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/*
* Copyright 2017 Anton Khirnov <anton@khirnov.net>
*
* This program is free software: you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation, either version 3 of the License, or
* (at your option) any later version.
*
* This program is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with this program. If not, see <http://www.gnu.org/licenses/>.
*/
#include <math.h>
#include "common.h"
#include "pssolve.h"
#include "td_constraints.h"
#define I_C sqrt(225.0 / (8.0 * M_PI))
static double I_m2(double x, double a)
{
return a * I_C * exp(-SQR(x));
}
static double I_m1(double x, double a)
{
return a * I_C * (-2.0 * x * exp(-SQR(x)));
}
static double I_0(double x, double a)
{
return a * I_C * (-2.0 + 4.0 * SQR(x)) * exp(-SQR(x));
}
static double I_p1(double x, double a)
{
return a * I_C * (12.0 * x - 8.0 * x * SQR(x)) * exp(-SQR(x));
}
static double I_p2(double x, double a)
{
return a * I_C * (12.0 - 48.0 * SQR(x) + 16.0 * SQR(SQR(x))) * exp(-SQR(x));
}
static double I_p3(double x, double a)
{
return a * I_C * (-120.0 * x + 144.0 * x * SQR(x) - 32.0 * x * SQR(SQR(x))) * exp(-SQR(x));
}
static double K_rtheta(double a, double r, double theta)
{
double r2 = r * r;
double r3 = r2 * r;
// equal to the below
return a * I_C * exp(-r2) * sin(2 * theta) * (32.0 * r3 - 48.0 * r);
//return ((I_p2(-r, a) + I_p2(r, a)) * r3 + 3.0 * (I_p1(-r, a) - I_p1(r, a)) * r2 +
// 6.0 * (I_0(-r, a) + I_0(r, a)) * r + 6.0 * (I_m1(-r, a) - I_m1(r, a))) * sin(2.0 * theta) / r4;
}
static double K_rtheta_dtheta(double a, double r, double theta)
{
return 2.0 * cos(2.0 * theta) * K_rtheta(a, r, theta) / sin(2.0 * theta);
}
static double K_rtheta_dr(double a, double r, double theta)
{
double r2 = r * r;
return -2 * r * K_rtheta(a, r, theta) + a * I_C * exp(-r2) * sin(2 * theta) * (3.0 * 32.0 * r2 - 48.0);
//return ((-I_p3(-r, a) + I_p3(r, a)) / r + 3.0 * (-I_p2(-r, a) - I_p2(r, a)) / (SQR(r)) +
// 6.0 * (-I_p1(-r, a) + I_p1(r, a)) / (r * SQR(r)) + 6.0 * (-I_0(-r, a) - I_0(r, a)) / (SQR(SQR(r))) +
// (I_p2(-r, a) + I_p2(r, a)) / (-SQR(r)) + 3.0 * (I_p1(-r, a) - I_p1(r, a)) * (-2.0 / (r * SQR(r))) +
// 6.0 * (I_0(-r, a) + I_0(r, a)) * (-3.0 / (SQR(SQR(r)))) + 6.0 * (I_m1(-r, a) - I_m1(r, a)) * (-4.0 / (r * SQR(SQR(r))))) * sin(2.0 * theta);
}
#include "eval_constraints.c"
#include "eval_k_rtheta.c"
//typedef void (*eval_metric_func)(double a, double L, double r_0, double x_0, double x_1, double psi_val_00, double psi_val_01, double psi_val_02, double psi_val_10, double psi_val_11, double psi_val_20, double *res);
//
//static const eval_metric_func eval_dmetric[3] = {
// eval_dmetric_0,
// eval_dmetric_1,
// eval_dmetric_2,
//};
//
//static const eval_metric_func eval_d2metric[3][3] = {
// {
// eval_d2metric_00,
// eval_d2metric_01,
// eval_d2metric_02,
// },
// {
// eval_d2metric_10,
// eval_d2metric_11,
// eval_d2metric_12,
// },
// {
// eval_d2metric_20,
// eval_d2metric_21,
// eval_d2metric_22,
// },
//};
#define EQNAME constraint_eq_ham
#define EQUATION TD_CONSTRAINT_EQ_HAM
#include "td_constraints_template.c"
#undef EQNAME
#undef EQUATION
#define EQNAME constraint_eq_mom_0
#define EQUATION TD_CONSTRAINT_EQ_MOM_0
#include "td_constraints_template.c"
#undef EQNAME
#undef EQUATION
#define EQNAME constraint_eq_mom_1
#define EQUATION TD_CONSTRAINT_EQ_MOM_1
#include "td_constraints_template.c"
#undef EQNAME
#undef EQUATION
void
(*constraint_funcs[TD_CONSTRAINT_EQ_NB])(const double a,
unsigned int nb_coords[2], double *coords[2],
double *vars[TD_CONSTRAINT_VAR_NB][PSSOLVE_DIFF_ORDER_NB],
double *out) = {
[TD_CONSTRAINT_EQ_HAM] = constraint_eq_ham,
[TD_CONSTRAINT_EQ_MOM_0] = constraint_eq_mom_0,
[TD_CONSTRAINT_EQ_MOM_1] = constraint_eq_mom_1,
};
static double q_gundlach(const double a, double rho, double z)
{
return a * SQR(rho) * exp(-(SQR(rho) + SQR(z)));
}
static double dq_rho_gundlach(const double a, double rho, double z)
{
return a * 2 * rho * exp(-SQR(rho) - SQR(z)) * (1.0 - rho * (rho));
}
static double d2q_rho_gundlach(const double a, double rho, double z)
{
double rho2 = SQR(rho);
return a * 2 * exp(-SQR(rho) - SQR(z)) * (1.0 - 4.0 * rho * (rho) - rho2 + 2.0 * rho2 * SQR(rho));
}
static double d2q_rho_z_gundlach(const double a, double rho, double z)
{
return a * 4 * z * rho * exp(-SQR(rho) - SQR(z)) * (rho * (rho) - 1.0);
}
static double dq_z_gundlach(const double a, double rho, double z)
{
return -a * 2 * z * SQR(rho) * exp(-SQR(rho) - SQR(z));
}
static double d2q_z_gundlach(const double a, double rho, double z)
{
return a * 2 * SQR(rho) * exp(-SQR(rho) - SQR(z)) * (2 * SQR(z) - 1.0);
}
int tdi_constraints_eval(enum TDConstraintEq eq,
const double a,
unsigned int nb_coords[2], double *coords[2],
double *vars[TD_CONSTRAINT_VAR_NB][PSSOLVE_DIFF_ORDER_NB],
double *out)
{
//for (int idx1 = 0; idx1 < nb_coords[1]; idx1++) {
// const double theta = coords[1][idx1];
// for (int idx0 = 0; idx0 < nb_coords[0]; idx0++) {
// const double r = coords[0][idx0];
// const double rho = r * sin(theta);
// const double z = r * cos(theta);
// const double ct = cos(theta);
// const double st = sin(theta);
// const int idx = idx1 * nb_coords[0] + idx0;
// const double laplace = vars[eq][PSSOLVE_DIFF_ORDER_20][idx] +
// vars[eq][PSSOLVE_DIFF_ORDER_10][idx] * (2.0 / r) +
// vars[eq][PSSOLVE_DIFF_ORDER_02][idx] * (1.0 / SQR(r)) +
// vars[eq][PSSOLVE_DIFF_ORDER_01][idx] * (ct / (SQR(r) * st));
// out[idx] = laplace + 0.25 * (d2q_z_gundlach(a, rho, z) + d2q_rho_gundlach(a, rho, z)) * (1.0 + vars[eq][PSSOLVE_DIFF_ORDER_00][idx]);
// }
//}
constraint_funcs[eq](a, nb_coords, coords, vars, out);
return 0;
}
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