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