1 static char help[] = "Heat Equation in 2d and 3d with finite elements.\n\ 2 We solve the heat equation in a rectangular\n\ 3 domain, using a parallel unstructured mesh (DMPLEX) to discretize it.\n\ 4 Contributed by: Julian Andrej <juan@tf.uni-kiel.de>\n\n\n"; 5 6 #include <petscdmplex.h> 7 #include <petscds.h> 8 #include <petscts.h> 9 10 /* 11 Heat equation: 12 13 du/dt - \Delta u + f = 0 14 */ 15 16 typedef enum {SOL_QUADRATIC_LINEAR, SOL_QUADRATIC_TRIG, SOL_TRIG_LINEAR, SOL_TRIG_TRIG, NUM_SOLUTION_TYPES} SolutionType; 17 const char *solutionTypes[NUM_SOLUTION_TYPES+1] = {"quadratic_linear", "quadratic_trig", "trig_linear", "trig_trig", "unknown"}; 18 19 typedef struct { 20 SolutionType solType; /* Type of exact solution */ 21 /* Solver setup */ 22 PetscBool expTS; /* Flag for explicit timestepping */ 23 PetscBool lumped; /* Lump the mass matrix */ 24 } AppCtx; 25 26 /* 27 Exact 2D solution: 28 u = 2t + x^2 + y^2 29 u_t = 2 30 \Delta u = 2 + 2 = 4 31 f = 2 32 F(u) = 2 - (2 + 2) + 2 = 0 33 34 Exact 3D solution: 35 u = 3t + x^2 + y^2 + z^2 36 F(u) = 3 - (2 + 2 + 2) + 3 = 0 37 */ 38 static PetscErrorCode mms_quad_lin(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nc, PetscScalar *u, void *ctx) 39 { 40 PetscInt d; 41 42 *u = dim*time; 43 for (d = 0; d < dim; ++d) *u += x[d]*x[d]; 44 return 0; 45 } 46 47 static PetscErrorCode mms_quad_lin_t(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nc, PetscScalar *u, void *ctx) 48 { 49 *u = dim; 50 return 0; 51 } 52 53 static void f0_quad_lin_exp(PetscInt dim, PetscInt Nf, PetscInt NfAux, 54 const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], 55 const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], 56 PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f0[]) 57 { 58 f0[0] = -(PetscScalar) dim; 59 } 60 static void f0_quad_lin(PetscInt dim, PetscInt Nf, PetscInt NfAux, 61 const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], 62 const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], 63 PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f0[]) 64 { 65 PetscScalar exp[1] = {0.}; 66 f0_quad_lin_exp(dim, Nf, NfAux, uOff, uOff_x, u, u_t, u_x, aOff, aOff_x, a, a_t, a_x, t, x, numConstants, constants, exp); 67 f0[0] = u_t[0] - exp[0]; 68 } 69 70 /* 71 Exact 2D solution: 72 u = 2*cos(t) + x^2 + y^2 73 F(u) = -2*sint(t) - (2 + 2) + 2*sin(t) + 4 = 0 74 75 Exact 3D solution: 76 u = 3*cos(t) + x^2 + y^2 + z^2 77 F(u) = -3*sin(t) - (2 + 2 + 2) + 3*sin(t) + 6 = 0 78 */ 79 static PetscErrorCode mms_quad_trig(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nc, PetscScalar *u, void *ctx) 80 { 81 PetscInt d; 82 83 *u = dim*PetscCosReal(time); 84 for (d = 0; d < dim; ++d) *u += x[d]*x[d]; 85 return 0; 86 } 87 88 static PetscErrorCode mms_quad_trig_t(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nc, PetscScalar *u, void *ctx) 89 { 90 *u = -dim*PetscSinReal(time); 91 return 0; 92 } 93 94 static void f0_quad_trig_exp(PetscInt dim, PetscInt Nf, PetscInt NfAux, 95 const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], 96 const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], 97 PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f0[]) 98 { 99 f0[0] = -dim*(PetscSinReal(t) + 2.0); 100 } 101 static void f0_quad_trig(PetscInt dim, PetscInt Nf, PetscInt NfAux, 102 const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], 103 const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], 104 PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f0[]) 105 { 106 PetscScalar exp[1] = {0.}; 107 f0_quad_trig_exp(dim, Nf, NfAux, uOff, uOff_x, u, u_t, u_x, aOff, aOff_x, a, a_t, a_x, t, x, numConstants, constants, exp); 108 f0[0] = u_t[0] - exp[0]; 109 } 110 111 /* 112 Exact 2D solution: 113 u = 2\pi^2 t + cos(\pi x) + cos(\pi y) 114 F(u) = 2\pi^2 - \pi^2 (cos(\pi x) + cos(\pi y)) + \pi^2 (cos(\pi x) + cos(\pi y)) - 2\pi^2 = 0 115 116 Exact 3D solution: 117 u = 3\pi^2 t + cos(\pi x) + cos(\pi y) + cos(\pi z) 118 F(u) = 3\pi^2 - \pi^2 (cos(\pi x) + cos(\pi y) + cos(\pi z)) + \pi^2 (cos(\pi x) + cos(\pi y) + cos(\pi z)) - 3\pi^2 = 0 119 */ 120 static PetscErrorCode mms_trig_lin(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nc, PetscScalar *u, void *ctx) 121 { 122 PetscInt d; 123 124 *u = dim*PetscSqr(PETSC_PI)*time; 125 for (d = 0; d < dim; ++d) *u += PetscCosReal(PETSC_PI*x[d]); 126 return 0; 127 } 128 129 static PetscErrorCode mms_trig_lin_t(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nc, PetscScalar *u, void *ctx) 130 { 131 *u = dim*PetscSqr(PETSC_PI); 132 return 0; 133 } 134 135 static void f0_trig_lin(PetscInt dim, PetscInt Nf, PetscInt NfAux, 136 const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], 137 const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], 138 PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f0[]) 139 { 140 PetscInt d; 141 f0[0] = u_t[0]; 142 for (d = 0; d < dim; ++d) f0[0] += PetscSqr(PETSC_PI)*(PetscCosReal(PETSC_PI*x[d]) - 1.0); 143 } 144 145 /* 146 Exact 2D solution: 147 u = pi^2 cos(t) + cos(\pi x) + cos(\pi y) 148 u_t = -pi^2 sin(t) 149 \Delta u = -\pi^2 (cos(\pi x) + cos(\pi y)) 150 f = pi^2 sin(t) - \pi^2 (cos(\pi x) + cos(\pi y)) 151 F(u) = -\pi^2 sin(t) + \pi^2 (cos(\pi x) + cos(\pi y)) - \pi^2 (cos(\pi x) + cos(\pi y)) + \pi^2 sin(t) = 0 152 153 Exact 3D solution: 154 u = pi^2 cos(t) + cos(\pi x) + cos(\pi y) + cos(\pi z) 155 u_t = -pi^2 sin(t) 156 \Delta u = -\pi^2 (cos(\pi x) + cos(\pi y) + cos(\pi z)) 157 f = pi^2 sin(t) - \pi^2 (cos(\pi x) + cos(\pi y) + cos(\pi z)) 158 F(u) = -\pi^2 sin(t) + \pi^2 (cos(\pi x) + cos(\pi y) + cos(\pi z)) - \pi^2 (cos(\pi x) + cos(\pi y) + cos(\pi z)) + \pi^2 sin(t) = 0 159 */ 160 static PetscErrorCode mms_trig_trig(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nc, PetscScalar *u, void *ctx) 161 { 162 PetscInt d; 163 164 *u = PetscSqr(PETSC_PI)*PetscCosReal(time); 165 for (d = 0; d < dim; ++d) *u += PetscCosReal(PETSC_PI*x[d]); 166 return 0; 167 } 168 169 static PetscErrorCode mms_trig_trig_t(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nc, PetscScalar *u, void *ctx) 170 { 171 *u = -PetscSqr(PETSC_PI)*PetscSinReal(time); 172 return 0; 173 } 174 175 static void f0_trig_trig_exp(PetscInt dim, PetscInt Nf, PetscInt NfAux, 176 const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], 177 const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], 178 PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f0[]) 179 { 180 PetscInt d; 181 f0[0] -= PetscSqr(PETSC_PI)*PetscSinReal(t); 182 for (d = 0; d < dim; ++d) f0[0] += PetscSqr(PETSC_PI)*PetscCosReal(PETSC_PI*x[d]); 183 } 184 static void f0_trig_trig(PetscInt dim, PetscInt Nf, PetscInt NfAux, 185 const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], 186 const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], 187 PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f0[]) 188 { 189 PetscScalar exp[1] = {0.}; 190 f0_trig_trig_exp(dim, Nf, NfAux, uOff, uOff_x, u, u_t, u_x, aOff, aOff_x, a, a_t, a_x, t, x, numConstants, constants, exp); 191 f0[0] = u_t[0] - exp[0]; 192 } 193 194 static void f1_temp_exp(PetscInt dim, PetscInt Nf, PetscInt NfAux, 195 const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], 196 const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], 197 PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f1[]) 198 { 199 PetscInt d; 200 for (d = 0; d < dim; ++d) f1[d] = -u_x[d]; 201 } 202 static void f1_temp(PetscInt dim, PetscInt Nf, PetscInt NfAux, 203 const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], 204 const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], 205 PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f1[]) 206 { 207 PetscInt d; 208 for (d = 0; d < dim; ++d) f1[d] = u_x[d]; 209 } 210 211 static void g3_temp(PetscInt dim, PetscInt Nf, PetscInt NfAux, 212 const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], 213 const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], 214 PetscReal t, PetscReal u_tShift, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar g3[]) 215 { 216 PetscInt d; 217 for (d = 0; d < dim; ++d) g3[d*dim+d] = 1.0; 218 } 219 220 static void g0_temp(PetscInt dim, PetscInt Nf, PetscInt NfAux, 221 const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], 222 const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], 223 PetscReal t, PetscReal u_tShift, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar g0[]) 224 { 225 g0[0] = u_tShift*1.0; 226 } 227 228 static PetscErrorCode ProcessOptions(MPI_Comm comm, AppCtx *options) 229 { 230 PetscInt sol; 231 232 PetscFunctionBeginUser; 233 options->solType = SOL_QUADRATIC_LINEAR; 234 options->expTS = PETSC_FALSE; 235 options->lumped = PETSC_TRUE; 236 237 PetscOptionsBegin(comm, "", "Heat Equation Options", "DMPLEX"); 238 PetscCall(PetscOptionsEList("-sol_type", "Type of exact solution", "ex45.c", solutionTypes, NUM_SOLUTION_TYPES, solutionTypes[options->solType], &sol, NULL)); 239 options->solType = (SolutionType) sol; 240 PetscCall(PetscOptionsBool("-explicit", "Use explicit timestepping", "ex45.c", options->expTS, &options->expTS, NULL)); 241 PetscCall(PetscOptionsBool("-lumped", "Lump the mass matrix", "ex45.c", options->lumped, &options->lumped, NULL)); 242 PetscOptionsEnd(); 243 PetscFunctionReturn(0); 244 } 245 246 static PetscErrorCode CreateMesh(MPI_Comm comm, DM *dm, AppCtx *ctx) 247 { 248 PetscFunctionBeginUser; 249 PetscCall(DMCreate(comm, dm)); 250 PetscCall(DMSetType(*dm, DMPLEX)); 251 PetscCall(DMSetFromOptions(*dm)); 252 PetscCall(DMViewFromOptions(*dm, NULL, "-dm_view")); 253 PetscFunctionReturn(0); 254 } 255 256 static PetscErrorCode SetupProblem(DM dm, AppCtx *ctx) 257 { 258 PetscDS ds; 259 DMLabel label; 260 const PetscInt id = 1; 261 262 PetscFunctionBeginUser; 263 PetscCall(DMGetLabel(dm, "marker", &label)); 264 PetscCall(DMGetDS(dm, &ds)); 265 PetscCall(PetscDSSetJacobian(ds, 0, 0, g0_temp, NULL, NULL, g3_temp)); 266 switch (ctx->solType) { 267 case SOL_QUADRATIC_LINEAR: 268 PetscCall(PetscDSSetResidual(ds, 0, f0_quad_lin, f1_temp)); 269 PetscCall(PetscDSSetRHSResidual(ds, 0, f0_quad_lin_exp, f1_temp_exp)); 270 PetscCall(PetscDSSetExactSolution(ds, 0, mms_quad_lin, ctx)); 271 PetscCall(PetscDSSetExactSolutionTimeDerivative(ds, 0, mms_quad_lin_t, ctx)); 272 PetscCall(DMAddBoundary(dm, DM_BC_ESSENTIAL, "wall", label, 1, &id, 0, 0, NULL, (void (*)(void)) mms_quad_lin, (void (*)(void)) mms_quad_lin_t, ctx, NULL)); 273 break; 274 case SOL_QUADRATIC_TRIG: 275 PetscCall(PetscDSSetResidual(ds, 0, f0_quad_trig, f1_temp)); 276 PetscCall(PetscDSSetRHSResidual(ds, 0, f0_quad_trig_exp, f1_temp_exp)); 277 PetscCall(PetscDSSetExactSolution(ds, 0, mms_quad_trig, ctx)); 278 PetscCall(PetscDSSetExactSolutionTimeDerivative(ds, 0, mms_quad_trig_t, ctx)); 279 PetscCall(DMAddBoundary(dm, DM_BC_ESSENTIAL, "wall", label, 1, &id, 0, 0, NULL, (void (*)(void)) mms_quad_trig, (void (*)(void)) mms_quad_trig_t, ctx, NULL)); 280 break; 281 case SOL_TRIG_LINEAR: 282 PetscCall(PetscDSSetResidual(ds, 0, f0_trig_lin, f1_temp)); 283 PetscCall(PetscDSSetExactSolution(ds, 0, mms_trig_lin, ctx)); 284 PetscCall(PetscDSSetExactSolutionTimeDerivative(ds, 0, mms_trig_lin_t, ctx)); 285 PetscCall(DMAddBoundary(dm, DM_BC_ESSENTIAL, "wall", label, 1, &id, 0, 0, NULL, (void (*)(void)) mms_trig_lin, (void (*)(void)) mms_trig_lin_t, ctx, NULL)); 286 break; 287 case SOL_TRIG_TRIG: 288 PetscCall(PetscDSSetResidual(ds, 0, f0_trig_trig, f1_temp)); 289 PetscCall(PetscDSSetRHSResidual(ds, 0, f0_trig_trig_exp, f1_temp_exp)); 290 PetscCall(PetscDSSetExactSolution(ds, 0, mms_trig_trig, ctx)); 291 PetscCall(PetscDSSetExactSolutionTimeDerivative(ds, 0, mms_trig_trig_t, ctx)); 292 break; 293 default: SETERRQ(PetscObjectComm((PetscObject) dm), PETSC_ERR_ARG_WRONG, "Invalid solution type: %s (%d)", solutionTypes[PetscMin(ctx->solType, NUM_SOLUTION_TYPES)], ctx->solType); 294 } 295 PetscFunctionReturn(0); 296 } 297 298 static PetscErrorCode SetupDiscretization(DM dm, AppCtx* ctx) 299 { 300 DM cdm = dm; 301 PetscFE fe; 302 DMPolytopeType ct; 303 PetscBool simplex; 304 PetscInt dim, cStart; 305 306 PetscFunctionBeginUser; 307 PetscCall(DMGetDimension(dm, &dim)); 308 PetscCall(DMPlexGetHeightStratum(dm, 0, &cStart, NULL)); 309 PetscCall(DMPlexGetCellType(dm, cStart, &ct)); 310 simplex = DMPolytopeTypeGetNumVertices(ct) == DMPolytopeTypeGetDim(ct)+1 ? PETSC_TRUE : PETSC_FALSE; 311 /* Create finite element */ 312 PetscCall(PetscFECreateDefault(PETSC_COMM_SELF, dim, 1, simplex, "temp_", -1, &fe)); 313 PetscCall(PetscObjectSetName((PetscObject) fe, "temperature")); 314 /* Set discretization and boundary conditions for each mesh */ 315 PetscCall(DMSetField(dm, 0, NULL, (PetscObject) fe)); 316 PetscCall(DMCreateDS(dm)); 317 if (ctx->expTS) { 318 PetscDS ds; 319 320 PetscCall(DMGetDS(dm, &ds)); 321 PetscCall(PetscDSSetImplicit(ds, 0, PETSC_FALSE)); 322 } 323 PetscCall(SetupProblem(dm, ctx)); 324 while (cdm) { 325 PetscCall(DMCopyDisc(dm, cdm)); 326 PetscCall(DMGetCoarseDM(cdm, &cdm)); 327 } 328 PetscCall(PetscFEDestroy(&fe)); 329 PetscFunctionReturn(0); 330 } 331 332 static PetscErrorCode SetInitialConditions(TS ts, Vec u) 333 { 334 DM dm; 335 PetscReal t; 336 337 PetscFunctionBeginUser; 338 PetscCall(TSGetDM(ts, &dm)); 339 PetscCall(TSGetTime(ts, &t)); 340 PetscCall(DMComputeExactSolution(dm, t, u, NULL)); 341 PetscFunctionReturn(0); 342 } 343 344 int main(int argc, char **argv) 345 { 346 DM dm; 347 TS ts; 348 Vec u; 349 AppCtx ctx; 350 351 PetscFunctionBeginUser; 352 PetscCall(PetscInitialize(&argc, &argv, NULL, help)); 353 PetscCall(ProcessOptions(PETSC_COMM_WORLD, &ctx)); 354 PetscCall(CreateMesh(PETSC_COMM_WORLD, &dm, &ctx)); 355 PetscCall(DMSetApplicationContext(dm, &ctx)); 356 PetscCall(SetupDiscretization(dm, &ctx)); 357 358 PetscCall(TSCreate(PETSC_COMM_WORLD, &ts)); 359 PetscCall(TSSetDM(ts, dm)); 360 PetscCall(DMTSSetBoundaryLocal(dm, DMPlexTSComputeBoundary, &ctx)); 361 if (ctx.expTS) { 362 PetscCall(DMTSSetRHSFunctionLocal(dm, DMPlexTSComputeRHSFunctionFEM, &ctx)); 363 if (ctx.lumped) PetscCall(DMTSCreateRHSMassMatrixLumped(dm)); 364 else PetscCall(DMTSCreateRHSMassMatrix(dm)); 365 } else { 366 PetscCall(DMTSSetIFunctionLocal(dm, DMPlexTSComputeIFunctionFEM, &ctx)); 367 PetscCall(DMTSSetIJacobianLocal(dm, DMPlexTSComputeIJacobianFEM, &ctx)); 368 } 369 PetscCall(TSSetExactFinalTime(ts, TS_EXACTFINALTIME_MATCHSTEP)); 370 PetscCall(TSSetFromOptions(ts)); 371 PetscCall(TSSetComputeInitialCondition(ts, SetInitialConditions)); 372 373 PetscCall(DMCreateGlobalVector(dm, &u)); 374 PetscCall(DMTSCheckFromOptions(ts, u)); 375 PetscCall(SetInitialConditions(ts, u)); 376 PetscCall(PetscObjectSetName((PetscObject) u, "temperature")); 377 PetscCall(TSSolve(ts, u)); 378 PetscCall(DMTSCheckFromOptions(ts, u)); 379 if (ctx.expTS) PetscCall(DMTSDestroyRHSMassMatrix(dm)); 380 381 PetscCall(VecDestroy(&u)); 382 PetscCall(TSDestroy(&ts)); 383 PetscCall(DMDestroy(&dm)); 384 PetscCall(PetscFinalize()); 385 return 0; 386 } 387 388 /*TEST 389 390 test: 391 suffix: 2d_p1 392 requires: triangle 393 args: -sol_type quadratic_linear -dm_refine 1 -temp_petscspace_degree 1 -dmts_check .0001 \ 394 -ts_type beuler -ts_max_steps 5 -ts_dt 0.1 -snes_error_if_not_converged -pc_type lu 395 test: 396 suffix: 2d_p1_exp 397 requires: triangle 398 args: -sol_type quadratic_linear -dm_refine 1 -temp_petscspace_degree 1 -explicit \ 399 -ts_type euler -ts_max_steps 4 -ts_dt 1e-3 -ts_monitor_error 400 test: 401 # -dm_refine 2 -convest_num_refine 3 get L_2 convergence rate: [1.9] 402 suffix: 2d_p1_sconv 403 requires: triangle 404 args: -sol_type quadratic_linear -temp_petscspace_degree 1 -ts_convergence_estimate -ts_convergence_temporal 0 -convest_num_refine 1 \ 405 -ts_type beuler -ts_max_steps 1 -ts_dt 0.00001 -snes_error_if_not_converged -pc_type lu 406 test: 407 # -dm_refine 2 -convest_num_refine 3 get L_2 convergence rate: [2.1] 408 suffix: 2d_p1_sconv_2 409 requires: triangle 410 args: -sol_type trig_trig -temp_petscspace_degree 1 -ts_convergence_estimate -ts_convergence_temporal 0 -convest_num_refine 1 \ 411 -ts_type beuler -ts_max_steps 1 -ts_dt 1e-6 -snes_error_if_not_converged -pc_type lu 412 test: 413 # -dm_refine 4 -convest_num_refine 3 get L_2 convergence rate: [1.2] 414 suffix: 2d_p1_tconv 415 requires: triangle 416 args: -sol_type quadratic_trig -temp_petscspace_degree 1 -ts_convergence_estimate -convest_num_refine 1 \ 417 -ts_type beuler -ts_max_steps 4 -ts_dt 0.1 -snes_error_if_not_converged -pc_type lu 418 test: 419 # -dm_refine 6 -convest_num_refine 3 get L_2 convergence rate: [1.0] 420 suffix: 2d_p1_tconv_2 421 requires: triangle 422 args: -sol_type trig_trig -temp_petscspace_degree 1 -ts_convergence_estimate -convest_num_refine 1 \ 423 -ts_type beuler -ts_max_steps 4 -ts_dt 0.1 -snes_error_if_not_converged -pc_type lu 424 test: 425 # The L_2 convergence rate cannot be seen since stability of the explicit integrator requires that is be more accurate than the grid 426 suffix: 2d_p1_exp_tconv_2 427 requires: triangle 428 args: -sol_type trig_trig -temp_petscspace_degree 1 -explicit -ts_convergence_estimate -convest_num_refine 1 \ 429 -ts_type euler -ts_max_steps 4 -ts_dt 1e-4 -lumped 0 -mass_pc_type lu 430 test: 431 # The L_2 convergence rate cannot be seen since stability of the explicit integrator requires that is be more accurate than the grid 432 suffix: 2d_p1_exp_tconv_2_lump 433 requires: triangle 434 args: -sol_type trig_trig -temp_petscspace_degree 1 -explicit -ts_convergence_estimate -convest_num_refine 1 \ 435 -ts_type euler -ts_max_steps 4 -ts_dt 1e-4 436 test: 437 suffix: 2d_p2 438 requires: triangle 439 args: -sol_type quadratic_linear -dm_refine 0 -temp_petscspace_degree 2 -dmts_check .0001 \ 440 -ts_type beuler -ts_max_steps 5 -ts_dt 0.1 -snes_error_if_not_converged -pc_type lu 441 test: 442 # -dm_refine 2 -convest_num_refine 3 get L_2 convergence rate: [2.9] 443 suffix: 2d_p2_sconv 444 requires: triangle 445 args: -sol_type trig_linear -temp_petscspace_degree 2 -ts_convergence_estimate -ts_convergence_temporal 0 -convest_num_refine 1 \ 446 -ts_type beuler -ts_max_steps 1 -ts_dt 0.00000001 -snes_error_if_not_converged -pc_type lu 447 test: 448 # -dm_refine 2 -convest_num_refine 3 get L_2 convergence rate: [3.1] 449 suffix: 2d_p2_sconv_2 450 requires: triangle 451 args: -sol_type trig_trig -temp_petscspace_degree 2 -ts_convergence_estimate -ts_convergence_temporal 0 -convest_num_refine 1 \ 452 -ts_type beuler -ts_max_steps 1 -ts_dt 0.00000001 -snes_error_if_not_converged -pc_type lu 453 test: 454 # -dm_refine 3 -convest_num_refine 3 get L_2 convergence rate: [1.0] 455 suffix: 2d_p2_tconv 456 requires: triangle 457 args: -sol_type quadratic_trig -temp_petscspace_degree 2 -ts_convergence_estimate -convest_num_refine 1 \ 458 -ts_type beuler -ts_max_steps 4 -ts_dt 0.1 -snes_error_if_not_converged -pc_type lu 459 test: 460 # -dm_refine 3 -convest_num_refine 3 get L_2 convergence rate: [1.0] 461 suffix: 2d_p2_tconv_2 462 requires: triangle 463 args: -sol_type trig_trig -temp_petscspace_degree 2 -ts_convergence_estimate -convest_num_refine 1 \ 464 -ts_type beuler -ts_max_steps 4 -ts_dt 0.1 -snes_error_if_not_converged -pc_type lu 465 test: 466 suffix: 2d_q1 467 args: -sol_type quadratic_linear -dm_plex_simplex 0 -dm_refine 1 -temp_petscspace_degree 1 -dmts_check .0001 \ 468 -ts_type beuler -ts_max_steps 5 -ts_dt 0.1 -snes_error_if_not_converged -pc_type lu 469 test: 470 # -dm_refine 2 -convest_num_refine 3 get L_2 convergence rate: [1.9] 471 suffix: 2d_q1_sconv 472 args: -sol_type quadratic_linear -dm_plex_simplex 0 -temp_petscspace_degree 1 -ts_convergence_estimate -ts_convergence_temporal 0 -convest_num_refine 1 \ 473 -ts_type beuler -ts_max_steps 1 -ts_dt 0.00001 -snes_error_if_not_converged -pc_type lu 474 test: 475 # -dm_refine 4 -convest_num_refine 3 get L_2 convergence rate: [1.2] 476 suffix: 2d_q1_tconv 477 args: -sol_type quadratic_trig -dm_plex_simplex 0 -temp_petscspace_degree 1 -ts_convergence_estimate -convest_num_refine 1 \ 478 -ts_type beuler -ts_max_steps 4 -ts_dt 0.1 -snes_error_if_not_converged -pc_type lu 479 test: 480 suffix: 2d_q2 481 args: -sol_type quadratic_linear -dm_plex_simplex 0 -dm_refine 0 -temp_petscspace_degree 2 -dmts_check .0001 \ 482 -ts_type beuler -ts_max_steps 5 -ts_dt 0.1 -snes_error_if_not_converged -pc_type lu 483 test: 484 # -dm_refine 2 -convest_num_refine 3 get L_2 convergence rate: [2.9] 485 suffix: 2d_q2_sconv 486 args: -sol_type trig_linear -dm_plex_simplex 0 -temp_petscspace_degree 2 -ts_convergence_estimate -ts_convergence_temporal 0 -convest_num_refine 1 \ 487 -ts_type beuler -ts_max_steps 1 -ts_dt 0.00000001 -snes_error_if_not_converged -pc_type lu 488 test: 489 # -dm_refine 3 -convest_num_refine 3 get L_2 convergence rate: [1.0] 490 suffix: 2d_q2_tconv 491 args: -sol_type quadratic_trig -dm_plex_simplex 0 -temp_petscspace_degree 2 -ts_convergence_estimate -convest_num_refine 1 \ 492 -ts_type beuler -ts_max_steps 4 -ts_dt 0.1 -snes_error_if_not_converged -pc_type lu 493 494 test: 495 suffix: 3d_p1 496 requires: ctetgen 497 args: -sol_type quadratic_linear -dm_refine 1 -temp_petscspace_degree 1 -dmts_check .0001 \ 498 -ts_type beuler -ts_max_steps 5 -ts_dt 0.1 -snes_error_if_not_converged -pc_type lu 499 test: 500 # -dm_refine 2 -convest_num_refine 3 get L_2 convergence rate: [1.9] 501 suffix: 3d_p1_sconv 502 requires: ctetgen 503 args: -sol_type quadratic_linear -temp_petscspace_degree 1 -ts_convergence_estimate -ts_convergence_temporal 0 -convest_num_refine 1 \ 504 -ts_type beuler -ts_max_steps 1 -ts_dt 0.00001 -snes_error_if_not_converged -pc_type lu 505 test: 506 # -dm_refine 4 -convest_num_refine 3 get L_2 convergence rate: [1.2] 507 suffix: 3d_p1_tconv 508 requires: ctetgen 509 args: -sol_type quadratic_trig -temp_petscspace_degree 1 -ts_convergence_estimate -convest_num_refine 1 \ 510 -ts_type beuler -ts_max_steps 4 -ts_dt 0.1 -snes_error_if_not_converged -pc_type lu 511 test: 512 suffix: 3d_p2 513 requires: ctetgen 514 args: -sol_type quadratic_linear -dm_refine 0 -temp_petscspace_degree 2 -dmts_check .0001 \ 515 -ts_type beuler -ts_max_steps 5 -ts_dt 0.1 -snes_error_if_not_converged -pc_type lu 516 test: 517 # -dm_refine 2 -convest_num_refine 3 get L_2 convergence rate: [2.9] 518 suffix: 3d_p2_sconv 519 requires: ctetgen 520 args: -sol_type trig_linear -temp_petscspace_degree 2 -ts_convergence_estimate -ts_convergence_temporal 0 -convest_num_refine 1 \ 521 -ts_type beuler -ts_max_steps 1 -ts_dt 0.00000001 -snes_error_if_not_converged -pc_type lu 522 test: 523 # -dm_refine 3 -convest_num_refine 3 get L_2 convergence rate: [1.0] 524 suffix: 3d_p2_tconv 525 requires: ctetgen 526 args: -sol_type quadratic_trig -temp_petscspace_degree 2 -ts_convergence_estimate -convest_num_refine 1 \ 527 -ts_type beuler -ts_max_steps 4 -ts_dt 0.1 -snes_error_if_not_converged -pc_type lu 528 test: 529 suffix: 3d_q1 530 args: -sol_type quadratic_linear -dm_plex_simplex 0 -dm_refine 1 -temp_petscspace_degree 1 -dmts_check .0001 \ 531 -ts_type beuler -ts_max_steps 5 -ts_dt 0.1 -snes_error_if_not_converged -pc_type lu 532 test: 533 # -dm_refine 2 -convest_num_refine 3 get L_2 convergence rate: [1.9] 534 suffix: 3d_q1_sconv 535 args: -sol_type quadratic_linear -dm_plex_simplex 0 -temp_petscspace_degree 1 -ts_convergence_estimate -ts_convergence_temporal 0 -convest_num_refine 1 \ 536 -ts_type beuler -ts_max_steps 1 -ts_dt 0.00001 -snes_error_if_not_converged -pc_type lu 537 test: 538 # -dm_refine 4 -convest_num_refine 3 get L_2 convergence rate: [1.2] 539 suffix: 3d_q1_tconv 540 args: -sol_type quadratic_trig -dm_plex_simplex 0 -temp_petscspace_degree 1 -ts_convergence_estimate -convest_num_refine 1 \ 541 -ts_type beuler -ts_max_steps 4 -ts_dt 0.1 -snes_error_if_not_converged -pc_type lu 542 test: 543 suffix: 3d_q2 544 args: -sol_type quadratic_linear -dm_plex_simplex 0 -dm_refine 0 -temp_petscspace_degree 2 -dmts_check .0001 \ 545 -ts_type beuler -ts_max_steps 5 -ts_dt 0.1 -snes_error_if_not_converged -pc_type lu 546 test: 547 # -dm_refine 2 -convest_num_refine 3 get L_2 convergence rate: [2.9] 548 suffix: 3d_q2_sconv 549 args: -sol_type trig_linear -dm_plex_simplex 0 -temp_petscspace_degree 2 -ts_convergence_estimate -ts_convergence_temporal 0 -convest_num_refine 1 \ 550 -ts_type beuler -ts_max_steps 1 -ts_dt 0.00000001 -snes_error_if_not_converged -pc_type lu 551 test: 552 # -dm_refine 3 -convest_num_refine 3 get L_2 convergence rate: [1.0] 553 suffix: 3d_q2_tconv 554 args: -sol_type quadratic_trig -dm_plex_simplex 0 -temp_petscspace_degree 2 -ts_convergence_estimate -convest_num_refine 1 \ 555 -ts_type beuler -ts_max_steps 4 -ts_dt 0.1 -snes_error_if_not_converged -pc_type lu 556 557 test: 558 # For a nice picture, -bd_dm_refine 2 -dm_refine 1 -dm_view hdf5:${PETSC_DIR}/sol.h5 -ts_monitor_solution hdf5:${PETSC_DIR}/sol.h5::append 559 suffix: egads_sphere 560 requires: egads ctetgen 561 args: -sol_type quadratic_linear \ 562 -dm_plex_boundary_filename ${wPETSC_DIR}/share/petsc/datafiles/meshes/unit_sphere.egadslite -dm_plex_boundary_label marker -bd_dm_plex_scale 40 \ 563 -temp_petscspace_degree 2 -dmts_check .0001 \ 564 -ts_type beuler -ts_max_steps 5 -ts_dt 0.1 -snes_error_if_not_converged -pc_type lu 565 566 TEST*/ 567