linear_system_banded.c 8.51 KB
 Jonathan Lambrechts committed Feb 02, 2017 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 ``````#include #include "mesh.h" #include "linear_system.h" #include #include #define CONMAX 12 void connectivity_insert(int *connectivity, int i, int j) { for (int k = 0; k < CONMAX; ++k) { int *p = connectivity + CONMAX*i + k; if (*p == -1) *p = j; if (*p == j) return; } printf("ERROR : node %i has more than %i neighbours\n", i, CONMAX); } int reverse_cuthill_mckee(Mesh *mesh, int *ordering) { int *node_connectivity = malloc(sizeof(int)*mesh->n_nodes*CONMAX); for (int i = 0; i < mesh->n_nodes*CONMAX; ++i) { node_connectivity[i] = -1; } for (int i = 0; i < mesh->n_triangles; ++i) { int *tri = mesh->triangles + i*3; connectivity_insert(node_connectivity, tri[0], tri[1]); connectivity_insert(node_connectivity, tri[1], tri[0]); connectivity_insert(node_connectivity, tri[0], tri[2]); connectivity_insert(node_connectivity, tri[2], tri[0]); connectivity_insert(node_connectivity, tri[1], tri[2]); connectivity_insert(node_connectivity, tri[2], tri[1]); } int *node_degree = malloc(sizeof(int)*mesh->n_nodes); for (int i = 0; i < mesh->n_nodes; ++i) { node_degree[i] = 0; for (int j = 0; j < CONMAX; ++j) { if (node_connectivity[CONMAX*i+j] == -1) break; node_degree[i] += 1; } } int *queue = malloc(sizeof(int)*mesh->n_nodes); queue[0] = 0; for (int i = 0; i < mesh->n_nodes; ++i){ ordering[i] = -1; if (node_degree[queue[0]] > node_degree[i] ) queue[0] = i; } int stage_start = 0; int stage_end = 1; int queue_end = 1; int id = 0; while(stage_start != stage_end) { for (int i = stage_start; i < stage_end; ++i) { int c = queue[i]; ordering[c] = mesh->n_nodes-1 -(id++); for(int j = 0; j < node_degree[c]; ++j) { int o = node_connectivity[c*CONMAX+j]; if (ordering[o] == -1) { ordering[o] = -2; #if 1 queue[queue_end++] = o; #else int k = stage_end; while(k < queue_end && node_degree[queue[k]] < node_degree[o]) k++; for (int l = queue_end; l > k; --l) queue[l] = queue[l-1]; queue[k] = o; queue_end++; #endif } } } stage_start = stage_end; stage_end = queue_end; } int final_bandwidth = 0; for (int i = 0; i < mesh->n_triangles; ++i) { int *tri = mesh->triangles + i*3; int m[3] = {ordering[tri[0]], ordering[tri[1]], ordering[tri[2]]}; int d[3] = {abs(m[0]-m[1]), abs(m[0]-m[2]), abs(m[1]-m[2])}; if (d[0] > final_bandwidth) final_bandwidth = d[0]; if (d[1] > final_bandwidth) final_bandwidth = d[1]; if (d[2] > final_bandwidth) final_bandwidth = d[2]; } printf("n_nodes : %i final bandwidth : %i\n",mesh->n_nodes, final_bandwidth); free(queue); free(node_degree); free(node_connectivity); return final_bandwidth; } //from wikipedia //INPUT: A - array of pointers to rows of a square matrix having dimension N // Tol - small tolerance number to detect failure when the matrix is near degenerate //OUTPUT: Matrix A is changed, it contains both matrices L-E and U as A=(L-E)+U such that P*A=L*U. // P - array of N+1 integers containing pivoting of A and P[N] is for determinant computation // (P[i] is an index of the row in A placed at the i-th row static int LUPDecompose(double *__restrict__*__restrict A,int N,double Tol,int *P, int bw){ int i,j,k; for(i=0;imaxA){ maxA=absA; imax=k; } if(maxA=0;i--){ for(int k=i+1;kn_fields = n_fields; system->mesh = mesh; system->n = mesh->n_nodes*system->n_fields; system->node_map = malloc(sizeof(int)*mesh->n_nodes); int mbw = reverse_cuthill_mckee(mesh, system->node_map); system->band_width = system->n_fields*(1+mbw); system->line_width = system->band_width*2+1; system->A = malloc(sizeof(double)*system->n*system->line_width); system->rows = malloc(sizeof(double*)*system->n); for (int i = 0; i < system->n; ++i) system->rows[i] = system->A + i*(system->line_width-1) + system->band_width; system->b = malloc(sizeof(double)*system->n); system->x = malloc(sizeof(double)*system->n); system->isfixed = malloc(sizeof(int)*system->n); for (int i = 0; i < system->n; ++i) { system->isfixed[i] = 0; } for (int ibnd = 0; ibnd < n_boundaries; ++ibnd) { const StrongBoundary *bnd = boundaries + ibnd; int iphys; for (iphys = 0; iphys < mesh->n_phys; ++iphys) { if (strcmp(bnd->tag, mesh->phys_name[iphys]) == 0) break; } if (iphys == mesh->n_phys) printf("Boundary tag \"%s\" not found.", bnd->tag); for (int i = 0; i < mesh->phys_n_nodes[iphys]; ++i){ system->isfixed[system->node_map[mesh->phys_nodes[iphys][i]]*system->n_fields+bnd->field] = 1; } } return system; } void linear_system_add_to_matrix(LinearSystem *system, int el0, int el1, const double *local_matrix){ int *tri0 = &system->mesh->triangles[el0*3]; int *tri1 = &system->mesh->triangles[el1*3]; int nf = system->n_fields; for (int i = 0; i < 3; ++i) { for (int inf = 0; inf < 3; ++inf) { int ii = system->node_map[tri0[i]]*nf + inf; for (int j = 0; j < 3; ++j) { for (int jnf = 0; jnf < nf; ++jnf) { int jj = system->node_map[tri1[j]]*nf + jnf; system->rows[ii][jj] += local_matrix[(inf*3+i)*nf*3+jnf*3+j]; } } } } } void linear_system_add_to_rhs(LinearSystem *system, int el0, const double *local_vector) { const int *tri = system->mesh->triangles + el0*3; int n_fields = system->n_fields; for (int i = 0; i < n_fields; ++i) { for (int j = 0; j < 3; ++j) { int m = system->node_map[tri[j]]*n_fields+i; system->b[m] += local_vector[i*3+j]; } } } void linear_system_zero_matrix_and_rhs(LinearSystem *system) { for (int i = 0; i < system->n; ++i){ system->b[i] = 0.; for (int j = 0; j < system->line_width; ++j) { system->A[i*system->line_width+j] = 0.; } } } void linear_system_solve(LinearSystem *system, double *solution){ int *P = malloc(sizeof(int)*(system->n)); double **rows = system->rows; for (int i = 0; i < system->n; ++i){ if (system->isfixed[i]) { for (int j = i-system->band_width; j <= i+system->band_width; ++j) rows[i][j] = 0.; rows[i][i] = 1.; system->b[i] = 0; } } LUPDecompose(rows, system->n, 1e-8, P, system->band_width); LUPSolve(rows, P, system->b, system->n, system->x, system->band_width); for (int i = 0; i < system->mesh->n_nodes; ++i){ int ii = system->node_map[i]; for (int j = 0; j < system->n_fields; ++j) solution[i*system->n_fields+j] = system->x[ii*system->n_fields+j]; } } void linear_system_free(LinearSystem *system) { free(system->b); free(system->x); free(system->A); free(system->rows); free(system->isfixed); free(system->node_map); free(system); } double linear_system_get_rhs_norm(LinearSystem *system) { double norm = 0; for (int i = 0; i < system->n;++i) if (!system->isfixed[i]) norm += system->b[i]*system->b[i]; return sqrt(norm); } void initialize_linear_solver(int argc, char **argv){}``````