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[], void *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 51 PetscFunctionReturn(PETSC_SUCCESS); 52 } 53 54 static PetscErrorCode CreateMesh(MPI_Comm comm, DM *dm) 55 { 56 PetscFunctionBegin; 57 PetscCall(DMCreate(comm, dm)); 58 PetscCall(DMSetType(*dm, DMPLEX)); 59 PetscCall(DMSetFromOptions(*dm)); 60 PetscCall(PetscObjectSetName((PetscObject)*dm, "DMinit")); 61 PetscCall(DMViewFromOptions(*dm, NULL, "-init_dm_view")); 62 PetscFunctionReturn(PETSC_SUCCESS); 63 } 64 65 static PetscErrorCode ComputeMetricSensor(DM dm, AppCtx *user, Vec *metric) 66 { 67 PetscSimplePointFn *funcs[1] = {sensor}; 68 DM dmSensor, dmGrad, dmHess, dmDet; 69 PetscFE fe; 70 Vec f, g, H, determinant; 71 PetscBool simplex; 72 PetscInt dim; 73 74 PetscFunctionBegin; 75 PetscCall(DMGetDimension(dm, &dim)); 76 PetscCall(DMPlexIsSimplex(dm, &simplex)); 77 78 PetscCall(DMClone(dm, &dmSensor)); 79 PetscCall(PetscFECreateLagrange(PETSC_COMM_SELF, dim, 1, simplex, 1, -1, &fe)); 80 PetscCall(DMSetField(dmSensor, 0, NULL, (PetscObject)fe)); 81 PetscCall(PetscFEDestroy(&fe)); 82 PetscCall(DMCreateDS(dmSensor)); 83 PetscCall(DMCreateLocalVector(dmSensor, &f)); 84 PetscCall(DMProjectFunctionLocal(dmSensor, 0., funcs, NULL, INSERT_VALUES, f)); 85 PetscCall(VecViewFromOptions(f, NULL, "-sensor_view")); 86 87 // Recover the gradient of the sensor function 88 PetscCall(DMClone(dm, &dmGrad)); 89 PetscCall(PetscFECreateLagrange(PETSC_COMM_SELF, dim, dim, simplex, 1, -1, &fe)); 90 PetscCall(DMSetField(dmGrad, 0, NULL, (PetscObject)fe)); 91 PetscCall(PetscFEDestroy(&fe)); 92 PetscCall(DMCreateDS(dmGrad)); 93 PetscCall(DMCreateLocalVector(dmGrad, &g)); 94 PetscCall(DMPlexComputeGradientClementInterpolant(dmSensor, f, g)); 95 PetscCall(VecDestroy(&f)); 96 PetscCall(VecViewFromOptions(g, NULL, "-gradient_view")); 97 98 // Recover the Hessian of the sensor function 99 PetscCall(DMClone(dm, &dmHess)); 100 PetscCall(DMPlexMetricCreate(dmHess, 0, &H)); 101 PetscCall(DMPlexComputeGradientClementInterpolant(dmGrad, g, H)); 102 PetscCall(VecDestroy(&g)); 103 PetscCall(VecViewFromOptions(H, NULL, "-hessian_view")); 104 105 // Obtain a metric by Lp normalization 106 PetscCall(DMPlexMetricCreate(dm, 0, metric)); 107 PetscCall(DMPlexMetricDeterminantCreate(dm, 0, &determinant, &dmDet)); 108 PetscCall(DMPlexMetricNormalize(dmHess, H, PETSC_TRUE, PETSC_TRUE, *metric, determinant)); 109 PetscCall(VecDestroy(&determinant)); 110 PetscCall(DMDestroy(&dmDet)); 111 PetscCall(VecDestroy(&H)); 112 PetscCall(DMDestroy(&dmHess)); 113 PetscCall(DMDestroy(&dmGrad)); 114 PetscCall(DMDestroy(&dmSensor)); 115 PetscFunctionReturn(PETSC_SUCCESS); 116 } 117 118 static PetscErrorCode ComputeMetric(DM dm, AppCtx *user, Vec *metric) 119 { 120 PetscReal lambda = 1 / (user->hmax * user->hmax); 121 122 PetscFunctionBeginUser; 123 if (user->metOpt == 0) { 124 /* Specify a uniform, isotropic metric */ 125 PetscCall(DMPlexMetricCreateUniform(dm, 0, lambda, metric)); 126 } else if (user->metOpt == 3) { 127 PetscCall(ComputeMetricSensor(dm, user, metric)); 128 } else { 129 DM cdm; 130 Vec coordinates; 131 const PetscScalar *coords; 132 PetscScalar *met; 133 PetscReal h; 134 PetscInt dim, i, j, vStart, vEnd, v; 135 136 PetscCall(DMPlexMetricCreate(dm, 0, metric)); 137 PetscCall(DMGetDimension(dm, &dim)); 138 PetscCall(DMGetCoordinateDM(dm, &cdm)); 139 PetscCall(DMGetCoordinatesLocal(dm, &coordinates)); 140 PetscCall(VecGetArrayRead(coordinates, &coords)); 141 PetscCall(VecGetArray(*metric, &met)); 142 PetscCall(DMPlexGetDepthStratum(dm, 0, &vStart, &vEnd)); 143 for (v = vStart; v < vEnd; ++v) { 144 PetscScalar *vcoords; 145 PetscScalar *pmet; 146 147 PetscCall(DMPlexPointLocalRead(cdm, v, coords, &vcoords)); 148 switch (user->metOpt) { 149 case 1: 150 h = user->hmax - (user->hmax - user->hmin) * PetscRealPart(vcoords[0]); 151 break; 152 case 2: 153 h = user->hmax * PetscAbsReal(((PetscReal)1.0) - PetscExpReal(-PetscAbsScalar(vcoords[0] - (PetscReal)0.5))) + user->hmin; 154 break; 155 default: 156 SETERRQ(PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_WRONG, "metOpt = 0, 1, 2 or 3, cannot be %d", user->metOpt); 157 } 158 PetscCall(DMPlexPointLocalRef(dm, v, met, &pmet)); 159 for (i = 0; i < dim; ++i) { 160 for (j = 0; j < dim; ++j) { 161 if (i == j) { 162 if (i == 0) pmet[i * dim + j] = 1 / (h * h); 163 else pmet[i * dim + j] = lambda; 164 } else pmet[i * dim + j] = 0.0; 165 } 166 } 167 } 168 PetscCall(VecRestoreArray(*metric, &met)); 169 PetscCall(VecRestoreArrayRead(coordinates, &coords)); 170 } 171 PetscFunctionReturn(PETSC_SUCCESS); 172 } 173 174 static PetscErrorCode linear(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nc, PetscScalar *u, void *ctx) 175 { 176 u[0] = x[0] + x[1]; 177 return 0; 178 } 179 180 static PetscErrorCode TestL2Projection(DM dm, DM dma, AppCtx *user) 181 { 182 PetscErrorCode (*funcs[1])(PetscInt, PetscReal, const PetscReal[], PetscInt, PetscScalar *, void *) = {linear}; 183 DM dmProj, dmaProj; 184 PetscFE fe; 185 KSP ksp; 186 Mat Interp, mass, mass2; 187 Vec u, ua, scaling, rhs, uproj; 188 PetscReal error; 189 PetscBool simplex; 190 PetscInt dim; 191 192 PetscFunctionBeginUser; 193 PetscCall(DMGetDimension(dm, &dim)); 194 PetscCall(DMPlexIsSimplex(dm, &simplex)); 195 196 PetscCall(DMClone(dm, &dmProj)); 197 PetscCall(PetscFECreateDefault(PETSC_COMM_SELF, dim, 1, simplex, NULL, -1, &fe)); 198 PetscCall(DMSetField(dmProj, 0, NULL, (PetscObject)fe)); 199 PetscCall(PetscFEDestroy(&fe)); 200 PetscCall(DMCreateDS(dmProj)); 201 202 PetscCall(DMClone(dma, &dmaProj)); 203 PetscCall(PetscFECreateDefault(PETSC_COMM_SELF, dim, 1, simplex, NULL, -1, &fe)); 204 PetscCall(DMSetField(dmaProj, 0, NULL, (PetscObject)fe)); 205 PetscCall(PetscFEDestroy(&fe)); 206 PetscCall(DMCreateDS(dmaProj)); 207 208 PetscCall(DMGetGlobalVector(dmProj, &u)); 209 PetscCall(DMGetGlobalVector(dmaProj, &ua)); 210 PetscCall(DMGetGlobalVector(dmaProj, &rhs)); 211 PetscCall(DMGetGlobalVector(dmaProj, &uproj)); 212 213 // Interpolate onto original mesh using dual basis 214 PetscCall(DMProjectFunction(dmProj, 0.0, funcs, NULL, INSERT_VALUES, u)); 215 PetscCall(PetscObjectSetName((PetscObject)u, "Original")); 216 PetscCall(VecViewFromOptions(u, NULL, "-orig_vec_view")); 217 PetscCall(DMComputeL2Diff(dmProj, 0.0, funcs, NULL, u, &error)); 218 PetscCall(PetscPrintf(PETSC_COMM_WORLD, "Original L2 Error: %g\n", (double)error)); 219 // Interpolate onto NEW mesh using dual basis 220 PetscCall(DMProjectFunction(dmaProj, 0.0, funcs, NULL, INSERT_VALUES, ua)); 221 PetscCall(PetscObjectSetName((PetscObject)ua, "Adapted")); 222 PetscCall(VecViewFromOptions(ua, NULL, "-adapt_vec_view")); 223 PetscCall(DMComputeL2Diff(dmaProj, 0.0, funcs, NULL, ua, &error)); 224 PetscCall(PetscPrintf(PETSC_COMM_WORLD, "Adapted L2 Error: %g\n", (double)error)); 225 // Interpolate between meshes using interpolation matrix 226 PetscCall(DMCreateInterpolation(dmProj, dmaProj, &Interp, &scaling)); 227 PetscCall(MatInterpolate(Interp, u, ua)); 228 PetscCall(MatDestroy(&Interp)); 229 PetscCall(VecDestroy(&scaling)); 230 PetscCall(PetscObjectSetName((PetscObject)ua, "Interpolation")); 231 PetscCall(VecViewFromOptions(ua, NULL, "-interp_vec_view")); 232 PetscCall(DMComputeL2Diff(dmaProj, 0.0, funcs, NULL, ua, &error)); 233 PetscCall(PetscPrintf(PETSC_COMM_WORLD, "Interpolated L2 Error: %g\n", (double)error)); 234 // L2 projection 235 PetscCall(DMCreateMassMatrix(dmaProj, dmaProj, &mass)); 236 PetscCall(MatViewFromOptions(mass, NULL, "-mass_mat_view")); 237 PetscCall(KSPCreate(PETSC_COMM_WORLD, &ksp)); 238 PetscCall(KSPSetOperators(ksp, mass, mass)); 239 PetscCall(KSPSetFromOptions(ksp)); 240 // Compute rhs as M f, could also directly project the analytic function but we might not have it 241 PetscCall(DMCreateMassMatrix(dmProj, dmaProj, &mass2)); 242 PetscCall(MatMult(mass2, u, rhs)); 243 PetscCall(MatDestroy(&mass2)); 244 PetscCall(KSPSolve(ksp, rhs, uproj)); 245 PetscCall(PetscObjectSetName((PetscObject)uproj, "L_2 Projection")); 246 PetscCall(VecViewFromOptions(uproj, NULL, "-proj_vec_view")); 247 PetscCall(DMComputeL2Diff(dmaProj, 0.0, funcs, NULL, uproj, &error)); 248 PetscCall(PetscPrintf(PETSC_COMM_WORLD, "Projected L2 Error: %g\n", (double)error)); 249 PetscCall(KSPDestroy(&ksp)); 250 PetscCall(MatDestroy(&mass)); 251 PetscCall(DMRestoreGlobalVector(dmProj, &u)); 252 PetscCall(DMRestoreGlobalVector(dmaProj, &ua)); 253 PetscCall(DMRestoreGlobalVector(dmaProj, &rhs)); 254 PetscCall(DMRestoreGlobalVector(dmaProj, &uproj)); 255 PetscCall(DMDestroy(&dmProj)); 256 PetscCall(DMDestroy(&dmaProj)); 257 PetscFunctionReturn(PETSC_SUCCESS); 258 } 259 260 int main(int argc, char *argv[]) 261 { 262 DM dm; 263 AppCtx user; /* user-defined work context */ 264 MPI_Comm comm; 265 DM dma, odm; 266 Vec metric; 267 PetscInt r; 268 269 PetscFunctionBeginUser; 270 PetscCall(PetscInitialize(&argc, &argv, NULL, help)); 271 comm = PETSC_COMM_WORLD; 272 PetscCall(ProcessOptions(comm, &user)); 273 PetscCall(CreateMesh(comm, &dm)); 274 275 odm = dm; 276 PetscCall(DMPlexDistributeOverlap(odm, 1, NULL, &dm)); 277 if (!dm) { 278 dm = odm; 279 } else PetscCall(DMDestroy(&odm)); 280 281 for (r = 0; r < user.Nr; ++r) { 282 DMLabel label; 283 284 PetscCall(ComputeMetric(dm, &user, &metric)); 285 PetscCall(DMGetLabel(dm, "marker", &label)); 286 PetscCall(DMAdaptMetric(dm, metric, label, NULL, &dma)); 287 PetscCall(VecDestroy(&metric)); 288 PetscCall(PetscObjectSetName((PetscObject)dma, "DMadapt")); 289 PetscCall(PetscObjectSetOptionsPrefix((PetscObject)dma, "adapt_")); 290 PetscCall(DMViewFromOptions(dma, NULL, "-dm_view")); 291 if (user.doL2) PetscCall(TestL2Projection(dm, dma, &user)); 292 PetscCall(DMDestroy(&dm)); 293 dm = dma; 294 } 295 PetscCall(PetscObjectSetOptionsPrefix((PetscObject)dm, "final_")); 296 PetscCall(DMViewFromOptions(dm, NULL, "-dm_view")); 297 PetscCall(DMDestroy(&dm)); 298 PetscCall(PetscFinalize()); 299 return 0; 300 } 301 302 /*TEST 303 304 build: 305 requires: pragmatic 306 307 testset: 308 args: -dm_plex_box_faces 4,4,4 -dm_adaptor pragmatic -met 2 -init_dm_view -adapt_dm_view -dm_adaptor pragmatic 309 310 test: 311 suffix: 2d 312 args: -dm_plex_separate_marker 0 313 test: 314 suffix: 2d_sep 315 args: -dm_plex_separate_marker 1 316 test: 317 suffix: 3d 318 args: -dm_plex_dim 3 319 320 # Pragmatic hangs for simple partitioner 321 testset: 322 requires: parmetis 323 args: -dm_plex_box_faces 2,2 -petscpartitioner_type parmetis -met 2 -init_dm_view -adapt_dm_view -dm_adaptor pragmatic 324 325 test: 326 suffix: 2d_parmetis_np2 327 nsize: 2 328 test: 329 suffix: 2d_parmetis_np4 330 nsize: 4 331 332 test: 333 requires: parmetis 334 suffix: 3d_parmetis_met0 335 nsize: 2 336 args: -dm_plex_dim 3 -dm_plex_box_faces 9,9,9 -dm_adaptor pragmatic -petscpartitioner_type parmetis \ 337 -met 0 -hmin 0.01 -hmax 0.03 -init_dm_view -adapt_dm_view -dm_adaptor pragmatic 338 test: 339 requires: parmetis 340 suffix: 3d_parmetis_met2 341 nsize: 2 342 args: -dm_plex_box_faces 19,19 -dm_adaptor pragmatic -petscpartitioner_type parmetis \ 343 -met 2 -hmax 0.5 -hmin 0.001 -init_dm_view -adapt_dm_view -dm_adaptor pragmatic 344 test: 345 suffix: proj2 346 args: -dm_plex_box_faces 2,2 -dm_plex_hash_location -dm_adaptor pragmatic -init_dm_view -adapt_dm_view -do_L2 \ 347 -petscspace_degree 1 -petscfe_default_quadrature_order 1 -pc_type lu -dm_adaptor pragmatic 348 test: 349 suffix: proj4 350 args: -dm_plex_box_faces 4,4 -dm_plex_hash_location -dm_adaptor pragmatic -init_dm_view -adapt_dm_view -do_L2 \ 351 -petscspace_degree 1 -petscfe_default_quadrature_order 1 -pc_type lu -dm_adaptor pragmatic 352 353 test: 354 suffix: 2d_met3 355 args: -dm_plex_box_faces 9,9 -met 3 -dm_adaptor pragmatic -init_dm_view -adapt_dm_view \ 356 -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 \ 357 -dm_plex_metric_target_complexity 10000.0 -dm_adaptor pragmatic 358 359 TEST*/ 360