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/*@@
@file Misner_standard.c
@date March 1997
@author Joan Masso
@desc
Set up initial data for two Misner black holes
@enddesc
@history
@hdate Sun Oct 17 11:05:48 1999 @hauthor Tom Goodale
@hdesc Converted to C
@endhistory
@@*/
#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#include "cctk.h"
#include "cctk_Arguments.h"
#include "cctk_Parameters.h"
#include "CactusEinstein/Einstein/src/Einstein.h"
#define SQR(a) ((a)*(a))
/*@@
@routine Misner_standard
@date
@author Joan Masso, Ed Seidel
@desc
Initialize the metric with a time symmetrical
black hole spacetime containing
two axially symmetric misner black holes with a
mass/length parameter mu. The mass is computed.
The spacetime line element has the form:
$$ ds^2 = -dt^2 + \Psi^4 (dx^2+dy^2+dz^2) $$
and only $\Psi$ differs.
(Conformal factor from Karen Camarda)
@enddesc
@calls
@history
@endhistory
@par mu
@pdesc Misner parameter.
@ptype real
@pcomment Values less than 1.8 do not really correspond to two
black holes, as there is an initial single event horizon
surrounding the throats. So, with low values of mu we also
have distorted single black holes.
@endpar
@par nmax
@pdesc Summation limit for the misner series in the 'twobh' case.
@ptype integer
@endpar
@@*/
void Misner_standard(CCTK_ARGUMENTS)
{
DECLARE_CCTK_ARGUMENTS
DECLARE_CCTK_PARAMETERS
int i, n;
int npoints;
CCTK_REAL *csch, *coth, inv_r1, inv_r2;
CCTK_REAL x_squared, y_squared, xy_squared;
CCTK_REAL inv_r1_cubed, inv_r2_cubed;
CCTK_REAL inv_r1_5, inv_r2_5;
CCTK_REAL inv_psi;
CCTK_INT powfac;
const CCTK_REAL zero = 0.0, one = 1.0, three = 3.0;
/* total number of points on this processor */
npoints = cctk_lsh[0] * cctk_lsh[1] * cctk_lsh[2];
/* Initialize so we can accumulate
* -------------------------------
*/
if (use_conformal_derivs)
{
memset (psix, 0, npoints * sizeof (CCTK_REAL));
memset (psiy, 0, npoints * sizeof (CCTK_REAL));
memset (psiz, 0, npoints * sizeof (CCTK_REAL));
memset (psixx, 0, npoints * sizeof (CCTK_REAL));
memset (psixy, 0, npoints * sizeof (CCTK_REAL));
memset (psixz, 0, npoints * sizeof (CCTK_REAL));
memset (psiyy, 0, npoints * sizeof (CCTK_REAL));
memset (psiyz, 0, npoints * sizeof (CCTK_REAL));
memset (psizz, 0, npoints * sizeof (CCTK_REAL));
}
csch = (CCTK_REAL *) malloc (2 * (nmax + 1) * sizeof (CCTK_REAL));
coth = csch + nmax + 1;
/* compute the ADM mass
* --------------------
*/
mass = zero;
for(n = 1; n <= nmax; n++)
{
csch[n] = one / sinh(mu*n);
coth[n] = one / tanh(mu*n);
mass += 4.0 * csch[n];
}
CCTK_VInfo(CCTK_THORNSTRING, "ADM mass is %f", (double) mass);
for(i = 0; i < npoints; i++)
{
psi [i] = one;
x_squared = SQR(x[i]);
y_squared = SQR(y[i]);
xy_squared = x_squared + y_squared;
for(n = nmax; n >= 1; n--)
{
inv_r1 = one / sqrt(xy_squared+SQR(z[i]+coth[n]));
inv_r2 = one / sqrt(xy_squared+SQR(z[i]-coth[n]));
psi[i] += csch[n]*(inv_r1 + inv_r2);
if (use_conformal_derivs)
{
inv_r1_cubed = inv_r1 * inv_r1 * inv_r1;
inv_r2_cubed = inv_r2 * inv_r2 * inv_r2;
inv_r1_5 = pow(inv_r1, 5);
inv_r2_5 = pow(inv_r2, 5);
psix[i] += -x[i] * (inv_r2_cubed + inv_r1_cubed) * csch[n];
psiy[i] += -y[i] * (inv_r2_cubed + inv_r1_cubed) * csch[n];
psiz[i] += (-(z[i]-coth[n])*inv_r2_cubed - (z[i]+coth[n])*inv_r1_cubed) * csch[n];
psixx[i] += (three*x_squared*(inv_r1_5 + inv_r2_5)
- inv_r1_cubed - inv_r2_cubed) * csch[n];
psixy[i] += three*x[i]*y[i]*(inv_r1_5 + inv_r2_5) * csch[n];
psixz[i] += (three*x[i]*(z[i] - coth[n])*inv_r2_5
+ three*x[i]*(z[i] + coth[n])*inv_r1_5) * csch[n];
psiyy[i] += (three*y_squared*(inv_r1_5 + inv_r2_5)
- inv_r1_cubed - inv_r2_cubed) * csch[n];
psiyz[i] += (three*y[i]*(z[i] - coth[n])*inv_r2_5
+ three*y[i]*(z[i] + coth[n])*inv_r1_5) * csch[n];
psizz[i] += (-inv_r2_cubed+three*SQR(z[i] - coth[n])*inv_r2_5
+ three*SQR(z[i] + coth[n])*inv_r1_5 - inv_r1_cubed) * csch[n];
}
}
/* Cactus convention
* -----------------
*/
if (use_conformal_derivs)
{
inv_psi = one / psi[i];
psix[i] *= inv_psi;
psiy[i] *= inv_psi;
psiz[i] *= inv_psi;
psixx[i] *= inv_psi;
psixy[i] *= inv_psi;
psixz[i] *= inv_psi;
psiyy[i] *= inv_psi;
psiyz[i] *= inv_psi;
psizz[i] *= inv_psi;
}
}
/* Should initialize lapse to Cadez value if possible
* --------------------------------------------------
*/
if (CCTK_Equals(initial_lapse,"cadez"))
{
CCTK_INFO("Initialise with cadez lapse");
for(i = 0; i < npoints; i++)
{
xy_squared = SQR(x[i]) + SQR(y[i]);
alp[i] = one;
powfac = 1;
for(n = 1; n <= nmax; n++)
{
inv_r1 = one / sqrt(xy_squared+SQR(z[i]+coth[n]));
inv_r2 = one / sqrt(xy_squared+SQR(z[i]-coth[n]));
powfac = -powfac;
alp[i] += powfac * csch[n] * (inv_r1 + inv_r2);
}
alp[i] /= psi[i];
}
}
/* Metric depends on conformal state
* ---------------------------------
*/
if (*conformal_state == CONFORMAL_METRIC)
{
for(i = 0; i < npoints; i++)
{
gxx[i] = one;
gyy[i] = one;
gzz[i] = one;
}
}
else
{
for(i = 0; i < npoints; i++)
{
gxx[i] = pow(psi[i],4);
gyy[i] = gxx[i];
gzz[i] = gxx[i];
}
}
memset (gxy, 0, npoints * sizeof (CCTK_REAL));
memset (gxz, 0, npoints * sizeof (CCTK_REAL));
memset (gyz, 0, npoints * sizeof (CCTK_REAL));
/* Time-symmetric data
* -------------------
*/
memset (kxx, 0, npoints * sizeof (CCTK_REAL));
memset (kyy, 0, npoints * sizeof (CCTK_REAL));
memset (kzz, 0, npoints * sizeof (CCTK_REAL));
memset (kxy, 0, npoints * sizeof (CCTK_REAL));
memset (kxz, 0, npoints * sizeof (CCTK_REAL));
memset (kyz, 0, npoints * sizeof (CCTK_REAL));
if (csch)
{
free (csch);
}
}
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