1 static char help[] = "Tests mesh adaptation with DMPlex and pragmatic.\n"; 2 3 #include <petsc/private/dmpleximpl.h> 4 5 #include <petscsnes.h> 6 7 typedef struct { 8 PetscInt Nr; /* The number of refinement passes */ 9 PetscInt metOpt; /* Different choices of metric */ 10 PetscReal hmax, hmin; /* Max and min sizes prescribed by the metric */ 11 PetscBool doL2; /* Test L2 projection */ 12 } AppCtx; 13 14 /* 15 Classic hyperbolic sensor function for testing multi-scale anisotropic mesh adaptation: 16 17 f:[-1, 1]x[-1, 1] \to R, 18 f(x, y) = sin(50xy)/100 if |xy| > 2\pi/50 else sin(50xy) 19 20 (mapped to have domain [0,1] x [0,1] in this case). 21 */ 22 static PetscErrorCode sensor(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nf, PetscScalar u[], PetscCtx ctx) 23 { 24 const PetscReal xref = 2. * x[0] - 1.; 25 const PetscReal yref = 2. * x[1] - 1.; 26 const PetscReal xy = xref * yref; 27 28 PetscFunctionBeginUser; 29 u[0] = PetscSinReal(50. * xy); 30 if (PetscAbsReal(xy) > 2. * PETSC_PI / 50.) u[0] *= 0.01; 31 PetscFunctionReturn(PETSC_SUCCESS); 32 } 33 34 static PetscErrorCode ProcessOptions(MPI_Comm comm, AppCtx *options) 35 { 36 PetscFunctionBegin; 37 options->Nr = 1; 38 options->metOpt = 1; 39 options->hmin = 0.05; 40 options->hmax = 0.5; 41 options->doL2 = PETSC_FALSE; 42 43 PetscOptionsBegin(comm, "", "Meshing Adaptation Options", "DMPLEX"); 44 PetscCall(PetscOptionsBoundedInt("-Nr", "Numberof refinement passes", "ex19.c", options->Nr, &options->Nr, NULL, 1)); 45 PetscCall(PetscOptionsBoundedInt("-met", "Different choices of metric", "ex19.c", options->metOpt, &options->metOpt, NULL, 0)); 46 PetscCall(PetscOptionsReal("-hmax", "Max size prescribed by the metric", "ex19.c", options->hmax, &options->hmax, NULL)); 47 PetscCall(PetscOptionsReal("-hmin", "Min size prescribed by the metric", "ex19.c", options->hmin, &options->hmin, NULL)); 48 PetscCall(PetscOptionsBool("-do_L2", "Test L2 projection", "ex19.c", options->doL2, &options->doL2, NULL)); 49 PetscOptionsEnd(); 50 PetscFunctionReturn(PETSC_SUCCESS); 51 } 52 53 static PetscErrorCode CreateMesh(MPI_Comm comm, DM *dm) 54 { 55 PetscFunctionBegin; 56 PetscCall(DMCreate(comm, dm)); 57 PetscCall(DMSetType(*dm, DMPLEX)); 58 PetscCall(DMSetFromOptions(*dm)); 59 PetscCall(PetscObjectSetName((PetscObject)*dm, "DMinit")); 60 PetscCall(DMViewFromOptions(*dm, NULL, "-init_dm_view")); 61 PetscFunctionReturn(PETSC_SUCCESS); 62 } 63 64 static PetscErrorCode ComputeMetricSensor(DM dm, AppCtx *user, Vec *metric) 65 { 66 PetscSimplePointFn *funcs[1] = {sensor}; 67 DM dmSensor, dmGrad, dmHess, dmDet; 68 PetscFE fe; 69 Vec f, g, H, determinant; 70 PetscBool simplex; 71 PetscInt dim; 72 73 PetscFunctionBegin; 74 PetscCall(DMGetDimension(dm, &dim)); 75 PetscCall(DMPlexIsSimplex(dm, &simplex)); 76 77 PetscCall(DMClone(dm, &dmSensor)); 78 PetscCall(PetscFECreateLagrange(PETSC_COMM_SELF, dim, 1, simplex, 1, -1, &fe)); 79 PetscCall(DMSetField(dmSensor, 0, NULL, (PetscObject)fe)); 80 PetscCall(PetscFEDestroy(&fe)); 81 PetscCall(DMCreateDS(dmSensor)); 82 PetscCall(DMCreateLocalVector(dmSensor, &f)); 83 PetscCall(DMProjectFunctionLocal(dmSensor, 0., funcs, NULL, INSERT_VALUES, f)); 84 PetscCall(VecViewFromOptions(f, NULL, "-sensor_view")); 85 86 // Recover the gradient of the sensor function 87 PetscCall(DMClone(dm, &dmGrad)); 88 PetscCall(PetscFECreateLagrange(PETSC_COMM_SELF, dim, dim, simplex, 1, -1, &fe)); 89 PetscCall(DMSetField(dmGrad, 0, NULL, (PetscObject)fe)); 90 PetscCall(PetscFEDestroy(&fe)); 91 PetscCall(DMCreateDS(dmGrad)); 92 PetscCall(DMCreateLocalVector(dmGrad, &g)); 93 PetscCall(DMPlexComputeGradientClementInterpolant(dmSensor, f, g)); 94 PetscCall(VecDestroy(&f)); 95 PetscCall(VecViewFromOptions(g, NULL, "-gradient_view")); 96 97 // Recover the Hessian of the sensor function 98 PetscCall(DMClone(dm, &dmHess)); 99 PetscCall(DMPlexMetricCreate(dmHess, 0, &H)); 100 PetscCall(DMPlexComputeGradientClementInterpolant(dmGrad, g, H)); 101 PetscCall(VecDestroy(&g)); 102 PetscCall(VecViewFromOptions(H, NULL, "-hessian_view")); 103 104 // Obtain a metric by Lp normalization 105 PetscCall(DMPlexMetricCreate(dm, 0, metric)); 106 PetscCall(DMPlexMetricDeterminantCreate(dm, 0, &determinant, &dmDet)); 107 PetscCall(DMPlexMetricNormalize(dmHess, H, PETSC_TRUE, PETSC_TRUE, *metric, determinant)); 108 PetscCall(VecDestroy(&determinant)); 109 PetscCall(DMDestroy(&dmDet)); 110 PetscCall(VecDestroy(&H)); 111 PetscCall(DMDestroy(&dmHess)); 112 PetscCall(DMDestroy(&dmGrad)); 113 PetscCall(DMDestroy(&dmSensor)); 114 PetscFunctionReturn(PETSC_SUCCESS); 115 } 116 117 static PetscErrorCode ComputeMetric(DM dm, AppCtx *user, Vec *metric) 118 { 119 PetscReal lambda = 1 / (user->hmax * user->hmax); 120 121 PetscFunctionBeginUser; 122 if (user->metOpt == 0) { 123 /* Specify a uniform, isotropic metric */ 124 PetscCall(DMPlexMetricCreateUniform(dm, 0, lambda, metric)); 125 } else if (user->metOpt == 3) { 126 PetscCall(ComputeMetricSensor(dm, user, metric)); 127 } else { 128 DM cdm; 129 Vec coordinates; 130 const PetscScalar *coords; 131 PetscScalar *met; 132 PetscReal h; 133 PetscInt dim, i, j, vStart, vEnd, v; 134 135 PetscCall(DMPlexMetricCreate(dm, 0, metric)); 136 PetscCall(DMGetDimension(dm, &dim)); 137 PetscCall(DMGetCoordinateDM(dm, &cdm)); 138 PetscCall(DMGetCoordinatesLocal(dm, &coordinates)); 139 PetscCall(VecGetArrayRead(coordinates, &coords)); 140 PetscCall(VecGetArray(*metric, &met)); 141 PetscCall(DMPlexGetDepthStratum(dm, 0, &vStart, &vEnd)); 142 for (v = vStart; v < vEnd; ++v) { 143 PetscScalar *vcoords; 144 PetscScalar *pmet; 145 146 PetscCall(DMPlexPointLocalRead(cdm, v, coords, &vcoords)); 147 switch (user->metOpt) { 148 case 1: 149 h = user->hmax - (user->hmax - user->hmin) * PetscRealPart(vcoords[0]); 150 break; 151 case 2: 152 h = user->hmax * PetscAbsReal(((PetscReal)1.0) - PetscExpReal(-PetscAbsScalar(vcoords[0] - (PetscReal)0.5))) + user->hmin; 153 break; 154 default: 155 SETERRQ(PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_WRONG, "metOpt = 0, 1, 2 or 3, cannot be %d", user->metOpt); 156 } 157 PetscCall(DMPlexPointLocalRef(dm, v, met, &pmet)); 158 for (i = 0; i < dim; ++i) { 159 for (j = 0; j < dim; ++j) { 160 if (i == j) { 161 if (i == 0) pmet[i * dim + j] = 1 / (h * h); 162 else pmet[i * dim + j] = lambda; 163 } else pmet[i * dim + j] = 0.0; 164 } 165 } 166 } 167 PetscCall(VecRestoreArray(*metric, &met)); 168 PetscCall(VecRestoreArrayRead(coordinates, &coords)); 169 } 170 PetscFunctionReturn(PETSC_SUCCESS); 171 } 172 173 static PetscErrorCode linear(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nc, PetscScalar *u, PetscCtx ctx) 174 { 175 u[0] = x[0] + x[1]; 176 return 0; 177 } 178 179 static PetscErrorCode TestL2Projection(DM dm, DM dma, AppCtx *user) 180 { 181 PetscErrorCode (*funcs[1])(PetscInt, PetscReal, const PetscReal[], PetscInt, PetscScalar *, void *) = {linear}; 182 DM dmProj, dmaProj; 183 PetscFE fe; 184 KSP ksp; 185 Mat Interp, mass, mass2; 186 Vec u, ua, scaling, rhs, uproj; 187 PetscReal error; 188 PetscBool simplex; 189 PetscInt dim; 190 191 PetscFunctionBeginUser; 192 PetscCall(DMGetDimension(dm, &dim)); 193 PetscCall(DMPlexIsSimplex(dm, &simplex)); 194 195 PetscCall(DMClone(dm, &dmProj)); 196 PetscCall(PetscFECreateDefault(PETSC_COMM_SELF, dim, 1, simplex, NULL, -1, &fe)); 197 PetscCall(DMSetField(dmProj, 0, NULL, (PetscObject)fe)); 198 PetscCall(PetscFEDestroy(&fe)); 199 PetscCall(DMCreateDS(dmProj)); 200 201 PetscCall(DMClone(dma, &dmaProj)); 202 PetscCall(PetscFECreateDefault(PETSC_COMM_SELF, dim, 1, simplex, NULL, -1, &fe)); 203 PetscCall(DMSetField(dmaProj, 0, NULL, (PetscObject)fe)); 204 PetscCall(PetscFEDestroy(&fe)); 205 PetscCall(DMCreateDS(dmaProj)); 206 207 PetscCall(DMGetGlobalVector(dmProj, &u)); 208 PetscCall(DMGetGlobalVector(dmaProj, &ua)); 209 PetscCall(DMGetGlobalVector(dmaProj, &rhs)); 210 PetscCall(DMGetGlobalVector(dmaProj, &uproj)); 211 212 // Interpolate onto original mesh using dual basis 213 PetscCall(DMProjectFunction(dmProj, 0.0, funcs, NULL, INSERT_VALUES, u)); 214 PetscCall(PetscObjectSetName((PetscObject)u, "Original")); 215 PetscCall(VecViewFromOptions(u, NULL, "-orig_vec_view")); 216 PetscCall(DMComputeL2Diff(dmProj, 0.0, funcs, NULL, u, &error)); 217 PetscCall(PetscPrintf(PETSC_COMM_WORLD, "Original L2 Error: %g\n", (double)error)); 218 // Interpolate onto NEW mesh using dual basis 219 PetscCall(DMProjectFunction(dmaProj, 0.0, funcs, NULL, INSERT_VALUES, ua)); 220 PetscCall(PetscObjectSetName((PetscObject)ua, "Adapted")); 221 PetscCall(VecViewFromOptions(ua, NULL, "-adapt_vec_view")); 222 PetscCall(DMComputeL2Diff(dmaProj, 0.0, funcs, NULL, ua, &error)); 223 PetscCall(PetscPrintf(PETSC_COMM_WORLD, "Adapted L2 Error: %g\n", (double)error)); 224 // Interpolate between meshes using interpolation matrix 225 PetscCall(DMCreateInterpolation(dmProj, dmaProj, &Interp, &scaling)); 226 PetscCall(MatInterpolate(Interp, u, ua)); 227 PetscCall(MatDestroy(&Interp)); 228 PetscCall(VecDestroy(&scaling)); 229 PetscCall(PetscObjectSetName((PetscObject)ua, "Interpolation")); 230 PetscCall(VecViewFromOptions(ua, NULL, "-interp_vec_view")); 231 PetscCall(DMComputeL2Diff(dmaProj, 0.0, funcs, NULL, ua, &error)); 232 PetscCall(PetscPrintf(PETSC_COMM_WORLD, "Interpolated L2 Error: %g\n", (double)error)); 233 // L2 projection 234 PetscCall(DMCreateMassMatrix(dmaProj, dmaProj, &mass)); 235 PetscCall(MatViewFromOptions(mass, NULL, "-mass_mat_view")); 236 PetscCall(KSPCreate(PETSC_COMM_WORLD, &ksp)); 237 PetscCall(KSPSetOperators(ksp, mass, mass)); 238 PetscCall(KSPSetFromOptions(ksp)); 239 // Compute rhs as M f, could also directly project the analytic function but we might not have it 240 PetscCall(DMCreateMassMatrix(dmProj, dmaProj, &mass2)); 241 PetscCall(MatMult(mass2, u, rhs)); 242 PetscCall(MatDestroy(&mass2)); 243 PetscCall(KSPSolve(ksp, rhs, uproj)); 244 PetscCall(PetscObjectSetName((PetscObject)uproj, "L_2 Projection")); 245 PetscCall(VecViewFromOptions(uproj, NULL, "-proj_vec_view")); 246 PetscCall(DMComputeL2Diff(dmaProj, 0.0, funcs, NULL, uproj, &error)); 247 PetscCall(PetscPrintf(PETSC_COMM_WORLD, "Projected L2 Error: %g\n", (double)error)); 248 PetscCall(KSPDestroy(&ksp)); 249 PetscCall(MatDestroy(&mass)); 250 PetscCall(DMRestoreGlobalVector(dmProj, &u)); 251 PetscCall(DMRestoreGlobalVector(dmaProj, &ua)); 252 PetscCall(DMRestoreGlobalVector(dmaProj, &rhs)); 253 PetscCall(DMRestoreGlobalVector(dmaProj, &uproj)); 254 PetscCall(DMDestroy(&dmProj)); 255 PetscCall(DMDestroy(&dmaProj)); 256 PetscFunctionReturn(PETSC_SUCCESS); 257 } 258 259 int main(int argc, char *argv[]) 260 { 261 DM dm; 262 AppCtx user; /* user-defined work context */ 263 MPI_Comm comm; 264 DM dma, odm; 265 Vec metric; 266 PetscInt r; 267 268 PetscFunctionBeginUser; 269 PetscCall(PetscInitialize(&argc, &argv, NULL, help)); 270 comm = PETSC_COMM_WORLD; 271 PetscCall(ProcessOptions(comm, &user)); 272 PetscCall(CreateMesh(comm, &dm)); 273 274 odm = dm; 275 PetscCall(DMPlexDistributeOverlap(odm, 1, NULL, &dm)); 276 if (!dm) { 277 dm = odm; 278 } else PetscCall(DMDestroy(&odm)); 279 280 for (r = 0; r < user.Nr; ++r) { 281 DMLabel label; 282 283 PetscCall(ComputeMetric(dm, &user, &metric)); 284 PetscCall(DMGetLabel(dm, "marker", &label)); 285 PetscCall(DMAdaptMetric(dm, metric, label, NULL, &dma)); 286 PetscCall(VecDestroy(&metric)); 287 PetscCall(PetscObjectSetName((PetscObject)dma, "DMadapt")); 288 PetscCall(PetscObjectSetOptionsPrefix((PetscObject)dma, "adapt_")); 289 PetscCall(DMViewFromOptions(dma, NULL, "-dm_view")); 290 if (user.doL2) PetscCall(TestL2Projection(dm, dma, &user)); 291 PetscCall(DMDestroy(&dm)); 292 dm = dma; 293 } 294 PetscCall(PetscObjectSetOptionsPrefix((PetscObject)dm, "final_")); 295 PetscCall(DMViewFromOptions(dm, NULL, "-dm_view")); 296 PetscCall(DMDestroy(&dm)); 297 PetscCall(PetscFinalize()); 298 return 0; 299 } 300 301 /*TEST 302 303 build: 304 requires: pragmatic 305 306 testset: 307 args: -dm_plex_box_faces 4,4,4 -dm_adaptor pragmatic -met 2 -init_dm_view -adapt_dm_view -dm_adaptor pragmatic 308 309 test: 310 suffix: 2d 311 args: -dm_plex_separate_marker 0 312 test: 313 suffix: 2d_sep 314 args: -dm_plex_separate_marker 1 315 test: 316 suffix: 3d 317 args: -dm_plex_dim 3 318 319 # Pragmatic hangs for simple partitioner 320 testset: 321 requires: parmetis 322 args: -dm_plex_box_faces 2,2 -petscpartitioner_type parmetis -met 2 -init_dm_view -adapt_dm_view -dm_adaptor pragmatic 323 324 test: 325 suffix: 2d_parmetis_np2 326 nsize: 2 327 test: 328 suffix: 2d_parmetis_np4 329 nsize: 4 330 331 test: 332 requires: parmetis 333 suffix: 3d_parmetis_met0 334 nsize: 2 335 args: -dm_plex_dim 3 -dm_plex_box_faces 9,9,9 -dm_adaptor pragmatic -petscpartitioner_type parmetis \ 336 -met 0 -hmin 0.01 -hmax 0.03 -init_dm_view -adapt_dm_view -dm_adaptor pragmatic 337 test: 338 requires: parmetis 339 suffix: 3d_parmetis_met2 340 nsize: 2 341 args: -dm_plex_box_faces 19,19 -dm_adaptor pragmatic -petscpartitioner_type parmetis \ 342 -met 2 -hmax 0.5 -hmin 0.001 -init_dm_view -adapt_dm_view -dm_adaptor pragmatic 343 test: 344 suffix: proj2 345 args: -dm_plex_box_faces 2,2 -dm_plex_hash_location -dm_adaptor pragmatic -init_dm_view -adapt_dm_view -do_L2 \ 346 -petscspace_degree 1 -petscfe_default_quadrature_order 1 -pc_type lu -dm_adaptor pragmatic 347 test: 348 suffix: proj4 349 args: -dm_plex_box_faces 4,4 -dm_plex_hash_location -dm_adaptor pragmatic -init_dm_view -adapt_dm_view -do_L2 \ 350 -petscspace_degree 1 -petscfe_default_quadrature_order 1 -pc_type lu -dm_adaptor pragmatic 351 352 test: 353 suffix: 2d_met3 354 args: -dm_plex_box_faces 9,9 -met 3 -dm_adaptor pragmatic -init_dm_view -adapt_dm_view \ 355 -dm_plex_metric_h_min 1.e-10 -dm_plex_metric_h_max 1.0e-01 -dm_plex_metric_a_max 1.0e+05 -dm_plex_metric_p 1.0 \ 356 -dm_plex_metric_target_complexity 10000.0 -dm_adaptor pragmatic 357 358 TEST*/ 359