xref: /petsc/src/ts/tutorials/ex45.c (revision d547623e237931bedb17b336da7d6656fbea55a4)
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, NUM_SOLUTION_TYPES} SolutionType;
17 const char *solutionTypes[NUM_SOLUTION_TYPES+1] = {"quadratic_linear", "quadratic_trig", "trig_linear", "unknown"};
18 
19 typedef struct {
20   char         filename[PETSC_MAX_PATH_LEN];   /* Mesh filename */
21   char         bdfilename[PETSC_MAX_PATH_LEN]; /* Mesh boundary filename */
22   PetscReal    scale;                          /* Scale factor for mesh */
23   SolutionType solType;                        /* Type of exact solution */
24 } AppCtx;
25 
26 /*
27 Exact 2D solution:
28   u = 2t + x^2 + y^2
29   F(u) = 2 - (2 + 2) + 2 = 0
30 
31 Exact 3D solution:
32   u = 3t + x^2 + y^2 + z^2
33   F(u) = 3 - (2 + 2 + 2) + 3 = 0
34 */
35 static PetscErrorCode mms_quad_lin(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nc, PetscScalar *u, void *ctx)
36 {
37   PetscInt d;
38 
39   *u = dim*time;
40   for (d = 0; d < dim; ++d) *u += x[d]*x[d];
41   return 0;
42 }
43 
44 static PetscErrorCode mms_quad_lin_t(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nc, PetscScalar *u, void *ctx)
45 {
46   *u = dim;
47   return 0;
48 }
49 
50 static void f0_quad_lin(PetscInt dim, PetscInt Nf, PetscInt NfAux,
51                         const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
52                         const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
53                         PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f0[])
54 {
55   f0[0] = u_t[0] + (PetscScalar) dim;
56 }
57 
58 /*
59 Exact 2D solution:
60   u = 2*cos(t) + x^2 + y^2
61   F(u) = -2*sint(t) - (2 + 2) + 2*sin(t) + 4 = 0
62 
63 Exact 3D solution:
64   u = 3*cos(t) + x^2 + y^2 + z^2
65   F(u) = -3*sin(t) - (2 + 2 + 2) + 3*sin(t) + 6 = 0
66 */
67 static PetscErrorCode mms_quad_trig(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nc, PetscScalar *u, void *ctx)
68 {
69   PetscInt d;
70 
71   *u = dim*PetscCosReal(time);
72   for (d = 0; d < dim; ++d) *u += x[d]*x[d];
73   return 0;
74 }
75 
76 static PetscErrorCode mms_quad_trig_t(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nc, PetscScalar *u, void *ctx)
77 {
78   *u = -dim*PetscSinReal(time);
79   return 0;
80 }
81 
82 static void f0_quad_trig(PetscInt dim, PetscInt Nf, PetscInt NfAux,
83                          const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
84                          const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
85                          PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f0[])
86 {
87   f0[0] = u_t[0] + dim*(PetscSinReal(t) + 2.0);
88 }
89 
90 /*
91 Exact 2D solution:
92   u = 2\pi^2 t + cos(\pi x) + cos(\pi y)
93   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
94 
95 Exact 3D solution:
96   u = 3\pi^2 t + cos(\pi x) + cos(\pi y) + cos(\pi z)
97   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
98 */
99 static PetscErrorCode mms_trig_lin(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nc, PetscScalar *u, void *ctx)
100 {
101   PetscInt d;
102 
103   *u = dim*PetscSqr(PETSC_PI)*time;
104   for (d = 0; d < dim; ++d) *u += PetscCosReal(PETSC_PI*x[d]);
105   return 0;
106 }
107 
108 static PetscErrorCode mms_trig_lin_t(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nc, PetscScalar *u, void *ctx)
109 {
110   *u = dim*PetscSqr(PETSC_PI);
111   return 0;
112 }
113 
114 static void f0_trig_lin(PetscInt dim, PetscInt Nf, PetscInt NfAux,
115                         const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
116                         const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
117                         PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f0[])
118 {
119   PetscInt d;
120   f0[0] = u_t[0];
121   for (d = 0; d < dim; ++d) f0[0] += PetscSqr(PETSC_PI)*(PetscCosReal(PETSC_PI*x[d]) - 1.0);
122 }
123 
124 static void f1_temp(PetscInt dim, PetscInt Nf, PetscInt NfAux,
125                     const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
126                     const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
127                     PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f1[])
128 {
129   PetscInt d;
130   for (d = 0; d < dim; ++d) f1[d] = u_x[d];
131 }
132 
133 static void g3_temp(PetscInt dim, PetscInt Nf, PetscInt NfAux,
134                     const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
135                     const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
136                     PetscReal t, PetscReal u_tShift, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar g3[])
137 {
138   PetscInt d;
139   for (d = 0; d < dim; ++d) g3[d*dim+d] = 1.0;
140 }
141 
142 static void g0_temp(PetscInt dim, PetscInt Nf, PetscInt NfAux,
143                     const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
144                     const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
145                     PetscReal t, PetscReal u_tShift, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar g0[])
146 {
147   g0[0] = u_tShift*1.0;
148 }
149 
150 static PetscErrorCode ProcessOptions(MPI_Comm comm, AppCtx *options)
151 {
152   PetscInt       sol;
153   PetscErrorCode ierr;
154 
155   PetscFunctionBeginUser;
156   options->filename[0]   = '\0';
157   options->bdfilename[0] = '\0';
158   options->scale         = 0.0;
159   options->solType       = SOL_QUADRATIC_LINEAR;
160 
161   ierr = PetscOptionsBegin(comm, "", "Heat Equation Options", "DMPLEX");CHKERRQ(ierr);
162   ierr = PetscOptionsString("-filename", "The mesh file", "ex45.c", options->filename, options->filename, PETSC_MAX_PATH_LEN, NULL);CHKERRQ(ierr);
163   ierr = PetscOptionsString("-bd_filename", "The mesh boundary file", "ex45.c", options->bdfilename, options->bdfilename, PETSC_MAX_PATH_LEN, NULL);CHKERRQ(ierr);
164   ierr = PetscOptionsReal("-scale", "Scale factor for the mesh", "ex45.c", options->scale, &options->scale, NULL);CHKERRQ(ierr);
165   sol  = options->solType;
166   ierr = PetscOptionsEList("-sol_type", "Type of exact solution", "ex45.c", solutionTypes, NUM_SOLUTION_TYPES, solutionTypes[options->solType], &sol, NULL);CHKERRQ(ierr);
167   options->solType = (SolutionType) sol;
168   ierr = PetscOptionsEnd();CHKERRQ(ierr);
169   PetscFunctionReturn(0);
170 }
171 
172 static PetscErrorCode CreateBCLabel(DM dm, const char name[])
173 {
174   DM             plex;
175   DMLabel        label;
176   PetscBool      hasLabel;
177   PetscErrorCode ierr;
178 
179   PetscFunctionBeginUser;
180   ierr = DMHasLabel(dm, name, &hasLabel);CHKERRQ(ierr);
181   if (hasLabel) PetscFunctionReturn(0);
182   ierr = DMCreateLabel(dm, name);CHKERRQ(ierr);
183   ierr = DMGetLabel(dm, name, &label);CHKERRQ(ierr);
184   ierr = DMConvert(dm, DMPLEX, &plex);CHKERRQ(ierr);
185   ierr = DMPlexMarkBoundaryFaces(plex, 1, label);CHKERRQ(ierr);
186   ierr = DMDestroy(&plex);CHKERRQ(ierr);
187   PetscFunctionReturn(0);
188 }
189 
190 static PetscErrorCode CreateMesh(MPI_Comm comm, DM *dm, AppCtx *ctx)
191 {
192   size_t         len, lenbd;
193   PetscErrorCode ierr;
194 
195   PetscFunctionBeginUser;
196   ierr = PetscStrlen(ctx->filename,   &len);CHKERRQ(ierr);
197   ierr = PetscStrlen(ctx->bdfilename, &lenbd);CHKERRQ(ierr);
198   if (lenbd) {
199     DM bdm;
200 
201     ierr = DMPlexCreateFromFile(comm, ctx->bdfilename, PETSC_TRUE, &bdm);CHKERRQ(ierr);
202     ierr = PetscObjectSetOptionsPrefix((PetscObject) bdm, "bd_");CHKERRQ(ierr);
203     ierr = DMSetFromOptions(bdm);CHKERRQ(ierr);
204     if (ctx->scale != 0.0) {
205       Vec coordinates, coordinatesLocal;
206 
207       ierr = DMGetCoordinates(bdm, &coordinates);CHKERRQ(ierr);
208       ierr = DMGetCoordinatesLocal(bdm, &coordinatesLocal);CHKERRQ(ierr);
209       ierr = VecScale(coordinates, ctx->scale);CHKERRQ(ierr);
210       ierr = VecScale(coordinatesLocal, ctx->scale);CHKERRQ(ierr);
211     }
212     ierr = DMViewFromOptions(bdm, NULL, "-dm_view");CHKERRQ(ierr);
213     ierr = DMPlexGenerate(bdm, NULL, PETSC_TRUE, dm);CHKERRQ(ierr);
214     ierr = DMDestroy(&bdm);CHKERRQ(ierr);
215   } else if (len) {
216     ierr = DMPlexCreateFromFile(comm, ctx->filename, PETSC_TRUE, dm);CHKERRQ(ierr);
217   } else {
218     ierr = DMPlexCreateBoxMesh(comm, 2, PETSC_TRUE, NULL, NULL, NULL, NULL, PETSC_TRUE, dm);CHKERRQ(ierr);
219   }
220   ierr = DMSetFromOptions(*dm);CHKERRQ(ierr);
221   ierr = PetscObjectSetName((PetscObject) *dm, "Mesh");CHKERRQ(ierr);
222   ierr = CreateBCLabel(*dm, "marker");CHKERRQ(ierr);
223   ierr = DMViewFromOptions(*dm, NULL, "-dm_view");CHKERRQ(ierr);
224   PetscFunctionReturn(0);
225 }
226 
227 static PetscErrorCode SetupProblem(DM dm, AppCtx *ctx)
228 {
229   PetscDS        ds;
230   DMLabel        label;
231   const PetscInt id = 1;
232   PetscErrorCode ierr;
233 
234   PetscFunctionBeginUser;
235   ierr = DMGetLabel(dm, "marker", &label);CHKERRQ(ierr);
236   ierr = DMGetDS(dm, &ds);CHKERRQ(ierr);
237   ierr = PetscDSSetJacobian(ds, 0, 0, g0_temp, NULL, NULL, g3_temp);CHKERRQ(ierr);
238   switch (ctx->solType) {
239     case SOL_QUADRATIC_LINEAR:
240       ierr = PetscDSSetResidual(ds, 0, f0_quad_lin,  f1_temp);CHKERRQ(ierr);
241       ierr = PetscDSSetExactSolution(ds, 0, mms_quad_lin, ctx);CHKERRQ(ierr);
242       ierr = PetscDSSetExactSolutionTimeDerivative(ds, 0, mms_quad_lin_t, ctx);CHKERRQ(ierr);
243       ierr = 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);CHKERRQ(ierr);
244       break;
245     case SOL_QUADRATIC_TRIG:
246       ierr = PetscDSSetResidual(ds, 0, f0_quad_trig, f1_temp);CHKERRQ(ierr);
247       ierr = PetscDSSetExactSolution(ds, 0, mms_quad_trig, ctx);CHKERRQ(ierr);
248       ierr = PetscDSSetExactSolutionTimeDerivative(ds, 0, mms_quad_trig_t, ctx);CHKERRQ(ierr);
249       ierr = 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);CHKERRQ(ierr);
250       break;
251     case SOL_TRIG_LINEAR:
252       ierr = PetscDSSetResidual(ds, 0, f0_trig_lin,  f1_temp);CHKERRQ(ierr);
253       ierr = PetscDSSetExactSolution(ds, 0, mms_trig_lin, ctx);CHKERRQ(ierr);
254       ierr = PetscDSSetExactSolutionTimeDerivative(ds, 0, mms_trig_lin_t, ctx);CHKERRQ(ierr);
255       ierr = 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);CHKERRQ(ierr);
256       break;
257     default: SETERRQ2(PetscObjectComm((PetscObject) dm), PETSC_ERR_ARG_WRONG, "Invalid solution type: %s (%D)", solutionTypes[PetscMin(ctx->solType, NUM_SOLUTION_TYPES)], ctx->solType);
258   }
259   PetscFunctionReturn(0);
260 }
261 
262 static PetscErrorCode SetupDiscretization(DM dm, AppCtx* ctx)
263 {
264   DM             cdm = dm;
265   PetscFE        fe;
266   DMPolytopeType ct;
267   PetscBool      simplex;
268   PetscInt       dim, cStart;
269   PetscErrorCode ierr;
270 
271   PetscFunctionBeginUser;
272   ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
273   ierr = DMPlexGetHeightStratum(dm, 0, &cStart, NULL);CHKERRQ(ierr);
274   ierr = DMPlexGetCellType(dm, cStart, &ct);CHKERRQ(ierr);
275   simplex = DMPolytopeTypeGetNumVertices(ct) == DMPolytopeTypeGetDim(ct)+1 ? PETSC_TRUE : PETSC_FALSE;
276   /* Create finite element */
277   ierr = PetscFECreateDefault(PETSC_COMM_SELF, dim, 1, simplex, "temp_", -1, &fe);CHKERRQ(ierr);
278   ierr = PetscObjectSetName((PetscObject) fe, "temperature");CHKERRQ(ierr);
279   /* Set discretization and boundary conditions for each mesh */
280   ierr = DMSetField(dm, 0, NULL, (PetscObject) fe);CHKERRQ(ierr);
281   ierr = DMCreateDS(dm);CHKERRQ(ierr);
282   ierr = SetupProblem(dm, ctx);CHKERRQ(ierr);
283   while (cdm) {
284     ierr = CreateBCLabel(cdm, "marker");CHKERRQ(ierr);
285     ierr = DMCopyDisc(dm, cdm);CHKERRQ(ierr);
286     ierr = DMGetCoarseDM(cdm, &cdm);CHKERRQ(ierr);
287   }
288   ierr = PetscFEDestroy(&fe);CHKERRQ(ierr);
289   PetscFunctionReturn(0);
290 }
291 
292 static PetscErrorCode SetInitialConditions(TS ts, Vec u)
293 {
294   DM             dm;
295   PetscReal      t;
296   PetscErrorCode ierr;
297 
298   PetscFunctionBegin;
299   ierr = TSGetDM(ts, &dm);CHKERRQ(ierr);
300   ierr = TSGetTime(ts, &t);CHKERRQ(ierr);
301   ierr = DMComputeExactSolution(dm, t, u, NULL);CHKERRQ(ierr);
302   PetscFunctionReturn(0);
303 }
304 
305 int main(int argc, char **argv)
306 {
307   DM             dm;
308   TS             ts;
309   Vec            u;
310   AppCtx         ctx;
311   PetscErrorCode ierr;
312 
313   ierr = PetscInitialize(&argc, &argv, NULL, help);if (ierr) return ierr;
314   ierr = ProcessOptions(PETSC_COMM_WORLD, &ctx);CHKERRQ(ierr);
315   ierr = CreateMesh(PETSC_COMM_WORLD, &dm, &ctx);CHKERRQ(ierr);
316   ierr = DMSetApplicationContext(dm, &ctx);CHKERRQ(ierr);
317   ierr = SetupDiscretization(dm, &ctx);CHKERRQ(ierr);
318 
319   ierr = TSCreate(PETSC_COMM_WORLD, &ts);CHKERRQ(ierr);
320   ierr = TSSetDM(ts, dm);CHKERRQ(ierr);
321   ierr = DMTSSetBoundaryLocal(dm, DMPlexTSComputeBoundary, &ctx);CHKERRQ(ierr);
322   ierr = DMTSSetIFunctionLocal(dm, DMPlexTSComputeIFunctionFEM, &ctx);CHKERRQ(ierr);
323   ierr = DMTSSetIJacobianLocal(dm, DMPlexTSComputeIJacobianFEM, &ctx);CHKERRQ(ierr);
324   ierr = TSSetExactFinalTime(ts, TS_EXACTFINALTIME_MATCHSTEP);CHKERRQ(ierr);
325   ierr = TSSetFromOptions(ts);CHKERRQ(ierr);
326   ierr = TSSetComputeInitialCondition(ts, SetInitialConditions);CHKERRQ(ierr);
327 
328   ierr = DMCreateGlobalVector(dm, &u);CHKERRQ(ierr);
329   ierr = DMTSCheckFromOptions(ts, u);CHKERRQ(ierr);
330   ierr = SetInitialConditions(ts, u);CHKERRQ(ierr);
331   ierr = PetscObjectSetName((PetscObject) u, "temperature");CHKERRQ(ierr);
332   ierr = TSSolve(ts, u);CHKERRQ(ierr);
333   ierr = DMTSCheckFromOptions(ts, u);CHKERRQ(ierr);
334 
335   ierr = VecDestroy(&u);CHKERRQ(ierr);
336   ierr = TSDestroy(&ts);CHKERRQ(ierr);
337   ierr = DMDestroy(&dm);CHKERRQ(ierr);
338   ierr = PetscFinalize();
339   return ierr;
340 }
341 
342 /*TEST
343 
344   test:
345     suffix: 2d_p1
346     requires: triangle
347     args: -sol_type quadratic_linear -dm_refine 1 -temp_petscspace_degree 1 -dmts_check .0001 \
348           -ts_type beuler -ts_max_steps 5 -ts_dt 0.1 -snes_error_if_not_converged -pc_type lu
349   test:
350     # -dm_refine 2 -convest_num_refine 3 get L_2 convergence rate: [1.9]
351     suffix: 2d_p1_sconv
352     requires: triangle
353     args: -sol_type quadratic_linear -temp_petscspace_degree 1 -ts_convergence_estimate -ts_convergence_temporal 0 -convest_num_refine 1 \
354           -ts_type beuler -ts_max_steps 1 -ts_dt 0.00001 -snes_error_if_not_converged -pc_type lu
355   test:
356     # -dm_refine 4 -convest_num_refine 3 get L_2 convergence rate: [1.2]
357     suffix: 2d_p1_tconv
358     requires: triangle
359     args: -sol_type quadratic_trig -temp_petscspace_degree 1 -ts_convergence_estimate -convest_num_refine 1 \
360           -ts_type beuler -ts_max_steps 4 -ts_dt 0.1 -snes_error_if_not_converged -pc_type lu
361   test:
362     suffix: 2d_p2
363     requires: triangle
364     args: -sol_type quadratic_linear -dm_refine 0 -temp_petscspace_degree 2 -dmts_check .0001 \
365           -ts_type beuler -ts_max_steps 5 -ts_dt 0.1 -snes_error_if_not_converged -pc_type lu
366   test:
367     # -dm_refine 2 -convest_num_refine 3 get L_2 convergence rate: [2.9]
368     suffix: 2d_p2_sconv
369     requires: triangle
370     args: -sol_type trig_linear -temp_petscspace_degree 2 -ts_convergence_estimate -ts_convergence_temporal 0 -convest_num_refine 1 \
371           -ts_type beuler -ts_max_steps 1 -ts_dt 0.00000001 -snes_error_if_not_converged -pc_type lu
372   test:
373     # -dm_refine 3 -convest_num_refine 3 get L_2 convergence rate: [1.0]
374     suffix: 2d_p2_tconv
375     requires: triangle
376     args: -sol_type quadratic_trig -temp_petscspace_degree 2 -ts_convergence_estimate -convest_num_refine 1 \
377           -ts_type beuler -ts_max_steps 4 -ts_dt 0.1 -snes_error_if_not_converged -pc_type lu
378   test:
379     suffix: 2d_q1
380     args: -sol_type quadratic_linear -dm_plex_box_simplex 0 -dm_refine 1 -temp_petscspace_degree 1 -dmts_check .0001 \
381           -ts_type beuler -ts_max_steps 5 -ts_dt 0.1 -snes_error_if_not_converged -pc_type lu
382   test:
383     # -dm_refine 2 -convest_num_refine 3 get L_2 convergence rate: [1.9]
384     suffix: 2d_q1_sconv
385     args: -sol_type quadratic_linear -dm_plex_box_simplex 0 -temp_petscspace_degree 1 -ts_convergence_estimate -ts_convergence_temporal 0 -convest_num_refine 1 \
386           -ts_type beuler -ts_max_steps 1 -ts_dt 0.00001 -snes_error_if_not_converged -pc_type lu
387   test:
388     # -dm_refine 4 -convest_num_refine 3 get L_2 convergence rate: [1.2]
389     suffix: 2d_q1_tconv
390     args: -sol_type quadratic_trig -dm_plex_box_simplex 0 -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     suffix: 2d_q2
394     args: -sol_type quadratic_linear -dm_plex_box_simplex 0 -dm_refine 0 -temp_petscspace_degree 2 -dmts_check .0001 \
395           -ts_type beuler -ts_max_steps 5 -ts_dt 0.1 -snes_error_if_not_converged -pc_type lu
396   test:
397     # -dm_refine 2 -convest_num_refine 3 get L_2 convergence rate: [2.9]
398     suffix: 2d_q2_sconv
399     args: -sol_type trig_linear -dm_plex_box_simplex 0 -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_q2_tconv
404     args: -sol_type quadratic_trig -dm_plex_box_simplex 0 -temp_petscspace_degree 2 -ts_convergence_estimate -convest_num_refine 1 \
405           -ts_type beuler -ts_max_steps 4 -ts_dt 0.1 -snes_error_if_not_converged -pc_type lu
406 
407   test:
408     suffix: 3d_p1
409     requires: ctetgen
410     args: -sol_type quadratic_linear -dm_refine 1 -temp_petscspace_degree 1 -dmts_check .0001 \
411           -ts_type beuler -ts_max_steps 5 -ts_dt 0.1 -snes_error_if_not_converged -pc_type lu
412   test:
413     # -dm_refine 2 -convest_num_refine 3 get L_2 convergence rate: [1.9]
414     suffix: 3d_p1_sconv
415     requires: ctetgen
416     args: -sol_type quadratic_linear -temp_petscspace_degree 1 -ts_convergence_estimate -ts_convergence_temporal 0 -convest_num_refine 1 \
417           -ts_type beuler -ts_max_steps 1 -ts_dt 0.00001 -snes_error_if_not_converged -pc_type lu
418   test:
419     # -dm_refine 4 -convest_num_refine 3 get L_2 convergence rate: [1.2]
420     suffix: 3d_p1_tconv
421     requires: ctetgen
422     args: -sol_type quadratic_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     suffix: 3d_p2
426     requires: ctetgen
427     args: -sol_type quadratic_linear -dm_refine 0 -temp_petscspace_degree 2 -dmts_check .0001 \
428           -ts_type beuler -ts_max_steps 5 -ts_dt 0.1 -snes_error_if_not_converged -pc_type lu
429   test:
430     # -dm_refine 2 -convest_num_refine 3 get L_2 convergence rate: [2.9]
431     suffix: 3d_p2_sconv
432     requires: ctetgen
433     args: -sol_type trig_linear -temp_petscspace_degree 2 -ts_convergence_estimate -ts_convergence_temporal 0 -convest_num_refine 1 \
434           -ts_type beuler -ts_max_steps 1 -ts_dt 0.00000001 -snes_error_if_not_converged -pc_type lu
435   test:
436     # -dm_refine 3 -convest_num_refine 3 get L_2 convergence rate: [1.0]
437     suffix: 3d_p2_tconv
438     requires: ctetgen
439     args: -sol_type quadratic_trig -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   test:
442     suffix: 3d_q1
443     args: -sol_type quadratic_linear -dm_plex_box_simplex 0 -dm_refine 1 -temp_petscspace_degree 1 -dmts_check .0001 \
444           -ts_type beuler -ts_max_steps 5 -ts_dt 0.1 -snes_error_if_not_converged -pc_type lu
445   test:
446     # -dm_refine 2 -convest_num_refine 3 get L_2 convergence rate: [1.9]
447     suffix: 3d_q1_sconv
448     args: -sol_type quadratic_linear -dm_plex_box_simplex 0 -temp_petscspace_degree 1 -ts_convergence_estimate -ts_convergence_temporal 0 -convest_num_refine 1 \
449           -ts_type beuler -ts_max_steps 1 -ts_dt 0.00001 -snes_error_if_not_converged -pc_type lu
450   test:
451     # -dm_refine 4 -convest_num_refine 3 get L_2 convergence rate: [1.2]
452     suffix: 3d_q1_tconv
453     args: -sol_type quadratic_trig -dm_plex_box_simplex 0 -temp_petscspace_degree 1 -ts_convergence_estimate -convest_num_refine 1 \
454           -ts_type beuler -ts_max_steps 4 -ts_dt 0.1 -snes_error_if_not_converged -pc_type lu
455   test:
456     suffix: 3d_q2
457     args: -sol_type quadratic_linear -dm_plex_box_simplex 0 -dm_refine 0 -temp_petscspace_degree 2 -dmts_check .0001 \
458           -ts_type beuler -ts_max_steps 5 -ts_dt 0.1 -snes_error_if_not_converged -pc_type lu
459   test:
460     # -dm_refine 2 -convest_num_refine 3 get L_2 convergence rate: [2.9]
461     suffix: 3d_q2_sconv
462     args: -sol_type trig_linear -dm_plex_box_simplex 0 -temp_petscspace_degree 2 -ts_convergence_estimate -ts_convergence_temporal 0 -convest_num_refine 1 \
463           -ts_type beuler -ts_max_steps 1 -ts_dt 0.00000001 -snes_error_if_not_converged -pc_type lu
464   test:
465     # -dm_refine 3 -convest_num_refine 3 get L_2 convergence rate: [1.0]
466     suffix: 3d_q2_tconv
467     args: -sol_type quadratic_trig -dm_plex_box_simplex 0 -temp_petscspace_degree 2 -ts_convergence_estimate -convest_num_refine 1 \
468           -ts_type beuler -ts_max_steps 4 -ts_dt 0.1 -snes_error_if_not_converged -pc_type lu
469 
470   test:
471     # 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
472     suffix: egads_sphere
473     requires: egads ctetgen
474     args: -sol_type quadratic_linear -bd_filename ${wPETSC_DIR}/share/petsc/datafiles/meshes/unit_sphere.egadslite -scale 40 \
475           -temp_petscspace_degree 2 -dmts_check .0001 \
476           -ts_type beuler -ts_max_steps 5 -ts_dt 0.1 -snes_error_if_not_converged -pc_type lu
477 
478 TEST*/
479