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/*@@
@file sor.F
@date Thu Mar 13 07:46:55 1997
@author Joan Masso + Paul Walker
@desc
The SOR solver
@enddesc
@@*/
#include "cctk.h"
#include "cctk_Arguments.h"
#include "cctk_Parameters.h"
/*@@
@routine sor
@date Thu Apr 24 13:29:52 1997
@author Joan Masso
@desc
This is a standalone sor solver which does all the MPI itself.
It is a pretty good example of doing pugh-based communications
in FORTRAN.
@enddesc
@@*/
subroutine sor_confmetric_core3d(_CCTK_FARGUMENTS,
$ Mlinear_lsh,Mlinear,
$ Nsource_lsh,Nsource,
$ gxx,gxy,gxz,gyy,gyz,gzz,
& psi,var, var_idx,
$ abstol,reltol)
implicit none
_DECLARE_CCTK_FARGUMENTS
DECLARE_CCTK_PARAMETERS
INTEGER CCTK_Equals
INTEGER Mlinear_lsh(3)
CCTK_REAL Mlinear(Mlinear_lsh(1),Mlinear_lsh(2),Mlinear_lsh(3))
INTEGER Nsource_lsh(3)
CCTK_REAL Nsource(Nsource_lsh(1),Nsource_lsh(2),Nsource_lsh(3))
CCTK_REAL gxx(cctk_lsh(1),cctk_lsh(2),cctk_lsh(3)), gxy(cctk_lsh(1),cctk_lsh(2),cctk_lsh(3))
CCTK_REAL gxz(cctk_lsh(1),cctk_lsh(2),cctk_lsh(3)), gyy(cctk_lsh(1),cctk_lsh(2),cctk_lsh(3))
CCTK_REAL gyz(cctk_lsh(1),cctk_lsh(2),cctk_lsh(3)), gzz(cctk_lsh(1),cctk_lsh(2),cctk_lsh(3))
CCTK_REAL psi(cctk_lsh(1),cctk_lsh(2),cctk_lsh(3))
CCTK_REAL var(cctk_lsh(1),cctk_lsh(2),cctk_lsh(3))
INTEGER var_idx
CCTK_REAL abstol(3),reltol(3)
CCTK_REAL tol
INTEGER toltype
CCTK_REAL dx,dy,dz
c Temporaries
INTEGER sor_iteration
CCTK_REAL pm4, tmp
CCTK_REAL psixp, psiyp, psizp
c Numbers...
CCTK_REAL two, four
c Total residual
CCTK_REAL resnorm, residual
c Stencil
CCTK_REAL a(-1:1,-1:1,-1:1)
c Loopers
INTEGER i,j,k
c Acceleration factor
CCTK_REAL omega, rjacobian
c conformal test
logical conformal
logical octant
c Loop bounds. Starts, Ends, and deltas (steps)
INTEGER is, js, ks, ie, je, ke, di, dj, dk, kstep
c Upper metric and determinant. What a pig.
CCTK_REAL uxx(cctk_lsh(1),cctk_lsh(2),cctk_lsh(3)), uyy(cctk_lsh(1),cctk_lsh(2),cctk_lsh(3))
CCTK_REAL uzz(cctk_lsh(1),cctk_lsh(2),cctk_lsh(3)), uxy(cctk_lsh(1),cctk_lsh(2),cctk_lsh(3))
CCTK_REAL uxz(cctk_lsh(1),cctk_lsh(2),cctk_lsh(3)), uyz(cctk_lsh(1),cctk_lsh(2),cctk_lsh(3))
CCTK_REAL det(cctk_lsh(1),cctk_lsh(2),cctk_lsh(3))
c Coeeficients for the solver: 19 point stencil...
CCTK_REAL ac,aw,ae,an,as,at,ab
CCTK_REAL ane,anw,ase,asw,ate,atw
CCTK_REAL abe,abw,atn,ats,abn,asb
CCTK_REAL finf
CCTK_INT npow
logical cheb, const, none, verb
integer Mlinear_storage,Nsource_storage
INTEGER reduction_handle,ierr
c stencil size
INTEGER sw(3)
tol = AbsTol(1)
c Get the reduction handel for the sum operation
call CCTK_ReductionArrayHandle(reduction_handle,"sum");
if (reduction_handle.lt.0) then
call CCTK_WARN(1,"Cannot get reduction handle.")
endif
c Set boundary related variables
if (CCTK_EQUALS(sor_bound,"robin")) then
sw(1)=1
sw(2)=1
sw(2)=1
call Ell_GetRealKey(ierr, finf, "EllLinConfMetric::Bnd::Robin::inf")
call Ell_GetIntKey (ierr, npow, "EllLinConfMetric::Bnd::Robin::falloff")
end if
c We have no storage for M/N if they are of size one in each direction
if ((Mlinear_lsh(1).eq.1).and.(Mlinear_lsh(2).eq.1).and.(Mlinear_lsh(3).eq.1)) then
Mlinear_storage=0
else
Mlinear_storage=1
endif
if ((Nsource_lsh(1).eq.1).and.(Nsource_lsh(2).eq.1).and.(Nsource_lsh(3).eq.1)) then
Nsource_storage=0
else
Nsource_storage=1
endif
c Set up shorthand for the grid spacings
dx=cctk_delta_space(1)
dy=cctk_delta_space(2)
dz=cctk_delta_space(3)
verb = CCTK_Equals(elliptic_verbose,"yes").eq.1
octant = CCTK_Equals(domain,"octant").eq.1
none = .false.
const = .false.
cheb = .false.
if (CCTK_EQUALS(sor_accel,"const")) then
const = .true.
else if (CCTK_EQUALS(sor_accel,"cheb")) then
cheb = .true.
else
none = .true.
endif
if (verb .and. cheb)
$ print *,"Chebyshev Acceleration with radius of 1"
if (verb .and. const)
$ print *,"SOR with omega = 1.8"
if (verb .and. none)
$ print *,"Un-accelearted relaxation (omega = 1)"
two = 2.0D0
four = 4.0D0
resnorm = 0.0d0
c compute determinant
det= -(gxz**2*gyy) + 2*gxy*gxz*gyz - gxx*gyz**2
& - gxy**2*gzz + gxx*gyy*gzz
c invert metric
uxx=(-gyz**2 + gyy*gzz)/det/psi**4
uxy=(gxz*gyz - gxy*gzz)/det/psi**4
uyy=(-gxz**2 + gxx*gzz)/det/psi**4
uxz=(-gxz*gyy + gxy*gyz)/det/psi**4
uyz=(gxy*gxz - gxx*gyz)/det/psi**4
uzz=(-gxy**2 + gxx*gyy)/det/psi**4
det = det * psi**12
if (Mlinear_storage.eq.1) then
Mlinear = Mlinear*sqrt(det)
endif
if (Nsource_storage.eq.1) then
Nsource = Nsource*sqrt(det)
endif
c Re-scaled uppwemetric. PATCHY but effective.... watch out: we get it back after
c the solve.
uxx=uxx/(2.*dx*dx)*sqrt(det)
uyy=uyy/(2.*dy*dy)*sqrt(det)
uzz=uzz/(2.*dz*dz)*sqrt(det)
uxy=uxy/(4.*dx*dy)*sqrt(det)
uxz=uxz/(4.*dx*dz)*sqrt(det)
uyz=uyz/(4.*dy*dz)*sqrt(det)
do sor_iteration=1,maxit
c We do not know the spectral radius of the Jacobi iteration, \
c so we will take it to be one
c which empirically seems to be pretty good
rjacobian = 1.
c Set up the omega factor
omega = 1.
if (cheb) then
do i=2,sor_iteration
omega = 1./(1. - .25*rjacobian**2*omega)
enddo
endif
if (const) then
omega = 1.8
endif
c Total norm of the residual zero
resnorm = 0.
c End of first-iteration stuff
c Start loop with Red Black
ks = mod(sor_iteration,2)+2
if (cctk_lsh(3) .eq. 3) then
ks = 2
endif
kstep = 2
do k=ks,cctk_lsh(3)-1,kstep
do j=2,cctk_lsh(2)-1
do i=2,cctk_lsh(1)-1
ac = -uxx(i+1,j,k) -2.*uxx(i,j,k) -uxx(i-1,j,k)
& -uyy(i,j+1,k) -2.*uyy(i,j,k) -uyy(i,j-1,k)
& -uzz(i,j,k+1) -2.*uzz(i,j,k) -uzz(i,j,k-1)
if (Mlinear_storage.eq.1) then
ac = ac + Mlinear(i,j,k)
endif
ae = uxx(i+1,j,k)+uxx(i,j,k)
aw = uxx(i-1,j,k)+uxx(i,j,k)
an = uyy(i,j+1,k)+uyy(i,j,k)
as = uyy(i,j-1,k)+uyy(i,j,k)
at = uzz(i,j,k+1)+uzz(i,j,k)
ab = uzz(i,j,k-1)+uzz(i,j,k)
ane = uxy(i,j+1,k)+uxy(i+1,j,k)
anw = - uxy(i-1,j,k)-uxy(i,j+1,k)
ase = - uxy(i+1,j,k)-uxy(i,j-1,k)
asw = uxy(i-1,j,k)+uxy(i,j-1,k)
ate = uxz(i,j,k+1)+uxz(i+1,j,k)
atw = - uxz(i-1,j,k)-uxz(i,j,k+1)
abe = - uxz(i+1,j,k)-uxz(i,j,k-1)
abw = uxz(i-1,j,k)+uxz(i,j,k-1)
atn = uyz(i,j+1,k)+uyz(i,j,k+1)
ats = - uyz(i,j,k+1)-uyz(i,j-1,k)
abn = - uyz(i,j,k-1)-uyz(i,j+1,k)
asb = uyz(i,j,k-1)+uyz(i,j-1,k)
residual = ac*var(i,j,k)
& + ae*var(i+1,j,k) + aw*var(i-1,j,k)
& + an*var(i,j+1,k) + as*var(i,j-1,k)
& + at*var(i,j,k+1) + ab*var(i,j,k-1)
& + ane*var(i+1,j+1,k) + anw*var(i-1,j+1,k)
& + ase*var(i+1,j-1,k) + asw*var(i-1,j-1,k)
& + ate*var(i+1,j,k+1) + atw*var(i-1,j,k+1)
& + abe*var(i+1,j,k-1) + abw*var(i-1,j,k-1)
& + atn*var(i,j+1,k+1) + ats*var(i,j-1,k+1)
& + abn*var(i,j+1,k-1) + asb*var(i,j-1,k-1)
if (Nsource_storage.eq.1) then
residual = residual + Nsource(i,j,k)
endif
c Accumulate to the total Norm of the residual
resnorm = resnorm + abs(residual)
c Update
var(i,j,k) = var(i,j,k) - omega*residual/ac
end do
end do
end do
c Reduce the norm
c Reduce the norm
call CCTK_ReduceLocalScalar(ierr, cctkGH, -1, reduction_handle,
$ resnorm, residual, CCTK_VARIABLE_REAL)
if (ierr.ne.0) then
call CCTK_WARN(1,"Reduction of norm failed!");
endif
residual = resnorm
residual = residual / (cctk_gsh(1)*cctk_gsh(2)*cctk_gsh(3))
call CCTK_SyncGroupWithVarI(cctkGH, var_idx)
if (residual .lt. tol) then
goto 123
endif
c Apply Robin boundary
if (CCTK_EQUALS(sor_bound,"robin")) then
call RobinBCVarI(ierr, cctkGH, finf, npow, sw, var_idx);
if (ierr.ne.0) then
call CCTK_WARN(1,"Could not apply Robin BC !")
endif
endif
c Apply octant Symmetries
call CartSymBCVarI(ierr, cctkGH, var_idx)
enddo
write (*,*) "!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!"
write (*,*) "!! WARNING: SOR SOLVER DID NOT CONVERGE !!"
write (*,*) "!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!"
123 continue
if (Mlinear_storage.eq.1) then
Mlinear = Mlinear/sqrt(det)
endif
if (Nsource_storage.eq.1) then
Nsource = Nsource/sqrt(det)
endif
if (verb) write (*,*) "Iteration/Norm",sor_iteration,residual
return
end
|
