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#include <ctype.h>
#include <math.h>
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <gsl/gsl_spline.h>
#include "cctk.h"
#include "cctk_Arguments.h"
#include "cctk_Parameters.h"
#define MAX(x,y) (x) > (y) ? (x) : (y)
#define SQR(x) ((x)*(x))
#define MASS 1
/*
* the constant C from e.g. 0908.1063v4
*/
#define TRUMPET_CONST (3*sqrt(3)*SQR(MASS)/4)
/*
* small number to avoid r=0 singularities
*/
#define EPS 1E-08
/*
* isotropic/coordinate radius
*/
#define ISO_R(index) (sqrt(SQR(x[index]) + SQR(y[index]) + SQR(z[index]) + EPS))
static inline double r_areal_to_isotropic(double r, double m)
{
double par = sqrt(4*r*r + 4*m*r + 3*m*m);
double term1 = (2*r + m + par)/4;
double term2 = (4 + 3*M_SQRT2)*(2*r - 3*m)/(8*r + 6*m + 3*M_SQRT2*par);
return term1*pow(term2, M_SQRT1_2);
}
/**
* get maximal isotropic r
*/
static CCTK_REAL get_max_r(CCTK_INT dim)
{
CCTK_REAL phys_min[dim], phys_max[dim], ext_min[dim], ext_max[dim], int_min[dim], int_max[dim], step[dim];
CCTK_REAL max = 0;
GetDomainSpecification(dim, phys_min, phys_max, int_min, int_max, ext_min, ext_max, step);
for (int i = 0; i < dim; i++) {
max = MAX(max, abs(phys_min[i]));
max = MAX(max, abs(phys_max[i]));
}
return sqrt(dim)*2*max;
}
static void get_r_tables(double **pr_iso, double **pr_areal, CCTK_INT *size, CCTK_INT dim)
{
#define STEP 0.0001
double *r_iso, *r_areal, max = get_max_r(dim);
int count = max*2/STEP, i = 0;
r_iso = malloc(count*sizeof(*r_iso));
r_areal = malloc(count*sizeof(*r_areal));
for (i = 0;;i++) {
if (i >= count) {
count *= 2;
r_iso = realloc(r_iso, count*sizeof(*r_iso));
r_areal = realloc(r_areal, count*sizeof(*r_areal));
}
r_areal[i] = i*STEP + 1.5;
r_iso[i] = r_areal_to_isotropic(r_areal[i], 1);
if (r_iso[i] > max)
break;
}
*pr_iso = r_iso;
*pr_areal = r_areal;
*size = i;
}
void trumpet_data(CCTK_ARGUMENTS)
{
DECLARE_CCTK_ARGUMENTS;
DECLARE_CCTK_PARAMETERS;
gsl_interp_accel *acc;
gsl_spline *spline;
double *r_iso, *r_areal;
CCTK_INT size;
get_r_tables(&r_iso, &r_areal, &size, cctk_dim);
spline = gsl_spline_alloc(gsl_interp_cspline, size);
gsl_spline_init(spline, r_iso, r_areal, size);
acc = gsl_interp_accel_alloc();
memset(gxy, 0, sizeof(*gxy)*CCTK_GFINDEX3D(cctkGH, cctk_lsh[0]-1, cctk_lsh[1]-1, cctk_lsh[2]-1));
memset(gxz, 0, sizeof(*gxy)*CCTK_GFINDEX3D(cctkGH, cctk_lsh[0]-1, cctk_lsh[1]-1, cctk_lsh[2]-1));
memset(gyz, 0, sizeof(*gxy)*CCTK_GFINDEX3D(cctkGH, cctk_lsh[0]-1, cctk_lsh[1]-1, cctk_lsh[2]-1));
#pragma omp parallel for
for (int k = 0; k < cctk_lsh[2]; k++)
for (int j = 0; j < cctk_lsh[1]; j++)
for (int i = 0; i < cctk_lsh[0]; i++) {
int index = CCTK_GFINDEX3D(cctkGH, i, j, k);
CCTK_REAL r = ISO_R(index);
CCTK_REAL R = gsl_spline_eval(spline, r, acc);
CCTK_REAL psi2 = R/r, psi4 = psi2*psi2;
CCTK_REAL k_fact = TRUMPET_CONST/(r*r*r*r*R);
gxx[index] = gyy[index] = gzz[index] = psi4;
kxx[index] = -k_fact*(3*SQR(x[index]) - SQR(r));
kyy[index] = -k_fact*(3*SQR(y[index]) - SQR(r));
kzz[index] = -k_fact*(3*SQR(z[index]) - SQR(r));
kxy[index] = -k_fact*3*x[index]*y[index];
kxz[index] = -k_fact*3*x[index]*z[index];
kyz[index] = -k_fact*3*y[index]*z[index];
}
}
void trumpet_lapse(CCTK_ARGUMENTS)
{
DECLARE_CCTK_ARGUMENTS;
DECLARE_CCTK_PARAMETERS;
gsl_interp_accel *acc;
gsl_spline *spline;
double *r_iso, *r_areal;
CCTK_INT size;
get_r_tables(&r_iso, &r_areal, &size, cctk_dim);
spline = gsl_spline_alloc(gsl_interp_cspline, size);
gsl_spline_init(spline, r_iso, r_areal, size);
acc = gsl_interp_accel_alloc();
#pragma omp parallel for
for (int k = 0; k < cctk_lsh[2]; k++)
for (int j = 0; j < cctk_lsh[1]; j++)
for (int i = 0; i < cctk_lsh[0]; i++) {
int index = CCTK_GFINDEX3D(cctkGH, i, j, k);
CCTK_REAL r = sqrt(SQR(x[index]) + SQR(y[index]) + SQR(z[index]) + EPS);
CCTK_REAL R = gsl_spline_eval(spline, r, acc);
alp[index] = sqrt(1 - 2*MASS/R + TRUMPET_CONST*TRUMPET_CONST/(R*R*R*R));
}
}
void trumpet_shift(CCTK_ARGUMENTS)
{
DECLARE_CCTK_ARGUMENTS;
DECLARE_CCTK_PARAMETERS;
gsl_interp_accel *acc;
gsl_spline *spline;
double *r_iso, *r_areal;
CCTK_INT size;
get_r_tables(&r_iso, &r_areal, &size, cctk_dim);
spline = gsl_spline_alloc(gsl_interp_cspline, size);
gsl_spline_init(spline, r_iso, r_areal, size);
acc = gsl_interp_accel_alloc();
#pragma omp parallel for
for (int k = 0; k < cctk_lsh[2]; k++)
for (int j = 0; j < cctk_lsh[1]; j++)
for (int i = 0; i < cctk_lsh[0]; i++) {
int index = CCTK_GFINDEX3D(cctkGH, i, j, k);
CCTK_REAL r = sqrt(SQR(x[index]) + SQR(y[index]) + SQR(z[index]) + EPS);
CCTK_REAL R = gsl_spline_eval(spline, r, acc);
betax[index] = TRUMPET_CONST*x[index]/(R*R*R);
betay[index] = TRUMPET_CONST*y[index]/(R*R*R);
betaz[index] = TRUMPET_CONST*z[index]/(R*R*R);
}
}
}
}
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