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(0); 32 } 33 34 static PetscErrorCode ProcessOptions(MPI_Comm comm, AppCtx *options) 35 { 36 PetscErrorCode ierr; 37 38 PetscFunctionBegin; 39 options->Nr = 1; 40 options->metOpt = 1; 41 options->hmin = 0.05; 42 options->hmax = 0.5; 43 options->doL2 = PETSC_FALSE; 44 45 ierr = PetscOptionsBegin(comm, "", "Meshing Adaptation Options", "DMPLEX");PetscCall(ierr); 46 PetscCall(PetscOptionsBoundedInt("-Nr", "Numberof refinement passes", "ex19.c", options->Nr, &options->Nr, NULL, 1)); 47 PetscCall(PetscOptionsBoundedInt("-met", "Different choices of metric", "ex19.c", options->metOpt, &options->metOpt, NULL,0)); 48 PetscCall(PetscOptionsReal("-hmax", "Max size prescribed by the metric", "ex19.c", options->hmax, &options->hmax, NULL)); 49 PetscCall(PetscOptionsReal("-hmin", "Min size prescribed by the metric", "ex19.c", options->hmin, &options->hmin, NULL)); 50 PetscCall(PetscOptionsBool("-do_L2", "Test L2 projection", "ex19.c", options->doL2, &options->doL2, NULL)); 51 ierr = PetscOptionsEnd();PetscCall(ierr); 52 53 PetscFunctionReturn(0); 54 } 55 56 static PetscErrorCode CreateMesh(MPI_Comm comm, DM *dm) 57 { 58 PetscFunctionBegin; 59 PetscCall(DMCreate(comm, dm)); 60 PetscCall(DMSetType(*dm, DMPLEX)); 61 PetscCall(DMSetFromOptions(*dm)); 62 PetscCall(PetscObjectSetName((PetscObject) *dm, "DMinit")); 63 PetscCall(DMViewFromOptions(*dm, NULL, "-init_dm_view")); 64 PetscFunctionReturn(0); 65 } 66 67 static PetscErrorCode ComputeMetricSensor(DM dm, AppCtx *user, Vec *metric) 68 { 69 PetscSimplePointFunc funcs[1] = {sensor}; 70 DM dmSensor, dmGrad, dmHess; 71 PetscFE fe; 72 Vec f, g, H; 73 PetscBool simplex; 74 PetscInt dim; 75 76 PetscFunctionBegin; 77 PetscCall(DMGetDimension(dm, &dim)); 78 PetscCall(DMPlexIsSimplex(dm, &simplex)); 79 80 PetscCall(DMClone(dm, &dmSensor)); 81 PetscCall(PetscFECreateLagrange(PETSC_COMM_SELF, dim, 1, simplex, 1, -1, &fe)); 82 PetscCall(DMSetField(dmSensor, 0, NULL, (PetscObject) fe)); 83 PetscCall(PetscFEDestroy(&fe)); 84 PetscCall(DMCreateDS(dmSensor)); 85 PetscCall(DMCreateLocalVector(dmSensor, &f)); 86 PetscCall(DMProjectFunctionLocal(dmSensor, 0., funcs, NULL, INSERT_VALUES, f)); 87 PetscCall(VecViewFromOptions(f, NULL, "-sensor_view")); 88 89 // Recover the gradient of the sensor function 90 PetscCall(DMClone(dm, &dmGrad)); 91 PetscCall(PetscFECreateLagrange(PETSC_COMM_SELF, dim, dim, simplex, 1, -1, &fe)); 92 PetscCall(DMSetField(dmGrad, 0, NULL, (PetscObject) fe)); 93 PetscCall(PetscFEDestroy(&fe)); 94 PetscCall(DMCreateDS(dmGrad)); 95 PetscCall(DMCreateLocalVector(dmGrad, &g)); 96 PetscCall(DMPlexComputeGradientClementInterpolant(dmSensor, f, g)); 97 PetscCall(VecDestroy(&f)); 98 PetscCall(VecViewFromOptions(g, NULL, "-gradient_view")); 99 100 // Recover the Hessian of the sensor function 101 PetscCall(DMClone(dm, &dmHess)); 102 PetscCall(DMPlexMetricCreate(dmHess, 0, &H)); 103 PetscCall(DMPlexComputeGradientClementInterpolant(dmGrad, g, H)); 104 PetscCall(VecDestroy(&g)); 105 PetscCall(VecViewFromOptions(H, NULL, "-hessian_view")); 106 107 // Obtain a metric by Lp normalization 108 PetscCall(DMPlexMetricNormalize(dmHess, H, PETSC_TRUE, PETSC_TRUE, metric)); 109 PetscCall(VecDestroy(&H)); 110 PetscCall(DMDestroy(&dmHess)); 111 PetscCall(DMDestroy(&dmGrad)); 112 PetscCall(DMDestroy(&dmSensor)); 113 PetscFunctionReturn(0); 114 } 115 116 static PetscErrorCode ComputeMetric(DM dm, AppCtx *user, Vec *metric) 117 { 118 PetscReal lambda = 1/(user->hmax*user->hmax); 119 120 PetscFunctionBeginUser; 121 if (user->metOpt == 0) { 122 /* Specify a uniform, isotropic metric */ 123 PetscCall(DMPlexMetricCreateUniform(dm, 0, lambda, metric)); 124 } else if (user->metOpt == 3) { 125 PetscCall(ComputeMetricSensor(dm, user, metric)); 126 } else { 127 DM cdm; 128 Vec coordinates; 129 const PetscScalar *coords; 130 PetscScalar *met; 131 PetscReal h; 132 PetscInt dim, i, j, vStart, vEnd, v; 133 134 PetscCall(DMPlexMetricCreate(dm, 0, metric)); 135 PetscCall(DMGetDimension(dm, &dim)); 136 PetscCall(DMGetCoordinateDM(dm, &cdm)); 137 PetscCall(DMGetCoordinatesLocal(dm, &coordinates)); 138 PetscCall(VecGetArrayRead(coordinates, &coords)); 139 PetscCall(VecGetArray(*metric, &met)); 140 PetscCall(DMPlexGetDepthStratum(dm, 0, &vStart, &vEnd)); 141 for (v = vStart; v < vEnd; ++v) { 142 PetscScalar *vcoords; 143 PetscScalar *pmet; 144 145 PetscCall(DMPlexPointLocalRead(cdm, v, coords, &vcoords)); 146 switch (user->metOpt) { 147 case 1: 148 h = user->hmax - (user->hmax-user->hmin)*PetscRealPart(vcoords[0]); 149 break; 150 case 2: 151 h = user->hmax*PetscAbsReal(((PetscReal) 1.0)-PetscExpReal(-PetscAbsScalar(vcoords[0]-(PetscReal)0.5))) + user->hmin; 152 break; 153 default: 154 SETERRQ(PetscObjectComm((PetscObject) dm), PETSC_ERR_ARG_WRONG, "metOpt = 0, 1, 2 or 3, cannot be %d", user->metOpt); 155 } 156 PetscCall(DMPlexPointLocalRef(dm, v, met, &pmet)); 157 for (i = 0; i < dim; ++i) { 158 for (j = 0; j < dim; ++j) { 159 if (i == j) { 160 if (i == 0) pmet[i*dim+j] = 1/(h*h); 161 else pmet[i*dim+j] = lambda; 162 } else pmet[i*dim+j] = 0.0; 163 } 164 } 165 } 166 PetscCall(VecRestoreArray(*metric, &met)); 167 PetscCall(VecRestoreArrayRead(coordinates, &coords)); 168 } 169 PetscFunctionReturn(0); 170 } 171 172 static PetscErrorCode linear(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nc, PetscScalar *u, void *ctx) 173 { 174 u[0] = x[0] + x[1]; 175 return 0; 176 } 177 178 static PetscErrorCode TestL2Projection(DM dm, DM dma, AppCtx *user) 179 { 180 PetscErrorCode (*funcs[1])(PetscInt, PetscReal, const PetscReal [], PetscInt, PetscScalar *, void *) = {linear}; 181 DM dmProj, dmaProj; 182 PetscFE fe; 183 KSP ksp; 184 Mat Interp, mass, mass2; 185 Vec u, ua, scaling, rhs, uproj; 186 PetscReal error; 187 PetscBool simplex; 188 PetscInt dim; 189 190 PetscFunctionBeginUser; 191 PetscCall(DMGetDimension(dm, &dim)); 192 PetscCall(DMPlexIsSimplex(dm, &simplex)); 193 194 PetscCall(DMClone(dm, &dmProj)); 195 PetscCall(PetscFECreateDefault(PETSC_COMM_SELF, dim, 1, simplex, NULL, -1, &fe)); 196 PetscCall(DMSetField(dmProj, 0, NULL, (PetscObject) fe)); 197 PetscCall(PetscFEDestroy(&fe)); 198 PetscCall(DMCreateDS(dmProj)); 199 200 PetscCall(DMClone(dma, &dmaProj)); 201 PetscCall(PetscFECreateDefault(PETSC_COMM_SELF, dim, 1, simplex, NULL, -1, &fe)); 202 PetscCall(DMSetField(dmaProj, 0, NULL, (PetscObject) fe)); 203 PetscCall(PetscFEDestroy(&fe)); 204 PetscCall(DMCreateDS(dmaProj)); 205 206 PetscCall(DMGetGlobalVector(dmProj, &u)); 207 PetscCall(DMGetGlobalVector(dmaProj, &ua)); 208 PetscCall(DMGetGlobalVector(dmaProj, &rhs)); 209 PetscCall(DMGetGlobalVector(dmaProj, &uproj)); 210 211 // Interpolate onto original mesh using dual basis 212 PetscCall(DMProjectFunction(dmProj, 0.0, funcs, NULL, INSERT_VALUES, u)); 213 PetscCall(PetscObjectSetName((PetscObject) u, "Original")); 214 PetscCall(VecViewFromOptions(u, NULL, "-orig_vec_view")); 215 PetscCall(DMComputeL2Diff(dmProj, 0.0, funcs, NULL, u, &error)); 216 PetscCall(PetscPrintf(PETSC_COMM_WORLD, "Original L2 Error: %g\n", (double) error)); 217 // Interpolate onto NEW mesh using dual basis 218 PetscCall(DMProjectFunction(dmaProj, 0.0, funcs, NULL, INSERT_VALUES, ua)); 219 PetscCall(PetscObjectSetName((PetscObject) ua, "Adapted")); 220 PetscCall(VecViewFromOptions(ua, NULL, "-adapt_vec_view")); 221 PetscCall(DMComputeL2Diff(dmaProj, 0.0, funcs, NULL, ua, &error)); 222 PetscCall(PetscPrintf(PETSC_COMM_WORLD, "Adapted L2 Error: %g\n", (double) error)); 223 // Interpolate between meshes using interpolation matrix 224 PetscCall(DMCreateInterpolation(dmProj, dmaProj, &Interp, &scaling)); 225 PetscCall(MatInterpolate(Interp, u, ua)); 226 PetscCall(MatDestroy(&Interp)); 227 PetscCall(VecDestroy(&scaling)); 228 PetscCall(PetscObjectSetName((PetscObject) ua, "Interpolation")); 229 PetscCall(VecViewFromOptions(ua, NULL, "-interp_vec_view")); 230 PetscCall(DMComputeL2Diff(dmaProj, 0.0, funcs, NULL, ua, &error)); 231 PetscCall(PetscPrintf(PETSC_COMM_WORLD, "Interpolated L2 Error: %g\n", (double) error)); 232 // L2 projection 233 PetscCall(DMCreateMassMatrix(dmaProj, dmaProj, &mass)); 234 PetscCall(MatViewFromOptions(mass, NULL, "-mass_mat_view")); 235 PetscCall(KSPCreate(PETSC_COMM_WORLD, &ksp)); 236 PetscCall(KSPSetOperators(ksp, mass, mass)); 237 PetscCall(KSPSetFromOptions(ksp)); 238 // Compute rhs as M f, could also direclty project the analytic function but we might not have it 239 PetscCall(DMCreateMassMatrix(dmProj, dmaProj, &mass2)); 240 PetscCall(MatMult(mass2, u, rhs)); 241 PetscCall(MatDestroy(&mass2)); 242 PetscCall(KSPSolve(ksp, rhs, uproj)); 243 PetscCall(PetscObjectSetName((PetscObject) uproj, "L_2 Projection")); 244 PetscCall(VecViewFromOptions(uproj, NULL, "-proj_vec_view")); 245 PetscCall(DMComputeL2Diff(dmaProj, 0.0, funcs, NULL, uproj, &error)); 246 PetscCall(PetscPrintf(PETSC_COMM_WORLD, "Projected L2 Error: %g\n", (double) error)); 247 PetscCall(KSPDestroy(&ksp)); 248 PetscCall(MatDestroy(&mass)); 249 PetscCall(DMRestoreGlobalVector(dmProj, &u)); 250 PetscCall(DMRestoreGlobalVector(dmaProj, &ua)); 251 PetscCall(DMRestoreGlobalVector(dmaProj, &rhs)); 252 PetscCall(DMRestoreGlobalVector(dmaProj, &uproj)); 253 PetscCall(DMDestroy(&dmProj)); 254 PetscCall(DMDestroy(&dmaProj)); 255 PetscFunctionReturn(0); 256 } 257 258 int main (int argc, char * argv[]) { 259 DM dm; 260 AppCtx user; /* user-defined work context */ 261 MPI_Comm comm; 262 DM dma, odm; 263 Vec metric; 264 PetscInt r; 265 266 PetscCall(PetscInitialize(&argc, &argv, NULL, help)); 267 comm = PETSC_COMM_WORLD; 268 PetscCall(ProcessOptions(comm, &user)); 269 PetscCall(CreateMesh(comm, &dm)); 270 271 odm = dm; 272 PetscCall(DMPlexDistributeOverlap(odm, 1, NULL, &dm)); 273 if (!dm) {dm = odm;} 274 else PetscCall(DMDestroy(&odm)); 275 276 for (r = 0; r < user.Nr; ++r) { 277 DMLabel label; 278 279 PetscCall(ComputeMetric(dm, &user, &metric)); 280 PetscCall(DMGetLabel(dm, "marker", &label)); 281 PetscCall(DMAdaptMetric(dm, metric, label, NULL, &dma)); 282 PetscCall(VecDestroy(&metric)); 283 PetscCall(PetscObjectSetName((PetscObject) dma, "DMadapt")); 284 PetscCall(PetscObjectSetOptionsPrefix((PetscObject) dma, "adapt_")); 285 PetscCall(DMViewFromOptions(dma, NULL, "-dm_view")); 286 if (user.doL2) PetscCall(TestL2Projection(dm, dma, &user)); 287 PetscCall(DMDestroy(&dm)); 288 dm = dma; 289 } 290 PetscCall(PetscObjectSetOptionsPrefix((PetscObject) dm, "final_")); 291 PetscCall(DMViewFromOptions(dm, NULL, "-dm_view")); 292 PetscCall(DMDestroy(&dm)); 293 PetscCall(PetscFinalize()); 294 return 0; 295 } 296 297 /*TEST 298 299 build: 300 requires: pragmatic 301 302 testset: 303 args: -dm_plex_box_faces 4,4,4 -dm_adaptor pragmatic -met 2 -init_dm_view -adapt_dm_view -dm_adaptor pragmatic 304 305 test: 306 suffix: 0 307 args: -dm_plex_separate_marker 0 308 test: 309 suffix: 1 310 args: -dm_plex_separate_marker 1 311 test: 312 suffix: 2 313 args: -dm_plex_dim 3 314 test: 315 suffix: 3 316 args: -dm_plex_dim 3 317 318 # Pragmatic hangs for simple partitioner 319 testset: 320 requires: parmetis 321 args: -dm_plex_box_faces 2,2 -dm_adaptor pragmatic -petscpartitioner_type parmetis -met 2 -init_dm_view -adapt_dm_view -dm_adaptor pragmatic 322 323 test: 324 suffix: 4 325 nsize: 2 326 test: 327 suffix: 5 328 nsize: 4 329 330 test: 331 requires: parmetis 332 suffix: 6 333 nsize: 2 334 args: -dm_plex_dim 3 -dm_plex_box_faces 9,9,9 -dm_adaptor pragmatic -petscpartitioner_type parmetis \ 335 -met 0 -hmin 0.01 -hmax 0.03 -init_dm_view -adapt_dm_view -dm_adaptor pragmatic 336 test: 337 requires: parmetis 338 suffix: 7 339 nsize: 2 340 args: -dm_plex_box_faces 19,19 -dm_adaptor pragmatic -petscpartitioner_type parmetis \ 341 -met 2 -hmax 0.5 -hmin 0.001 -init_dm_view -adapt_dm_view -dm_adaptor pragmatic 342 test: 343 suffix: proj_0 344 args: -dm_plex_box_faces 2,2 -dm_plex_hash_location -dm_adaptor pragmatic -init_dm_view -adapt_dm_view -do_L2 \ 345 -petscspace_degree 1 -petscfe_default_quadrature_order 1 -pc_type lu -dm_adaptor pragmatic 346 test: 347 suffix: proj_1 348 args: -dm_plex_box_faces 4,4 -dm_plex_hash_location -dm_adaptor pragmatic -init_dm_view -adapt_dm_view -do_L2 \ 349 -petscspace_degree 1 -petscfe_default_quadrature_order 1 -pc_type lu -dm_adaptor pragmatic 350 351 test: 352 suffix: sensor 353 args: -dm_plex_box_faces 9,9 -met 3 -dm_adaptor pragmatic -init_dm_view -adapt_dm_view \ 354 -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 \ 355 -dm_plex_metric_target_complexity 10000.0 -dm_adaptor pragmatic 356 357 TEST*/ 358