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