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/* set_bound_axisym.c, BB */
/*@@
@file SetBoundAxisym.c
@date Sat Nov 6 16:35:46 MET 1999
@author Sai Iyer
@desc
An implementation of Steve Brandt's idea for doing
axisymmetry with 3d stencils.
Cactus 4 version of Bernd Bruegmann's set_bound_axisym_GT.
@enddesc
@@*/
static char *rcsid = "$Id$"
#include "cctk.h"
#include "cctk_arguments.h"
#include "cctk_parameters.h"
#include "cartoon2D.h"
#include "math.h"
/* Number of components */
int tensor_type_n[N_TENSOR_TYPES] = {1, 3, 6};
/* set boundaries of a grid tensor assuming axisymmetry
- handles lower boundary in x
- does not touch other boundaries
- coordinates and rotation coefficients are independent of z and should
be precomputed
- this is also true for the constants in interpolator, but this may
be too messy
- minimizes conceptual warpage, not computationally optimized
*/
/* uses rotation matrix and its inverse as linear transformation on
arbitrary tensor indices -- I consider this a good compromise
between doing index loops versus using explicit formulas in
cos(phi) etc with messy signs
*/
int SetBoundAxiSym(cGH *GH, int vi, int tensortype) {
{
int i, j, k, di, dj, dk, ijk;
int jj, n, s;
Double x, y, rho;
Double rxx, rxy, ryx, ryy;
Double sxx, sxy, syx, syy;
Double f[6], fx, fy, fz, fxx, fxy, fxz, fyy, fyz, fzz;
Double *t, *tx, *ty, *tz, *txx, *txy, *txz, *tyy, *tyz, *tzz;
if (0) printf("sba(%s)\n", GT->gf[0]->name);
/* stencil width: in x-direction use ghost zone width,
in y-direction use ny/2, see below */
s = GH->stencil_width;
/* Cactus loop in C: grid points with y = 0 */
/* compare thorn_BAM_Elliptic */
/* strides used in stencils, should be provided by cactus */
di = 1;
dj = GH->lnx;
dk = GH->lnx*GH->lny;
/* y = 0 */
j = GH->ny/2;
/* z-direction: include lower and upper boundary */
for (k = 0; k < GH->lnz; k++)
/* y-direction: as many zombies as the evolution stencil needs */
for (jj = 1, dj = jj*GH->lnx; jj <= GH->ny/2; jj++, dj = jj*GH->lnx)
/* x-direction: zombie for x < 0, including upper boundary for extrapol */
for (i = -s; i < GH->lnx; i++) {
/* index into linear memory */
ijk = DI(GH,i,j,k);
/* what a neat way to hack in the zombie for x < 0, y = 0 */
if (i < 0) {i += s; ijk += s; dj = 0;}
/* compute coordinates (could also use Cactus grid function) */
x = GH->lx0 + GH->dx0 * i;
y = (dj) ? GH->dy0 * jj : 0;
rho = sqrt(x*x + y*y);
/* compute rotation matrix
note that this also works for x <= 0 (at lower boundary in x)
note that rho is nonzero by definition if cactus checks dy ...
*/
rxx = x/rho;
ryx = y/rho;
rxy = -ryx;
ryy = rxx;
/* inverse rotation matrix, assuming detr = 1 */
sxx = ryy;
syx = -ryx;
sxy = -rxy;
syy = rxx;
/* interpolate grid functions */
for (n = 0; n < GT->n; n++)
f[n] = axisym_interpolate(GH, GT->gf[n], i, di, ijk, rho);
/* rotate grid tensor by matrix multiplication */
if (GT->tensor_type == TENSOR_TYPE_SCALAR) {
t = GT->gf[0]->data;
t[ijk+dj] = f[0];
t[ijk-dj] = f[0];
}
else if (GT->tensor_type == TENSOR_TYPE_U) {
tx = GT->gf[0]->data;
ty = GT->gf[1]->data;
tz = GT->gf[2]->data;
fx = f[0];
fy = f[1];
fz = f[2];
tx[ijk+dj] = rxx * fx + rxy * fy;
ty[ijk+dj] = ryx * fx + ryy * fy;
tz[ijk+dj] = fz;
tx[ijk-dj] = sxx * fx + sxy * fy;
ty[ijk-dj] = syx * fx + syy * fy;
tz[ijk-dj] = fz;
}
else if (GT->tensor_type == TENSOR_TYPE_DDSYM) {
txx = GT->gf[0]->data;
txy = GT->gf[1]->data;
txz = GT->gf[2]->data;
tyy = GT->gf[3]->data;
tyz = GT->gf[4]->data;
tzz = GT->gf[5]->data;
fxx = f[0];
fxy = f[1];
fxz = f[2];
fyy = f[3];
fyz = f[4];
fzz = f[5];
txx[ijk+dj] = fxx*sxx*sxx + 2*fxy*sxx*syx + fyy*syx*syx;
tyy[ijk+dj] = fxx*sxy*sxy + 2*fxy*sxy*syy + fyy*syy*syy;
txy[ijk+dj] = fxx*sxx*sxy + fxy*(sxy*syx+sxx*syy) + fyy*syx*syy;
txz[ijk+dj] = fxz*sxx + fyz*syx;
tyz[ijk+dj] = fxz*sxy + fyz*syy;
tzz[ijk+dj] = fzz;
txx[ijk-dj] = fxx*rxx*rxx + 2*fxy*rxx*ryx + fyy*ryx*ryx;
tyy[ijk-dj] = fxx*rxy*rxy + 2*fxy*rxy*ryy + fyy*ryy*ryy;
txy[ijk-dj] = fxx*rxx*rxy + fxy*(rxy*ryx+rxx*ryy) + fyy*ryx*ryy;
txz[ijk-dj] = fxz*rxx + fyz*ryx;
tyz[ijk-dj] = fxz*rxy + fyz*ryy;
tzz[ijk-dj] = fzz;
}
else {
/* oops */
}
/* what a neat way to hack out the zombies for x < 0, y = 0 */
if (dj == 0) {i -= s; ijk -= s; dj = jj*GH->lnx;}
}
/* syncs needed after interpolation (actually only for x direction) */
for (n = 0; n < GT->n; n++)
SyncGF(GH, GT->gf[n]);
}
/* interpolation on x-axis */
Double axisym_interpolate(pGH *GH, pGF *GF, int i, int di, int ijk, Double x)
{
Double *f = GF->data;
Double c, d, x0;
/* find i such that x(i) < x <= x(i+1)
for rotation on entry always x > x(i), but sometimes also x > x(i+1) */
while (x > GH->lx0 + GH->dx0 * (i+1)) {i++; ijk++;}
/* the original demo */
if (0) {
c = (f[ijk+di] - f[ijk])/GH->dx0;
d = f[ijk];
x0 = GH->lx0 + GH->dx0 * i;
return c*(x-x0) + d;
}
/* first attempt to interface to JT's interpolator */
if (1) {
double interpolate_local(int order, double x0, double dx,
double y[], double x);
double y[6], r;
int n, offset;
int order = cartoon_order;
/* offset of stencil, note that rotation leads to x close to x0
for large x */
offset = order/2;
/* shift stencil at boundaries */
/* note that for simplicity we don't distinguish between true boundaries
and decomposition boundaries: the sync fixes that! */
if (i-offset < 0) offset = i;
if (i-offset+order >= GH->lnx) offset = i+order-GH->lnx+1;
/* fill in info */
/* fills in old data near axis, but as long as stencil at axis is
centered, no interpolation happens anyway */
x0 = GH->lx0 + GH->dx0 * (i-offset);
for (n = 0; n <= order; n++) {
y[n] = f[ijk-offset+n];
if (0) printf("y[%d]=%6.4f ", n, y[n]);
}
/* call interpolator */
r = interpolate_local(order, x0, GH->dx0, y, x);
if (0) printf("i %d x %7.4f x0 %7.4f r %7.4f\n", i, x, x0, r);
return r;
}
return 0;
}
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