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// TwoPunctures: File "TwoPunctures.c"
#include <assert.h>
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <math.h>
#include <ctype.h>
#include "cctk.h"
#include "cctk_Arguments.h"
#include "cctk_Parameters.h"
#include "TP_utilities.h"
#include "TwoPunctures.h"
static inline double pow2 (const double x)
{
return x*x;
}
static inline double pow4 (const double x)
{
return x*x*x*x;
}
// -------------------------------------------------------------------
void
TwoPunctures (CCTK_ARGUMENTS)
{
DECLARE_CCTK_ARGUMENTS;
DECLARE_CCTK_PARAMETERS;
enum GRID_SETUP_METHOD { GSM_Taylor_expansion, GSM_evaluation };
enum GRID_SETUP_METHOD gsm;
int nvar = 1, n1 = npoints_A, n2 = npoints_B, n3 = npoints_phi;
int i, j, k, ntotal = n1 * n2 * n3 * nvar;
static double *F = NULL;
static derivs u, v;
double admMass;
if (! F) {
/* Solve only when called for the first time */
F = dvector (0, ntotal - 1);
allocate_derivs (&u, ntotal);
allocate_derivs (&v, ntotal);
CCTK_INFO ("Solving puncture equation");
Newton (cctkGH, nvar, n1, n2, n3, v, Newton_tol, Newton_maxit);
F_of_v (cctkGH, nvar, n1, n2, n3, v, F, u);
/* print out ADM mass, eq.: \Delta M_ADM=2*r*u=4*b*V for A=1,B=0,phi=0 */
admMass = (par_m_plus + par_m_minus
- 4*par_b*PunctEvalAtArbitPosition(v.d0, 1, 0, 0, n1, n2, n3));
CCTK_VInfo (CCTK_THORNSTRING, "ADM mass is %g\n", admMass);
}
if (CCTK_EQUALS(grid_setup_method, "Taylor expansion"))
{
gsm = GSM_Taylor_expansion;
}
else if (CCTK_EQUALS(grid_setup_method, "evaluation"))
{
gsm = GSM_evaluation;
}
else
{
CCTK_WARN (0, "internal error");
}
CCTK_INFO ("Interpolating result");
if (CCTK_EQUALS(metric_type, "static conformal")) {
if (CCTK_EQUALS(conformal_storage, "factor")) {
*conformal_state = 1;
} else if (CCTK_EQUALS(conformal_storage, "factor+derivs")) {
*conformal_state = 2;
} else if (CCTK_EQUALS(conformal_storage, "factor+derivs+2nd derivs")) {
*conformal_state = 3;
}
} else {
*conformal_state = 0;
}
for (k = 0; k < cctk_lsh[2]; ++k)
{
for (j = 0; j < cctk_lsh[1]; ++j)
{
for (i = 0; i < cctk_lsh[0]; ++i)
{
const int ind = CCTK_GFINDEX3D (cctkGH, i, j, k);
const double r_plus
= sqrt(pow2(x[ind] - par_b) + pow2(y[ind]) + pow2(z[ind]));
const double r_minus
= sqrt(pow2(x[ind] + par_b) + pow2(y[ind]) + pow2(z[ind]));
double U;
switch (gsm)
{
case GSM_Taylor_expansion:
U = PunctTaylorExpandAtArbitPosition
(0, nvar, n1, n2, n3, v, x[ind], y[ind], z[ind]);
break;
case GSM_evaluation:
U = PunctIntPolAtArbitPosition
(0, nvar, n1, n2, n3, v, x[ind], y[ind], z[ind]);
break;
default:
assert (0);
}
const double psi1 = 1
+ 0.5 * par_m_plus / r_plus
+ 0.5 * par_m_minus / r_minus + U;
double static_psi = 1;
double Aij[3][3];
BY_Aijofxyz (x[ind], y[ind], z[ind], Aij);
if (*conformal_state > 0) {
double xp, yp, zp, rp, ir;
double s1, s3, s5;
double p, px, py, pz, pxx, pxy, pxz, pyy, pyz, pzz;
p = 1.0;
px = py = pz = 0.0;
pxx = pxy = pxz = 0.0;
pyy = pyz = pzz = 0.0;
/* first puncture */
xp = x[ind] - par_b;
yp = y[ind];
zp = z[ind];
rp = sqrt (xp*xp + yp*yp + zp*zp);
ir = 1.0/rp;
s1 = 0.5*par_m_plus*ir;
s3 = -s1*ir*ir;
s5 = -3.0*s3*ir*ir;
p += s1;
px += xp*s3;
py += yp*s3;
pz += zp*s3;
pxx += xp*xp*s5 + s3;
pxy += xp*yp*s5;
pxz += xp*zp*s5;
pyy += yp*yp*s5 + s3;
pyz += yp*zp*s5;
pzz += zp*zp*s5 + s3;
/* second puncture */
xp = x[ind] + par_b;
yp = y[ind];
zp = z[ind];
rp = sqrt (xp*xp + yp*yp + zp*zp);
ir = 1.0/rp;
s1 = 0.5*par_m_minus*ir;
s3 = -s1*ir*ir;
s5 = -3.0*s3*ir*ir;
p += s1;
px += xp*s3;
py += yp*s3;
pz += zp*s3;
pxx += xp*xp*s5 + s3;
pxy += xp*yp*s5;
pxz += xp*zp*s5;
pyy += yp*yp*s5 + s3;
pyz += yp*zp*s5;
pzz += zp*zp*s5 + s3;
if (*conformal_state >= 1) {
static_psi = p;
psi[ind] = static_psi;
}
if (*conformal_state >= 2) {
psix[ind] = px / static_psi;
psiy[ind] = py / static_psi;
psiz[ind] = pz / static_psi;
}
if (*conformal_state >= 3) {
psixx[ind] = pxx / static_psi;
psixy[ind] = pxy / static_psi;
psixz[ind] = pxz / static_psi;
psiyy[ind] = pyy / static_psi;
psiyz[ind] = pyz / static_psi;
psizz[ind] = pzz / static_psi;
}
} /* if conformal-state > 0 */
puncture_u[ind] = U;
gxx[ind] = pow4 (psi1 / static_psi);
gxy[ind] = 0;
gxz[ind] = 0;
gyy[ind] = pow4 (psi1 / static_psi);
gyz[ind] = 0;
gzz[ind] = pow4 (psi1 / static_psi);
kxx[ind] = Aij[0][0] / pow2(psi1);
kxy[ind] = Aij[0][1] / pow2(psi1);
kxz[ind] = Aij[0][2] / pow2(psi1);
kyy[ind] = Aij[1][1] / pow2(psi1);
kyz[ind] = Aij[1][2] / pow2(psi1);
kzz[ind] = Aij[2][2] / pow2(psi1);
}
}
}
if (0) {
/* Keep the result around for the next time */
free_dvector (F, 0, ntotal - 1);
free_derivs (&u, ntotal);
free_derivs (&v, ntotal);
}
}
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