diff options
Diffstat (limited to 'td_constraints_template.c')
| -rw-r--r-- | td_constraints_template.c | 198 |
1 files changed, 198 insertions, 0 deletions
diff --git a/td_constraints_template.c b/td_constraints_template.c new file mode 100644 index 0000000..df09290 --- /dev/null +++ b/td_constraints_template.c @@ -0,0 +1,198 @@ +/* + * Teukolsky data -- template for the constraint equations definitions + * Copyright (C) 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/>. + */ + +#define L 1.0 +#define R_0 0.0 + +static void EQNAME(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 coord1 = coords[1][idx1]; + + for (int idx0 = 0; idx0 < nb_coords[0]; idx0++) { + const double coord0 = coords[0][idx0]; + + const double r = coord0; + const double theta = coord1; + + const int idx = idx1 * nb_coords[0] + idx0; + + const double psi = vars[TD_CONSTRAINT_VAR_CONFFAC][PSSOLVE_DIFF_ORDER_00][idx] + 1.0; + const double K_rr = vars[TD_CONSTRAINT_VAR_CURV_RR][PSSOLVE_DIFF_ORDER_00][idx]; + const double K_phiphi = vars[TD_CONSTRAINT_VAR_CURV_PHIPHI][PSSOLVE_DIFF_ORDER_00][idx]; + + const double dpsi_10 = vars[TD_CONSTRAINT_VAR_CONFFAC][PSSOLVE_DIFF_ORDER_10][idx]; + const double dpsi_01 = vars[TD_CONSTRAINT_VAR_CONFFAC][PSSOLVE_DIFF_ORDER_01][idx]; + const double dpsi_11 = vars[TD_CONSTRAINT_VAR_CONFFAC][PSSOLVE_DIFF_ORDER_11][idx]; + const double dpsi_20 = vars[TD_CONSTRAINT_VAR_CONFFAC][PSSOLVE_DIFF_ORDER_20][idx]; + const double dpsi_02 = vars[TD_CONSTRAINT_VAR_CONFFAC][PSSOLVE_DIFF_ORDER_02][idx]; + + const double dK_rr_10 = vars[TD_CONSTRAINT_VAR_CURV_RR][PSSOLVE_DIFF_ORDER_10][idx]; + const double dK_rr_01 = vars[TD_CONSTRAINT_VAR_CURV_RR][PSSOLVE_DIFF_ORDER_01][idx]; + const double dK_phiphi_10 = vars[TD_CONSTRAINT_VAR_CURV_PHIPHI][PSSOLVE_DIFF_ORDER_10][idx]; + const double dK_phiphi_01 = vars[TD_CONSTRAINT_VAR_CURV_PHIPHI][PSSOLVE_DIFF_ORDER_01][idx]; + + //const double K_rtheta_val = K_rtheta(a, r, theta); + //const double dK_rtheta_r_val = K_rtheta_dr(a, r, theta); + //const double dK_rtheta_theta_val = K_rtheta_dtheta(a, r, theta); + const double K_rtheta_val = eval_K_rtheta(a, L, R_0, coord0, coord1); + const double dK_rtheta_r_val = eval_dK_rtheta_r(a, L, R_0, coord0, coord1); + const double dK_rtheta_theta_val = eval_dK_rtheta_theta(a, L, R_0, coord0, coord1); + + const double Km[3][3] = {{ K_rr, K_rtheta_val, 0 }, + { K_rtheta_val / SQR(r), -(K_rr + K_phiphi), 0 }, + { 0, 0, K_phiphi }}; + +#if 0 + double gu[3][3]; + double dgu[3][3][3], G[3][3][3], dG[3][3][3][3]; + double Ric[3][3]; + + double g[3][3], dg[3][3][3], d2g[3][3][3][3]; + + eval_metric (a, L, R_0, coord0, coord1, psi, dpsi_01, dpsi_02, dpsi_10, dpsi_11, dpsi_20, g); + for (int i = 0; i < 3; i++) + eval_dmetric[i] (a, L, R_0, coord0, coord1, psi, dpsi_01, dpsi_02, dpsi_10, dpsi_11, dpsi_20, dg[i]); + for (int i = 0; i < 3; i++) + for (int j = 0; j < 3; j++) + eval_d2metric[i][j](a, L, R_0, coord0, coord1, psi, dpsi_01, dpsi_02, dpsi_10, dpsi_11, dpsi_20, d2g[i][j]); + + const double det = g[0][0] * g[1][1] * g[2][2] + 2 * g[0][1] * g[1][2] * g[0][2] - g[2][2] * SQR(g[0][1]) - SQR(g[0][2]) * g[1][1] - g[0][0] * SQR(g[1][2]); + + // γ^{ij} + gu[0][0] = (g[1][1] * g[2][2] - SQR(g[1][2])) / det; + gu[1][1] = (g[0][0] * g[2][2] - SQR(g[0][2])) / det; + gu[2][2] = (g[0][0] * g[1][1] - SQR(g[0][1])) / det; + gu[0][1] = -(g[0][1] * g[2][2] - g[1][2] * g[0][2]) / det; + gu[0][2] = (g[0][1] * g[1][2] - g[1][1] * g[0][2]) / det; + gu[1][2] = -(g[0][0] * g[1][2] - g[0][1] * g[0][2]) / det; + gu[1][0] = gu[0][1]; + gu[2][0] = gu[0][2]; + gu[2][1] = gu[1][2]; + + // ∂_j γ^{kl} + for (int j = 0; j < 3; j++) + for (int k = 0; k < 3; k++) + for (int l = 0; l < 3; l++) { + double val = 0.0; + for (int m = 0; m < 3; m++) + for (int n = 0; n < 3; n++) + val += -gu[k][m] * gu[l][n] * dg[j][m][n]; + dgu[j][k][l] = val; + } + + // Γ^j_{kl} + for (int j = 0; j < 3; j++) + for (int k = 0; k < 3; k++) + for (int l = 0; l < 3; l++) { + double val = 0.0; + for (int m = 0; m < 3; m++) + val += 0.5 * gu[j][m] * (dg[k][l][m] + dg[l][k][m] - dg[m][k][l]); + G[j][k][l] = val; + } + + // ∂_j Γ^k_{lm} + for (int j = 0; j < 3; j++) + for (int k = 0; k < 3; k++) + for (int l = 0; l < 3; l++) + for (int m = 0; m < 3; m++) { + double val = 0.0; + for (int n = 0; n < 3; n++) { + val += dgu[j][k][n] * (dg [l][m][n] + dg [m][l][n] - dg [n][l][m]) + + gu [k][n] * (d2g[j][l][m][n] + d2g[j][m][l][n] - d2g[j][n][l][m]); + } + dG[j][k][l][m] = 0.5 * val; + } + + // Ric_{jk} + for (int j = 0; j < 3; j++) + for (int k = 0; k < 3; k++) { + double val = 0.0; + for (int m = 0; m < 3; m++) + val += dG[m][m][j][k] - dG[k][m][j][m]; + for (int m = 0; m < 3; m++) + for (int l = 0; l < 3; l++) + val += G[l][l][m] * G[m][j][k] - G[l][k][m] * G[m][j][l]; + Ric[j][k] = val; + } + + double Rscal = 0.0; + for (int i = 0; i < 3; i++) + for (int j = 0; j < 3; j++) + Rscal += gu[i][j] * Ric[i][j]; + + const double dKm[3][3][3] = { + { + { dK_rr_10, dK_rtheta_r_val, 0 }, + { gu[1][1] / gu[0][0] * dK_rtheta_r_val + dgu[0][1][1] / gu[0][0] * K_rtheta_val - dgu[0][0][0] / SQR(gu[0][0]) * gu[1][1] * K_rtheta_val, + -(dK_rr_10 + dK_phiphi_10), 0 }, + { 0, 0, dK_phiphi_10 }, + }, + { + { dK_rr_01, dK_rtheta_theta_val, 0 }, + { gu[1][1] / gu[0][0] * dK_rtheta_theta_val + dgu[1][1][1] / gu[0][0] * K_rtheta_val - dgu[1][0][0] / SQR(gu[0][0]) * gu[1][1] * K_rtheta_val, + -(dK_rr_01 + dK_phiphi_01), 0 }, + { 0, 0, dK_phiphi_01 }, + }, + { 0 }, + }; +#endif + + if (EQUATION == TD_CONSTRAINT_EQ_HAM) { + double Rscal = eval_R_scalar(a, L, coord0, coord1, psi, dpsi_01, dpsi_02, dpsi_10, dpsi_11, dpsi_20, + K_rr, dK_rr_01, dK_rr_10, K_phiphi, dK_phiphi_01, dK_phiphi_10); + double K2 = 0.0; + for (int i = 0; i < 3; i++) + for (int j = 0; j < 3; j++) + K2 += Km[i][j] * Km[j][i]; + + out[idx] = Rscal - K2; + } else if (EQUATION == TD_CONSTRAINT_EQ_MOM_0) { + out[idx] = eval_Dcurv_m_r(a, L, coord0, coord1, psi, dpsi_01, dpsi_02, dpsi_10, dpsi_11, dpsi_20, + K_rr, dK_rr_01, dK_rr_10, K_phiphi, dK_phiphi_01, dK_phiphi_10); + } else { + out[idx] = eval_Dcurv_m_t(a, L, coord0, coord1, psi, dpsi_01, dpsi_02, dpsi_10, dpsi_11, dpsi_20, + K_rr, dK_rr_01, dK_rr_10, K_phiphi, dK_phiphi_01, dK_phiphi_10); + } +#if 0 + } else { + int mom_comp = (EQUATION == TD_CONSTRAINT_EQ_MOM_0) ? 0 : 1; + + double dKm_sum = 0.0; + for (int i = 0; i < 3; i++) + dKm_sum += dKm[i][i][mom_comp]; + + double Gterm1 = 0.0; + for (int i = 0; i < 3; i++) + for (int j = 0; j < 3; j++) + Gterm1 += G[i][i][j] * Km[j][mom_comp]; + + double Gterm2 = 0.0; + for (int i = 0; i < 3; i++) + for (int j = 0; j < 3; j++) + Gterm2 += G[j][i][mom_comp] * Km[i][j]; + + out[idx] = dKm_sum + Gterm1 - Gterm2; + } +#endif + } + } +} |