nq-1)
dqqpsi2d(i,1)=dqqpsi2d(i,2)
dqqpsi2d(i,nq)=dqqpsi2d(i,nq-1)
dqpsi2d(i,1)=-dqpsi2d(i,2)
dqpsi2d(i,nq)=-dqpsi2d(i,nq-1)
enddo
do j=2,nq-1
do i=2,ne-1
detaqpsi2d(i,j)=0.5*(detapsi2d(i,j+1)-detapsi2d(i,j-1))/dq
enddo
enddo
do j=1,nq
detaqpsi2d(1,j)=-detaqpsi2d(3,j)
detaqpsi2d(ne,j)=detaqpsi2d(ne-2,j) ! simplified
enddo
do i=1,ne
detaqpsi2d(i,1)=-detaqpsi2d(i,2)
detaqpsi2d(i,nq)=-detaqpsi2d(i,nq-1)
enddo
do j=1,nq
psi2d(:,j)=psi2d(:,j)+2.*cosh(0.5*etagrd)
enddo
c Now evaluate each of the following at x(i,j,k), y(i,j,k) and
c z(i,j,k) where i,j,k go from 1 to nx,ny,nz
c Conformal factor
eta = 0.5d0 * dlog (x**2 + y**2 + z**2)
abseta = abs (eta)
q = datan2 (sqrt (x**2 + y**2), z)
phi = datan2 (y, x)
do k=1,nz
do j=1,ny
do i=1,nx
c eta(i,j,k) = 0.5d0*dlog(x(i,j,k)**2+y(i,j,k)**2+z(i,j,k)**2)
c abseta(i,j,k) = abs(eta(i,j,k))
if(eta(i,j,k) .lt. 0)then
sign_eta(i,j,k) = -1
else
sign_eta(i,j,k) = 1
endif
c q(i,j,k) = datan2(sqrt(x(i,j,k)**2+y(i,j,k)**2),z(i,j,k))
c TYPO HERE ???????????
c |
c |
c phi(i,j,k)= datan2(y(i,j,k),x(i,j,k))
enddo
enddo
enddo
call CCTK_GetInterpHandle (handle, "simple_local")
npoints = nx*ny*nz
call CCTK_Interp (ierror,cctkGH,handle,npoints,2,6,6,
$ ne,nq,abseta,q,
$ CCTK_VARIABLE_REAL,CCTK_VARIABLE_REAL,
$ etagrd(1),qgrd(1),deta,dq,
$ psi2d,detapsi2d,dqpsi2d,detaetapsi2d,detaqpsi2d,dqqpsi2d,
$ CCTK_VARIABLE_REAL,CCTK_VARIABLE_REAL,CCTK_VARIABLE_REAL,
$ CCTK_VARIABLE_REAL,CCTK_VARIABLE_REAL,CCTK_VARIABLE_REAL,
$ psi2dv,detapsi2dv,dqpsi2dv,detaetapsi2dv,detaqpsi2dv,
$ dqqpsi2dv,
$ CCTK_VARIABLE_REAL,CCTK_VARIABLE_REAL,CCTK_VARIABLE_REAL,
$ CCTK_VARIABLE_REAL,CCTK_VARIABLE_REAL,CCTK_VARIABLE_REAL)
psi = psi2dv * exp (-0.5 * eta)
detapsi2dv = sign_eta * detapsi2dv
detaqpsi2dv = sign_eta * detaqpsi2dv
do k=1,nz
do j=1,ny
do i=1,nx
c psi(i,j,k) = psi2dv(i,j,k)*exp(-0.5*eta(i,j,k))
c detapsi2dv(i,j,k) = sign_eta(i,j,k)*detapsi2dv(i,j,k)
c psix = \partial psi / \partial x / psi
#include "Development/IDAxiBrillBH/src/psi_1st_deriv.x"
c detaqpsi2dv(i,j,k) = sign_eta(i,j,k)*detaqpsi2dv(i,j,k)
c psixx = \partial^2\psi / \partial x^2 / psi
#include "Development/IDAxiBrillBH/src/psi_2nd_deriv.x"
enddo
enddo
enddo
c Conformal metric
c gxx = ...
c Derivatives of the metric
c dxgxx = 1/2 \partial gxx / \partial x
do k=1,nz
do j=1,ny
do i=1,nx
c THESE WERE ALREADY CALCULATED ABOVE !!!
c eta(i,j,k) = 0.5d0*dlog(x(i,j,k)**2+y(i,j,k)**2+z(i,j,k)**2)
c q(i,j,k) = datan2(sqrt(x(i,j,k)**2+y(i,j,k)**2),z(i,j,k))
c phi(i,j,k) = datan2(y(i,j,k),x(i,j,k))
#include "Development/IDAxiBrillBH/src/gij.x"
enddo
enddo
enddo
c Curvature
kxx = 0.0D0
kxy = 0.0D0
kxz = 0.0D0
kyy = 0.0D0
kyz = 0.0D0
kzz = 0.0D0
111 continue
c Set ADM mass
i = ne-15
adm = 0.0
do j=2,nq-1
adm=adm+(psi2d(i,j)-(psi2d(i+1,j)-psi2d(i-1,j))/deta)*exp(0.5*
$ etagrd(i))
enddo
adm=adm/(nq-2)
print *,'ADM mass: ',adm
if (CCTK_Equals(initial_lapse,"schwarz")==1) then
write (*,*)"Initial with schwarzschild-like lapse"
write (*,*)"using alp = (2.*r - adm)/(2.*r+adm)."
alp = (2.*r - adm)/(2.*r+adm)
endif
conformal_state = CONFORMAL_METRIC
deallocate(cc,ce,cw,cn,cs,rhs,psi2d,detapsi2d,dqpsi2d,
$ detaetapsi2d,detaqpsi2d,dqqpsi2d,
$ etagrd,qgrd,
$ eta,abseta,sign_eta,q,phi,psi2dv,detapsi2dv,dqpsi2dv,
$ detaetapsi2dv,detaqpsi2dv,dqqpsi2dv)
return
end
|
