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/*@@
@file sor_confmetric.c
@date Tue Sep 26 11:29:18 2000
@author Gerd Lanfermann
@desc
Provides sor solver engine routines
@enddesc
@@*/
#include <stdlib.h>
#include <stdio.h>
#include <math.h>
#include "cctk.h"
#include "cctk_Arguments.h"
#include "cctk_Parameters.h"
#include "CactusBase/Boundary/src/Boundary.h"
#include "CactusBase/CartGrid3D/src/Symmetry.h"
#include "CactusElliptic/EllBase/src/Ell_DBstructure.h"
#define SQR(a) ((a)*(a))
/*@@
@routine sor_confmetric
@date Tue Sep 26 11:28:08 2000
@author Joan Masso, Paul Walker, Gerd Lanfermann
@desc
This is a standalone sor solver engine,
called by the wrapper functions
@enddesc
@calls
@calledby
@history
@endhistory
@@*/
void sor_confmetric_3d(cGH *GH, int *MetricPsiI, int conformal,
int FieldIndex, int MIndex, int NIndex,
CCTK_REAL *AbsTol, CCTK_REAL *RelTol)
{
DECLARE_CCTK_PARAMETERS
/* The pointer to the metric fields */
CCTK_REAL *gxx =NULL, *gxy =NULL;
CCTK_REAL *gxz =NULL, *gyy =NULL;
CCTK_REAL *gyz =NULL, *gzz =NULL;
CCTK_REAL *psi =NULL;
CCTK_REAL *Mlin=NULL, *Nlin=NULL;
CCTK_REAL *var =NULL;
/* The inverse metric, allocated here */
CCTK_REAL *uxx=NULL, *uyy=NULL,
*uzz=NULL, *uxz=NULL,
*uxy=NULL, *uyz=NULL;
/* shortcuts for metric, psi, deltas, etc. */
CCTK_REAL pm4, p12, det;
CCTK_REAL dx,dy,dz;
CCTK_REAL dxdx, dydy, dzdz,
dxdy, dxdz, dydz;
/* Some physical variables */
int accel_cheb=0, accel_const=0;
int chebit;
CCTK_REAL omega, resnorm=0.0, residual=0.0;
CCTK_REAL glob_residual=0.0, rjacobian=0.0;
CCTK_REAL finf;
CCTK_INT npow;
CCTK_REAL tol;
/* Iteration / stepping variables */
int sorit;
int i,is,ie;
int j,js,je;
int k,ks,ke,kstep;
int nxyz;
/* 19 point stencil index */
int ijk;
int ipjk, ijpk, ijkp, imjk, ijmk, ijkm;
int ipjpk, ipjmk, imjpk, imjmk;
int ipjkp, ipjkm, imjkp, imjkm;
int ijpkp, ijpkm, ijmkp, ijmkm;
/* 19 point stencil coefficients */
CCTK_REAL ac;
CCTK_REAL ae,aw,an,as,at,ab;
CCTK_REAL ane, anw, ase, asw, ate, atw, abe, abw;
CCTK_REAL atn, ats, abn, abs;
/* Miscellaneous */
int sum_handle=-1;
int sw[3], ierr;
int Mstorage=0, Nstorage=0;
size_t varsize;
static int firstcall = 1;
CCTK_REAL detrec_pm4, sqrtdet;
/* Get the reduction handle */
sum_handle = CCTK_ReductionArrayHandle("sum");
if (sum_handle<0)
CCTK_WARN(1,"Cannot get reduction handle for operation >sum<");
/* IF Robin BCs are set, prepare for a boundary call:
setup stencil width and get Robin constants (set by the routine
which is calling the solver interface) */
if (CCTK_EQUALS(sor_bound,"robin")) {
sw[0]=1;
sw[1]=1;
sw[2]=1;
ierr = Ell_GetRealKey(&finf, "EllLinConfMetric::Bnd::Robin::inf");
ierr = Ell_GetIntKey (&npow, "EllLinConfMetric::Bnd::Robin::falloff");
}
/* Only supports absolute tolerance */
tol = AbsTol[0];
if (CCTK_EQUALS(sor_accel,"const"))
accel_const = 1;
else if (CCTK_EQUALS(sor_accel,"cheb"))
accel_cheb = 1;
/* Things to do only once! */
if (firstcall==1) {
if (CCTK_Equals(elliptic_verbose, "yes"))
{
if (accel_cheb)
printf("SOR with Chebyshev acceleration with radius of 1\n");
else if (accel_const)
printf("SOR with hardcoded omega = 1.8\n");
else
printf("SOR with unaccelearted relaxation (omega = 1)\n");
}
firstcall = 0;
}
/* Get the data ptr of these GFs, They all have to be
on the same timelevel; derive the metric data pointer from
the index array. Note the ordering in the metric */
var = (CCTK_REAL*) CCTK_VarDataPtrI(GH, 0, FieldIndex);
gxx = (CCTK_REAL*) CCTK_VarDataPtrI(GH, 0, MetricPsiI[0]);
gxy = (CCTK_REAL*) CCTK_VarDataPtrI(GH, 0, MetricPsiI[1]);
gxz = (CCTK_REAL*) CCTK_VarDataPtrI(GH, 0, MetricPsiI[2]);
gyy = (CCTK_REAL*) CCTK_VarDataPtrI(GH, 0, MetricPsiI[3]);
gyz = (CCTK_REAL*) CCTK_VarDataPtrI(GH, 0, MetricPsiI[4]);
gzz = (CCTK_REAL*) CCTK_VarDataPtrI(GH, 0, MetricPsiI[5]);
if (conformal)
psi = (CCTK_REAL*) CCTK_VarDataPtrI(GH, 0, MetricPsiI[6]);
/* if we have a negative index for M/N, this GF is not needed,
there for don't even look for it. when index positive,
set flag Mstorage=1, dito for N */
if (MIndex>=0) {
Mlin = (CCTK_REAL*) CCTK_VarDataPtrI(GH,0,MIndex);
Mstorage = 1;
}
if (NIndex>=0) {
Nlin = (CCTK_REAL*) CCTK_VarDataPtrI(GH,0,NIndex);
Nstorage = 1;
}
/* Shortcuts */
dx = GH->cctk_delta_space[0];
dy = GH->cctk_delta_space[1];
dz = GH->cctk_delta_space[2];
nxyz = GH->cctk_lsh[0]*GH->cctk_lsh[1]*GH->cctk_lsh[2];
/* Allocate the inverse metric */
varsize = (size_t)CCTK_VarTypeSize(CCTK_VarTypeI(FieldIndex))*nxyz;
if (!(uxx = (CCTK_REAL*) malloc(varsize))) CCTK_WARN(0,"Allocation failed");
if (!(uyy = (CCTK_REAL*) malloc(varsize))) CCTK_WARN(0,"Allocation failed");
if (!(uzz = (CCTK_REAL*) malloc(varsize))) CCTK_WARN(0,"Allocation failed");
if (!(uxy = (CCTK_REAL*) malloc(varsize))) CCTK_WARN(0,"Allocation failed");
if (!(uxz = (CCTK_REAL*) malloc(varsize))) CCTK_WARN(0,"Allocation failed");
if (!(uyz = (CCTK_REAL*) malloc(varsize))) CCTK_WARN(0,"Allocation failed");
/* PreCalc the differential coeff. */
dxdx = 1.0/(2.0*dx*dx);
dydy = 1.0/(2.0*dy*dy);
dzdz = 1.0/(2.0*dz*dz);
dxdy = 1.0/(4.0*dx*dy);
dxdz = 1.0/(4.0*dx*dz);
dydz = 1.0/(4.0*dy*dz);
/* Calculate the inverse metric */
for (ijk=0;ijk<nxyz;ijk++) {
/* determinant */
det = -(SQR(gxz[ijk])*gyy[ijk]) +
2*gxy[ijk]*gxz[ijk]*gyz[ijk] -
gxx[ijk]*SQR(gyz[ijk]) -
SQR(gxy[ijk])*gzz[ijk] +
gxx[ijk]*gyy[ijk]*gzz[ijk];
if (conformal) {
pm4 = 1.0/pow(psi[ijk],4.0);
p12 = pow(psi[ijk],12.0);
} else {
pm4 = 1.0;
p12 = 1.0;
}
/* try to avoid constly division */
detrec_pm4 = 1.0/det*pm4;
sqrtdet = sqrt(det);
uxx[ijk]=(-SQR(gyz[ijk]) + gyy[ijk]*gzz[ijk])*detrec_pm4;
uxy[ijk]=( gxz[ijk]*gyz[ijk] - gxy[ijk]*gzz[ijk])*detrec_pm4;
uxz[ijk]=(-gxz[ijk]*gyy[ijk] + gxy[ijk]*gyz[ijk])*detrec_pm4;
uyy[ijk]=(-SQR(gxz[ijk]) + gxx[ijk]*gzz[ijk])*detrec_pm4;
uyz[ijk]=( gxy[ijk]*gxz[ijk] - gxx[ijk]*gyz[ijk])*detrec_pm4;
uzz[ijk]=(-SQR(gxy[ijk]) + gxx[ijk]*gyy[ijk])*detrec_pm4;
det = det*p12;
sqrtdet= sqrt(det);
/* Rescaling for the uppermetric solver */
if (Mstorage) Mlin[ijk] = Mlin[ijk]*sqrt(det);
if (Nstorage) Nlin[ijk] = Nlin[ijk]*sqrt(det);
uxx[ijk]=uxx[ijk]*dxdx*sqrtdet;
uyy[ijk]=uyy[ijk]*dydy*sqrtdet;
uzz[ijk]=uzz[ijk]*dzdz*sqrtdet;
uxy[ijk]=uxy[ijk]*dxdy*sqrtdet;
uxz[ijk]=uxz[ijk]*dxdz*sqrtdet;
uyz[ijk]=uyz[ijk]*dydz*sqrtdet;
}
/*$for (k=1;k<GH->cctk_lsh[2]-1;k++) {
for (j=1;j<GH->cctk_lsh[1]-1;j++) {
for (i=1;i<GH->cctk_lsh[0]-1;i++) {
ijk = CCTK_GFINDEX3D(GH,i,j,k);
printf("U G : %d %d %d %7.8g %7.8g %7.8g \n",
i,j,k,uxx[ijk],uyy[ijk],gxx[ijk]);
}
}
}$*/
/* iteration boundaries (ks set inside loop)*/
is = 1;
js = 1;
ie = GH->cctk_lsh[0]-1;
je = GH->cctk_lsh[1]-1;
ke = GH->cctk_lsh[2]-1;
kstep = 2;
/* start at 1 for historic (Fortran) reasons */
for (sorit=1; sorit<=maxit; sorit++) {
omega = 1.0;
rjacobian = 1.0;
if (accel_cheb)
for (chebit=2;chebit<sorit;chebit++)
omega = 1.0/(1.0 - 0.25*rjacobian*rjacobian*omega);
if (accel_const)
omega = 1.8;
resnorm = 0.0;
ks = (sorit%2)+1;
if (GH->cctk_lsh[2]==3)
ks = 1;
for (k=ks;k<ke;k+=kstep) {
for (j=js;j<je;j++) {
for (i=is;i<ie;i++) {
ijk = CCTK_GFINDEX3D(GH,i ,j ,k );
ipjk = CCTK_GFINDEX3D(GH,i+1,j ,k );
imjk = CCTK_GFINDEX3D(GH,i-1,j ,k );
ijpk = CCTK_GFINDEX3D(GH,i ,j+1,k );
ijmk = CCTK_GFINDEX3D(GH,i ,j-1,k );
ijkp = CCTK_GFINDEX3D(GH,i ,j ,k+1);
ijkm = CCTK_GFINDEX3D(GH,i ,j ,k-1);
ipjpk = CCTK_GFINDEX3D(GH,i+1,j+1,k );
ipjmk = CCTK_GFINDEX3D(GH,i+1,j-1,k );
imjpk = CCTK_GFINDEX3D(GH,i-1,j+1,k );
imjmk = CCTK_GFINDEX3D(GH,i-1,j-1,k );
ijpkp = CCTK_GFINDEX3D(GH,i ,j+1,k+1);
ijpkm = CCTK_GFINDEX3D(GH,i ,j+1,k-1);
ijmkp = CCTK_GFINDEX3D(GH,i ,j-1,k+1);
ijmkm = CCTK_GFINDEX3D(GH,i ,j-1,k-1);
ipjkp = CCTK_GFINDEX3D(GH,i+1,j ,k+1);
ipjkm = CCTK_GFINDEX3D(GH,i+1,j ,k-1);
imjkp = CCTK_GFINDEX3D(GH,i-1,j ,k+1);
imjkm = CCTK_GFINDEX3D(GH,i-1,j ,k-1);
ac = -1.0*uxx[ipjk] - 2.0*uxx[ijk] - 1.0*uxx[imjk]
-1.0*uyy[ijpk] - 2.0*uyy[ijk] - 1.0*uyy[ijmk]
-1.0*uzz[ijkp] - 2.0*uzz[ijk] - 1.0*uzz[ijkm];
if (Mstorage)
ac += Mlin[ijk];
ae = uxx[ipjk]+uxx[ijk];
aw = uxx[imjk]+uxx[ijk];
an = uyy[ijpk]+uyy[ijk];
as = uyy[ijmk]+uyy[ijk];
at = uzz[ijkp]+uzz[ijk];
ab = uzz[ijkm]+uzz[ijk];
ane = uxy[ijpk]+uxy[ipjk];
anw =-uxy[imjk]-uxy[ijpk];
ase =-uxy[ipjk]-uxy[ijmk];
asw = uxy[imjk]+uxy[ijmk];
ate = uxz[ijkp]+uxz[ipjk];
atw =-uxz[imjk]-uxz[ijkp];
abe =-uxz[ipjk]-uxz[ijkm];
abw = uxz[imjk]+uxz[ijkm];
atn = uyz[ijpk]+uyz[ijkp];
ats =-uyz[ijkp]-uyz[ijmk];
abn =-uyz[ijkm]-uyz[ijpk];
abs = uyz[ijkm]+uyz[ijmk];
residual = ac * var[ijk]
+ ae *var[ipjk] + aw*var[imjk]
+ an *var[ijpk] + as*var[ijmk]
+ at *var[ijkp] + ab*var[ijkm];
residual = residual
+ ane*var[ipjpk] + anw*var[imjpk];
residual = residual
+ ase*var[ipjmk] + asw*var[imjmk];
residual = residual
+ ate*var[ipjkp] + atw*var[imjkp]
+ abe*var[ipjkm] + abw*var[imjkm]
+ atn*var[ijpkp] + ats*var[ijmkp]
+ abn*var[ijpkm] + abs*var[ijmkm];
if (Nstorage)
residual +=Nlin[ijk];
resnorm = resnorm + fabs(residual);
var[ijk] = var[ijk] - omega*residual/ac;
}
}
}
/* reduction operation on processor-local residual values */
ierr = CCTK_ReduceLocScalar(GH, -1, sum_handle,
&resnorm, &glob_residual, CCTK_VARIABLE_REAL);
if (ierr<0)
CCTK_WARN(1,"Reduction of residual failed");
glob_residual = glob_residual /
(GH->cctk_gsh[0]*GH->cctk_gsh[1]*GH->cctk_gsh[2]);
/* apply symmetry boundary conditions within loop */
if (CartSymVI(GH,FieldIndex)<0)
CCTK_WARN(1,"CartSymVI failed in EllSOR loop");
/* apply boundary conditions within loop */
if (CCTK_EQUALS(sor_bound,"robin"))
ierr = BndRobinVI(GH, sw, finf, npow, FieldIndex);
/* synchronization of grid variable */
CCTK_SyncGroupWithVarI(GH, FieldIndex);
/* Leave iteration loop if tolerance criterium is met */
if (glob_residual<tol)
break;
}
/* Information for the user if the solve did not converge within
the given constraints of max.iteration and tolerance */
if (residual>tol)
CCTK_VWarn(1,__LINE__,__FILE__,CCTK_THORNSTRING,
"SOR SOLVER DID NOT CONVERGE within given "
"tolerance/max.number of iterations.\n "
"max. iteration %d residual (tolerance): %g (%g)\n",
maxit, glob_residual, tol );
if (uxx) free(uxx);
if (uyy) free(uyy);
if (uzz) free(uzz);
if (uxy) free(uxy);
if (uxz) free(uxz);
if (uyz) free(uyz);
return;
}
|
