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c/*@@
c @file IDAxiBrillBH.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 IDAxiBrillBH
c @date
c @author
c @desc
c
c @enddesc
c @calls
c @calledby
c @history
c
c @endhistory
c@@*/
subroutine IDAxiBrillBH(CCTK_ARGUMENTS)
implicit none
DECLARE_CCTK_ARGUMENTS
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
integer i22
real*8 pi
real*8 adm
integer :: nx,ny,nz
integer i,j,k,nquads
integer npoints,handle,ierror
integer neb, nqb
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 Solve on this sized cartesian grid
c 2D grid size NE x NQ
c Add 2 zones for boundaries...
c 21/11/00 TR: dont change parameters in place
c but keep a copy in local variables
c Otherwise the changed parameters cause trouble
c after recovery.
neb = ne+2
nqb = nq+2
! do I need to call free?
allocate(cc(neb,nqb),ce(neb,nqb),cw(neb,nqb),cn(neb,nqb),cs(neb,nqb),
$ rhs(neb,nqb),psi2d(neb,nqb),detapsi2d(neb,nqb),dqpsi2d(neb,nqb),
$ detaetapsi2d(neb,nqb),detaqpsi2d(neb,nqb),dqqpsi2d(neb,nqb),
$ etagrd(neb),qgrd(nqb))
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/(nqb-2)
deta = etamax/(neb-3)
do j=1,nqb
qgrd(j) = (j-1.5)*dq
do i=1,neb
etagrd(i) = (i-2)*deta
#include "CactusEinstein/IDAxiBrillBH/src/bhbrill.x"
enddo
enddo
c Boundary conditions
do j=1,nqb
ce(2,j)=ce(2,j)+cw(2,j)
cw(2,j)=0.0
cw(neb-1,j)=cw(neb-1,j)+ce(neb-1,j)
cc(neb-1,j)=cc(neb-1,j)-deta*ce(neb-1,j)
ce(neb-1,j)=0.0
enddo
do i=1,neb
cc(i,2)=cc(i,2)+cs(i,2)
cs(i,2)=0.0
cc(i,nqb-1)=cc(i,nqb-1)+cn(i,nqb-1)
cn(i,nqb-1)=0.0
enddo
c Do the solve
call CCTK_INFO("Calling axisymmetric solver")
call mgparm (levels,5,id5,id9,idi,idg,neb,nqb)
call mg5 (neb,2,neb-1,nqb,2,nqb-1,
$ cc,cn,cs,cw,ce,psi2d,rhs,
$ id5,id9,idi,idg,1,axibheps,rmax,ier)
call CCTK_INFO("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) then
call CCTK_WARN(0,"Solution to BH+Brill Wave not found")
end if
print *,'rmax = ',rmax
print *,'axibheps = ',axibheps
print *,'psi2d = ',maxval(psi2d),' ',minval(psi2d)
ep2 = 0.0
do j=2,nqb-1
do i=2,neb-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
do j=1,nqb
psi2d(1,j)=psi2d(3,j)
psi2d(neb,j)=-deta*psi2d(neb-1,j)+psi2d(neb-2,j)
enddo
do i=1,neb
psi2d(i,1)=psi2d(i,2)
psi2d(i,nqb)=psi2d(i,nqb-1)
enddo
do j=2,nqb-1
do i=2,neb-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,nqb
detapsi2d(1,j)=-detapsi2d(3,j)
detapsi2d(neb,j)=detapsi2d(neb-2,j) ! simplified
detaetapsi2d(1,j)=detaetapsi2d(3,j)
detaetapsi2d(neb,j)=detaetapsi2d(neb-2,j) ! simplified...
dqqpsi2d(1,j)=dqqpsi2d(3,j)
dqqpsi2d(neb,j)=dqqpsi2d(neb-2,j) ! simplified
dqpsi2d(1,j)=dqpsi2d(3,j)
dqpsi2d(neb,j)=-dq*dqpsi2d(neb-1,j)+dqpsi2d(neb-2,j)
enddo
do i=1,neb
detapsi2d(i,1)=detapsi2d(i,2)
detapsi2d(i,nqb)=detapsi2d(i,nqb-1)
detaetapsi2d(i,1)=detaetapsi2d(i,2)
detaetapsi2d(i,nqb)=detaetapsi2d(i,nqb-1)
dqqpsi2d(i,1)=dqqpsi2d(i,2)
dqqpsi2d(i,nqb)=dqqpsi2d(i,nqb-1)
dqpsi2d(i,1)=-dqpsi2d(i,2)
dqpsi2d(i,nqb)=-dqpsi2d(i,nqb-1)
enddo
do j=2,nqb-1
do i=2,neb-1
detaqpsi2d(i,j)=0.5*(detapsi2d(i,j+1)-detapsi2d(i,j-1))/dq
enddo
enddo
do j=1,nqb
detaqpsi2d(1,j)=-detaqpsi2d(3,j)
detaqpsi2d(neb,j)=detaqpsi2d(neb-2,j) ! simplified
enddo
do i=1,ne
detaqpsi2d(i,1)=-detaqpsi2d(i,2)
detaqpsi2d(i,nqb)=-detaqpsi2d(i,nqb-1)
enddo
do j=1,nqb
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
npoints = nx*ny*nz
! Interpolator handle.
handle = -1
if (interpolation_order .eq. 1) then
call CCTK_InterpHandle (handle, "first-order uniform cartesian")
else if (interpolation_order .eq. 2) then
call CCTK_InterpHandle (handle, "second-order uniform cartesian")
else if (interpolation_order .eq. 3) then
call CCTK_InterpHandle (handle, "third-order uniform cartesian")
endif
if (handle .lt. 0) then
call CCTK_WARN (0, "Couldn't get handle for interpolation operator")
endif
call CCTK_InterpLocal (ierror, cctkGH, handle, npoints, 2, 6, 6,
$ neb, nqb, etagrd, qgrd,
$ CCTK_VARIABLE_REAL, CCTK_VARIABLE_REAL,
$ abseta, q,
$ CCTK_VARIABLE_REAL,CCTK_VARIABLE_REAL,
$ 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 "CactusEinstein/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 "CactusEinstein/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 "CactusEinstein/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 = neb-15
adm = 0.0
do j=2,nqb-1
adm=adm+(psi2d(i,j)-(psi2d(i+1,j)-psi2d(i-1,j))/deta)*exp(0.5*
$ etagrd(i))
enddo
adm=adm/(nqb-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
c conformal_state = CONFORMAL_METRIC (What is CONFORMAL_METRIC?)
conformal_state = 3
c 3 ==> 'all' derivatives were calculated
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
|
