/* * Teukolsky data -- template for the constraint equations definitions * Copyright (C) 2017 Anton Khirnov * * 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 . */ #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 } } }