Actual source code: ex62.c
petsc-3.7.5 2017-01-01
1: static char help[] = "Stokes Problem in 2d and 3d with simplicial finite elements.\n\
2: We solve the Stokes problem in a rectangular\n\
3: domain, using a parallel unstructured mesh (DMPLEX) to discretize it.\n\n\n";
5: /*
6: The isoviscous Stokes problem, which we discretize using the finite
7: element method on an unstructured mesh. The weak form equations are
9: < \nabla v, \nabla u + {\nabla u}^T > - < \nabla\cdot v, p > + < v, f > = 0
10: < q, \nabla\cdot u > = 0
12: We start with homogeneous Dirichlet conditions. We will expand this as the set
13: of test problems is developed.
15: Discretization:
17: We use PetscFE to generate a tabulation of the finite element basis functions
18: at quadrature points. We can currently generate an arbitrary order Lagrange
19: element.
21: Field Data:
23: DMPLEX data is organized by point, and the closure operation just stacks up the
24: data from each sieve point in the closure. Thus, for a P_2-P_1 Stokes element, we
25: have
27: cl{e} = {f e_0 e_1 e_2 v_0 v_1 v_2}
28: x = [u_{e_0} v_{e_0} u_{e_1} v_{e_1} u_{e_2} v_{e_2} u_{v_0} v_{v_0} p_{v_0} u_{v_1} v_{v_1} p_{v_1} u_{v_2} v_{v_2} p_{v_2}]
30: The problem here is that we would like to loop over each field separately for
31: integration. Therefore, the closure visitor in DMPlexVecGetClosure() reorders
32: the data so that each field is contiguous
34: x' = [u_{e_0} v_{e_0} u_{e_1} v_{e_1} u_{e_2} v_{e_2} u_{v_0} v_{v_0} u_{v_1} v_{v_1} u_{v_2} v_{v_2} p_{v_0} p_{v_1} p_{v_2}]
36: Likewise, DMPlexVecSetClosure() takes data partitioned by field, and correctly
37: puts it into the Sieve ordering.
39: Next Steps:
41: - Refine and show convergence of correct order automatically (use femTest.py)
42: - Fix InitialGuess for arbitrary disc (means making dual application work again)
43: - Redo slides from GUCASTutorial for this new example
45: For tensor product meshes, see SNES ex67, ex72
46: */
48: #include <petscdmplex.h>
49: #include <petscsnes.h>
50: #include <petscds.h>
52: PetscInt spatialDim = 0;
54: typedef enum {NEUMANN, DIRICHLET} BCType;
55: typedef enum {RUN_FULL, RUN_TEST} RunType;
57: typedef struct {
58: PetscInt debug; /* The debugging level */
59: RunType runType; /* Whether to run tests, or solve the full problem */
60: PetscLogEvent createMeshEvent;
61: PetscBool showInitial, showSolution, showError;
62: /* Domain and mesh definition */
63: PetscInt dim; /* The topological mesh dimension */
64: PetscBool interpolate; /* Generate intermediate mesh elements */
65: PetscBool simplex; /* Use simplices or tensor product cells */
66: PetscReal refinementLimit; /* The largest allowable cell volume */
67: PetscBool testPartition; /* Use a fixed partitioning for testing */
68: /* Problem definition */
69: BCType bcType;
70: PetscErrorCode (**exactFuncs)(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nf, PetscScalar *u, void *ctx);
71: } AppCtx;
73: PetscErrorCode zero_scalar(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nf, PetscScalar *u, void *ctx)
74: {
75: u[0] = 0.0;
76: return 0;
77: }
78: PetscErrorCode zero_vector(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nf, PetscScalar *u, void *ctx)
79: {
80: PetscInt d;
81: for (d = 0; d < spatialDim; ++d) u[d] = 0.0;
82: return 0;
83: }
85: /*
86: In 2D we use exact solution:
88: u = x^2 + y^2
89: v = 2 x^2 - 2xy
90: p = x + y - 1
91: f_x = f_y = 3
93: so that
95: -\Delta u + \nabla p + f = <-4, -4> + <1, 1> + <3, 3> = 0
96: \nabla \cdot u = 2x - 2x = 0
97: */
98: PetscErrorCode quadratic_u_2d(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nf, PetscScalar *u, void *ctx)
99: {
100: u[0] = x[0]*x[0] + x[1]*x[1];
101: u[1] = 2.0*x[0]*x[0] - 2.0*x[0]*x[1];
102: return 0;
103: }
105: PetscErrorCode linear_p_2d(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nf, PetscScalar *p, void *ctx)
106: {
107: *p = x[0] + x[1] - 1.0;
108: return 0;
109: }
110: PetscErrorCode constant_p(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nf, PetscScalar *p, void *ctx)
111: {
112: *p = 1.0;
113: return 0;
114: }
116: void f0_u(PetscInt dim, PetscInt Nf, PetscInt NfAux,
117: const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
118: const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
119: PetscReal t, const PetscReal x[], PetscScalar f0[])
120: {
121: PetscInt c;
122: for (c = 0; c < dim; ++c) f0[c] = 3.0;
123: }
125: /* gradU[comp*dim+d] = {u_x, u_y, v_x, v_y} or {u_x, u_y, u_z, v_x, v_y, v_z, w_x, w_y, w_z}
126: u[Ncomp] = {p} */
127: void f1_u(PetscInt dim, PetscInt Nf, PetscInt NfAux,
128: const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
129: const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
130: PetscReal t, const PetscReal x[], PetscScalar f1[])
131: {
132: const PetscInt Ncomp = dim;
133: PetscInt comp, d;
135: for (comp = 0; comp < Ncomp; ++comp) {
136: for (d = 0; d < dim; ++d) {
137: /* f1[comp*dim+d] = 0.5*(gradU[comp*dim+d] + gradU[d*dim+comp]); */
138: f1[comp*dim+d] = u_x[comp*dim+d];
139: }
140: f1[comp*dim+comp] -= u[Ncomp];
141: }
142: }
144: /* gradU[comp*dim+d] = {u_x, u_y, v_x, v_y} or {u_x, u_y, u_z, v_x, v_y, v_z, w_x, w_y, w_z} */
145: void f0_p(PetscInt dim, PetscInt Nf, PetscInt NfAux,
146: const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
147: const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
148: PetscReal t, const PetscReal x[], PetscScalar f0[])
149: {
150: PetscInt d;
151: for (d = 0, f0[0] = 0.0; d < dim; ++d) f0[0] += u_x[d*dim+d];
152: }
154: void f1_p(PetscInt dim, PetscInt Nf, PetscInt NfAux,
155: const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
156: const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
157: PetscReal t, const PetscReal x[], PetscScalar f1[])
158: {
159: PetscInt d;
160: for (d = 0; d < dim; ++d) f1[d] = 0.0;
161: }
163: /* < q, \nabla\cdot u >
164: NcompI = 1, NcompJ = dim */
165: void g1_pu(PetscInt dim, PetscInt Nf, PetscInt NfAux,
166: const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
167: const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
168: PetscReal t, PetscReal u_tShift, const PetscReal x[], PetscScalar g1[])
169: {
170: PetscInt d;
171: for (d = 0; d < dim; ++d) g1[d*dim+d] = 1.0; /* \frac{\partial\phi^{u_d}}{\partial x_d} */
172: }
174: /* -< \nabla\cdot v, p >
175: NcompI = dim, NcompJ = 1 */
176: void g2_up(PetscInt dim, PetscInt Nf, PetscInt NfAux,
177: const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
178: const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
179: PetscReal t, PetscReal u_tShift, const PetscReal x[], PetscScalar g2[])
180: {
181: PetscInt d;
182: for (d = 0; d < dim; ++d) g2[d*dim+d] = -1.0; /* \frac{\partial\psi^{u_d}}{\partial x_d} */
183: }
185: /* < \nabla v, \nabla u + {\nabla u}^T >
186: This just gives \nabla u, give the perdiagonal for the transpose */
187: void g3_uu(PetscInt dim, PetscInt Nf, PetscInt NfAux,
188: const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
189: const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
190: PetscReal t, PetscReal u_tShift, const PetscReal x[], PetscScalar g3[])
191: {
192: const PetscInt Ncomp = dim;
193: PetscInt compI, d;
195: for (compI = 0; compI < Ncomp; ++compI) {
196: for (d = 0; d < dim; ++d) {
197: g3[((compI*Ncomp+compI)*dim+d)*dim+d] = 1.0;
198: }
199: }
200: }
202: /*
203: In 3D we use exact solution:
205: u = x^2 + y^2
206: v = y^2 + z^2
207: w = x^2 + y^2 - 2(x+y)z
208: p = x + y + z - 3/2
209: f_x = f_y = f_z = 3
211: so that
213: -\Delta u + \nabla p + f = <-4, -4, -4> + <1, 1, 1> + <3, 3, 3> = 0
214: \nabla \cdot u = 2x + 2y - 2(x + y) = 0
215: */
216: PetscErrorCode quadratic_u_3d(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nf, PetscScalar *u, void *ctx)
217: {
218: u[0] = x[0]*x[0] + x[1]*x[1];
219: u[1] = x[1]*x[1] + x[2]*x[2];
220: u[2] = x[0]*x[0] + x[1]*x[1] - 2.0*(x[0] + x[1])*x[2];
221: return 0;
222: }
224: PetscErrorCode linear_p_3d(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nf, PetscScalar *p, void *ctx)
225: {
226: *p = x[0] + x[1] + x[2] - 1.5;
227: return 0;
228: }
232: PetscErrorCode ProcessOptions(MPI_Comm comm, AppCtx *options)
233: {
234: const char *bcTypes[2] = {"neumann", "dirichlet"};
235: const char *runTypes[2] = {"full", "test"};
236: PetscInt bc, run;
240: options->debug = 0;
241: options->runType = RUN_FULL;
242: options->dim = 2;
243: options->interpolate = PETSC_FALSE;
244: options->simplex = PETSC_TRUE;
245: options->refinementLimit = 0.0;
246: options->testPartition = PETSC_FALSE;
247: options->bcType = DIRICHLET;
248: options->showInitial = PETSC_FALSE;
249: options->showSolution = PETSC_TRUE;
250: options->showError = PETSC_FALSE;
252: PetscOptionsBegin(comm, "", "Stokes Problem Options", "DMPLEX");
253: PetscOptionsInt("-debug", "The debugging level", "ex62.c", options->debug, &options->debug, NULL);
254: run = options->runType;
255: PetscOptionsEList("-run_type", "The run type", "ex62.c", runTypes, 2, runTypes[options->runType], &run, NULL);
257: options->runType = (RunType) run;
259: PetscOptionsInt("-dim", "The topological mesh dimension", "ex62.c", options->dim, &options->dim, NULL);
260: spatialDim = options->dim;
261: PetscOptionsBool("-interpolate", "Generate intermediate mesh elements", "ex62.c", options->interpolate, &options->interpolate, NULL);
262: PetscOptionsBool("-simplex", "Use simplices or tensor product cells", "ex62.c", options->simplex, &options->simplex, NULL);
263: PetscOptionsReal("-refinement_limit", "The largest allowable cell volume", "ex62.c", options->refinementLimit, &options->refinementLimit, NULL);
264: PetscOptionsBool("-test_partition", "Use a fixed partition for testing", "ex62.c", options->testPartition, &options->testPartition, NULL);
265: bc = options->bcType;
266: PetscOptionsEList("-bc_type","Type of boundary condition","ex62.c",bcTypes,2,bcTypes[options->bcType],&bc,NULL);
268: options->bcType = (BCType) bc;
270: PetscOptionsBool("-show_initial", "Output the initial guess for verification", "ex62.c", options->showInitial, &options->showInitial, NULL);
271: PetscOptionsBool("-show_solution", "Output the solution for verification", "ex62.c", options->showSolution, &options->showSolution, NULL);
272: PetscOptionsBool("-show_error", "Output the error for verification", "ex62.c", options->showError, &options->showError, NULL);
273: PetscOptionsEnd();
275: PetscLogEventRegister("CreateMesh", DM_CLASSID, &options->createMeshEvent);
276: return(0);
277: }
281: PetscErrorCode DMVecViewLocal(DM dm, Vec v, PetscViewer viewer)
282: {
283: Vec lv;
284: PetscInt p;
285: PetscMPIInt rank, numProcs;
289: MPI_Comm_rank(PetscObjectComm((PetscObject)dm), &rank);
290: MPI_Comm_size(PetscObjectComm((PetscObject)dm), &numProcs);
291: DMGetLocalVector(dm, &lv);
292: DMGlobalToLocalBegin(dm, v, INSERT_VALUES, lv);
293: DMGlobalToLocalEnd(dm, v, INSERT_VALUES, lv);
294: PetscPrintf(PETSC_COMM_WORLD, "Local function\n");
295: for (p = 0; p < numProcs; ++p) {
296: if (p == rank) {VecView(lv, PETSC_VIEWER_STDOUT_SELF);}
297: PetscBarrier((PetscObject) dm);
298: }
299: DMRestoreLocalVector(dm, &lv);
300: return(0);
301: }
305: PetscErrorCode CreateMesh(MPI_Comm comm, AppCtx *user, DM *dm)
306: {
307: PetscInt dim = user->dim;
308: PetscBool interpolate = user->interpolate;
309: PetscReal refinementLimit = user->refinementLimit;
310: const PetscInt cells[3] = {3, 3, 3};
314: PetscLogEventBegin(user->createMeshEvent,0,0,0,0);
315: if (user->simplex) {DMPlexCreateBoxMesh(comm, dim, interpolate, dm);}
316: else {DMPlexCreateHexBoxMesh(comm, dim, cells, DM_BOUNDARY_NONE, DM_BOUNDARY_NONE, DM_BOUNDARY_NONE, dm);}
317: {
318: DM refinedMesh = NULL;
319: DM distributedMesh = NULL;
321: /* Refine mesh using a volume constraint */
322: DMPlexSetRefinementLimit(*dm, refinementLimit);
323: if (user->simplex) {DMRefine(*dm, comm, &refinedMesh);}
324: if (refinedMesh) {
325: DMDestroy(dm);
326: *dm = refinedMesh;
327: }
328: /* Setup test partitioning */
329: if (user->testPartition) {
330: PetscInt triSizes_n2[2] = {4, 4};
331: PetscInt triPoints_n2[8] = {3, 5, 6, 7, 0, 1, 2, 4};
332: PetscInt triSizes_n3[3] = {2, 3, 3};
333: PetscInt triPoints_n3[8] = {3, 5, 1, 6, 7, 0, 2, 4};
334: PetscInt triSizes_n5[5] = {1, 2, 2, 1, 2};
335: PetscInt triPoints_n5[8] = {3, 5, 6, 4, 7, 0, 1, 2};
336: PetscInt triSizes_ref_n2[2] = {8, 8};
337: PetscInt triPoints_ref_n2[16] = {1, 5, 6, 7, 10, 11, 14, 15, 0, 2, 3, 4, 8, 9, 12, 13};
338: PetscInt triSizes_ref_n3[3] = {5, 6, 5};
339: PetscInt triPoints_ref_n3[16] = {1, 7, 10, 14, 15, 2, 6, 8, 11, 12, 13, 0, 3, 4, 5, 9};
340: PetscInt triSizes_ref_n5[5] = {3, 4, 3, 3, 3};
341: PetscInt triPoints_ref_n5[16] = {1, 7, 10, 2, 11, 13, 14, 5, 6, 15, 0, 8, 9, 3, 4, 12};
342: const PetscInt *sizes = NULL;
343: const PetscInt *points = NULL;
344: PetscPartitioner part;
345: PetscInt cEnd;
346: PetscMPIInt rank, numProcs;
348: MPI_Comm_rank(comm, &rank);
349: MPI_Comm_size(comm, &numProcs);
350: DMPlexGetHeightStratum(*dm, 0, NULL, &cEnd);
351: if (!rank) {
352: if (dim == 2 && user->simplex && numProcs == 2 && cEnd == 8) {
353: sizes = triSizes_n2; points = triPoints_n2;
354: } else if (dim == 2 && user->simplex && numProcs == 3 && cEnd == 8) {
355: sizes = triSizes_n3; points = triPoints_n3;
356: } else if (dim == 2 && user->simplex && numProcs == 5 && cEnd == 8) {
357: sizes = triSizes_n5; points = triPoints_n5;
358: } else if (dim == 2 && user->simplex && numProcs == 2 && cEnd == 16) {
359: sizes = triSizes_ref_n2; points = triPoints_ref_n2;
360: } else if (dim == 2 && user->simplex && numProcs == 3 && cEnd == 16) {
361: sizes = triSizes_ref_n3; points = triPoints_ref_n3;
362: } else if (dim == 2 && user->simplex && numProcs == 5 && cEnd == 16) {
363: sizes = triSizes_ref_n5; points = triPoints_ref_n5;
364: } else SETERRQ(comm, PETSC_ERR_ARG_WRONG, "No stored partition matching run parameters");
365: }
366: DMPlexGetPartitioner(*dm, &part);
367: PetscPartitionerSetType(part, PETSCPARTITIONERSHELL);
368: PetscPartitionerShellSetPartition(part, numProcs, sizes, points);
369: }
370: /* Distribute mesh over processes */
371: DMPlexDistribute(*dm, 0, NULL, &distributedMesh);
372: if (distributedMesh) {
373: DMDestroy(dm);
374: *dm = distributedMesh;
375: }
376: }
377: DMSetFromOptions(*dm);
378: DMViewFromOptions(*dm, NULL, "-dm_view");
379: PetscLogEventEnd(user->createMeshEvent,0,0,0,0);
380: return(0);
381: }
385: PetscErrorCode SetupProblem(DM dm, AppCtx *user)
386: {
387: PetscDS prob;
391: DMGetDS(dm, &prob);
392: PetscDSSetResidual(prob, 0, f0_u, f1_u);
393: PetscDSSetResidual(prob, 1, f0_p, f1_p);
394: PetscDSSetJacobian(prob, 0, 0, NULL, NULL, NULL, g3_uu);
395: PetscDSSetJacobian(prob, 0, 1, NULL, NULL, g2_up, NULL);
396: PetscDSSetJacobian(prob, 1, 0, NULL, g1_pu, NULL, NULL);
397: switch (user->dim) {
398: case 2:
399: user->exactFuncs[0] = quadratic_u_2d;
400: user->exactFuncs[1] = linear_p_2d;
401: break;
402: case 3:
403: user->exactFuncs[0] = quadratic_u_3d;
404: user->exactFuncs[1] = linear_p_3d;
405: break;
406: default:
407: SETERRQ1(PETSC_COMM_WORLD, PETSC_ERR_ARG_OUTOFRANGE, "Invalid dimension %d", user->dim);
408: }
409: return(0);
410: }
414: PetscErrorCode SetupDiscretization(DM dm, AppCtx *user)
415: {
416: DM cdm = dm;
417: const PetscInt dim = user->dim;
418: const PetscInt id = 1;
419: PetscFE fe[2];
420: PetscQuadrature q;
421: PetscDS prob;
422: PetscInt order;
423: PetscErrorCode ierr;
426: /* Create finite element */
427: PetscFECreateDefault(dm, dim, dim, user->simplex, "vel_", -1, &fe[0]);
428: PetscObjectSetName((PetscObject) fe[0], "velocity");
429: PetscFEGetQuadrature(fe[0], &q);
430: PetscQuadratureGetOrder(q, &order);
431: PetscFECreateDefault(dm, dim, 1, user->simplex, "pres_", order, &fe[1]);
432: PetscObjectSetName((PetscObject) fe[1], "pressure");
433: /* Set discretization and boundary conditions for each mesh */
434: while (cdm) {
435: DMGetDS(cdm, &prob);
436: PetscDSSetDiscretization(prob, 0, (PetscObject) fe[0]);
437: PetscDSSetDiscretization(prob, 1, (PetscObject) fe[1]);
438: SetupProblem(cdm, user);
439: DMAddBoundary(cdm, user->bcType == DIRICHLET ? PETSC_TRUE : PETSC_FALSE, "wall", user->bcType == NEUMANN ? "boundary" : "marker", 0, 0, NULL, (void (*)()) user->exactFuncs[0], 1, &id, user);
440: DMGetCoarseDM(cdm, &cdm);
441: }
442: PetscFEDestroy(&fe[0]);
443: PetscFEDestroy(&fe[1]);
444: return(0);
445: }
449: PetscErrorCode CreatePressureNullSpace(DM dm, AppCtx *user, Vec *v, MatNullSpace *nullSpace)
450: {
451: Vec vec;
452: PetscErrorCode (*funcs[2])(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nf, PetscScalar *u, void* ctx) = {zero_vector, constant_p};
453: PetscErrorCode ierr;
456: DMGetGlobalVector(dm, &vec);
457: DMProjectFunction(dm, 0.0, funcs, NULL, INSERT_ALL_VALUES, vec);
458: VecNormalize(vec, NULL);
459: if (user->debug) {
460: PetscPrintf(PetscObjectComm((PetscObject)dm), "Pressure Null Space\n");
461: VecView(vec, PETSC_VIEWER_STDOUT_WORLD);
462: }
463: MatNullSpaceCreate(PetscObjectComm((PetscObject)dm), PETSC_FALSE, 1, &vec, nullSpace);
464: if (v) {
465: DMCreateGlobalVector(dm, v);
466: VecCopy(vec, *v);
467: }
468: DMRestoreGlobalVector(dm, &vec);
469: /* New style for field null spaces */
470: {
471: PetscObject pressure;
472: MatNullSpace nullSpacePres;
474: DMGetField(dm, 1, &pressure);
475: MatNullSpaceCreate(PetscObjectComm(pressure), PETSC_TRUE, 0, NULL, &nullSpacePres);
476: PetscObjectCompose(pressure, "nullspace", (PetscObject) nullSpacePres);
477: MatNullSpaceDestroy(&nullSpacePres);
478: }
479: return(0);
480: }
484: int main(int argc, char **argv)
485: {
486: SNES snes; /* nonlinear solver */
487: DM dm; /* problem definition */
488: Vec u,r; /* solution, residual vectors */
489: Mat A,J; /* Jacobian matrix */
490: MatNullSpace nullSpace; /* May be necessary for pressure */
491: AppCtx user; /* user-defined work context */
492: PetscInt its; /* iterations for convergence */
493: PetscReal error = 0.0; /* L_2 error in the solution */
494: PetscReal ferrors[2];
497: PetscInitialize(&argc, &argv, NULL, help);
498: ProcessOptions(PETSC_COMM_WORLD, &user);
499: SNESCreate(PETSC_COMM_WORLD, &snes);
500: CreateMesh(PETSC_COMM_WORLD, &user, &dm);
501: SNESSetDM(snes, dm);
502: DMSetApplicationContext(dm, &user);
504: PetscMalloc(2 * sizeof(void (*)(const PetscReal[], PetscScalar *, void *)), &user.exactFuncs);
505: SetupDiscretization(dm, &user);
506: DMPlexCreateClosureIndex(dm, NULL);
508: DMCreateGlobalVector(dm, &u);
509: VecDuplicate(u, &r);
511: DMSetMatType(dm,MATAIJ);
512: DMCreateMatrix(dm, &J);
513: A = J;
514: CreatePressureNullSpace(dm, &user, NULL, &nullSpace);
515: MatSetNullSpace(A, nullSpace);
517: DMPlexSetSNESLocalFEM(dm,&user,&user,&user);
518: SNESSetJacobian(snes, A, J, NULL, NULL);
520: SNESSetFromOptions(snes);
522: DMProjectFunction(dm, 0.0, user.exactFuncs, NULL, INSERT_ALL_VALUES, u);
523: if (user.showInitial) {DMVecViewLocal(dm, u, PETSC_VIEWER_STDOUT_SELF);}
524: if (user.runType == RUN_FULL) {
525: PetscErrorCode (*initialGuess[2])(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nf, PetscScalar *u, void* ctx) = {zero_vector, zero_scalar};
527: DMProjectFunction(dm, 0.0, initialGuess, NULL, INSERT_VALUES, u);
528: if (user.debug) {
529: PetscPrintf(PETSC_COMM_WORLD, "Initial guess\n");
530: VecView(u, PETSC_VIEWER_STDOUT_WORLD);
531: }
532: SNESSolve(snes, NULL, u);
533: SNESGetIterationNumber(snes, &its);
534: PetscPrintf(PETSC_COMM_WORLD, "Number of SNES iterations = %D\n", its);
535: DMComputeL2Diff(dm, 0.0, user.exactFuncs, NULL, u, &error);
536: DMComputeL2FieldDiff(dm, 0.0, user.exactFuncs, NULL, u, ferrors);
537: PetscPrintf(PETSC_COMM_WORLD, "L_2 Error: %.3g [%.3g, %.3g]\n", error, ferrors[0], ferrors[1]);
538: if (user.showError) {
539: Vec r;
540: DMGetGlobalVector(dm, &r);
541: DMProjectFunction(dm, 0.0, user.exactFuncs, NULL, INSERT_ALL_VALUES, r);
542: VecAXPY(r, -1.0, u);
543: PetscPrintf(PETSC_COMM_WORLD, "Solution Error\n");
544: VecView(r, PETSC_VIEWER_STDOUT_WORLD);
545: DMRestoreGlobalVector(dm, &r);
546: }
547: if (user.showSolution) {
548: PetscPrintf(PETSC_COMM_WORLD, "Solution\n");
549: VecChop(u, 3.0e-9);
550: VecView(u, PETSC_VIEWER_STDOUT_WORLD);
551: }
552: } else {
553: PetscReal res = 0.0;
555: /* Check discretization error */
556: PetscPrintf(PETSC_COMM_WORLD, "Initial guess\n");
557: VecView(u, PETSC_VIEWER_STDOUT_WORLD);
558: DMComputeL2Diff(dm, 0.0, user.exactFuncs, NULL, u, &error);
559: if (error >= 1.0e-11) {PetscPrintf(PETSC_COMM_WORLD, "L_2 Error: %g\n", error);}
560: else {PetscPrintf(PETSC_COMM_WORLD, "L_2 Error: < 1.0e-11\n");}
561: /* Check residual */
562: SNESComputeFunction(snes, u, r);
563: PetscPrintf(PETSC_COMM_WORLD, "Initial Residual\n");
564: VecChop(r, 1.0e-10);
565: VecView(r, PETSC_VIEWER_STDOUT_WORLD);
566: VecNorm(r, NORM_2, &res);
567: PetscPrintf(PETSC_COMM_WORLD, "L_2 Residual: %g\n", res);
568: /* Check Jacobian */
569: {
570: Vec b;
571: PetscBool isNull;
573: SNESComputeJacobian(snes, u, A, A);
574: MatNullSpaceTest(nullSpace, J, &isNull);
575: //if (!isNull) SETERRQ(PETSC_COMM_WORLD, PETSC_ERR_PLIB, "The null space calculated for the system operator is invalid.");
576: VecDuplicate(u, &b);
577: VecSet(r, 0.0);
578: SNESComputeFunction(snes, r, b);
579: MatMult(A, u, r);
580: VecAXPY(r, 1.0, b);
581: VecDestroy(&b);
582: PetscPrintf(PETSC_COMM_WORLD, "Au - b = Au + F(0)\n");
583: VecChop(r, 1.0e-10);
584: VecView(r, PETSC_VIEWER_STDOUT_WORLD);
585: VecNorm(r, NORM_2, &res);
586: PetscPrintf(PETSC_COMM_WORLD, "Linear L_2 Residual: %g\n", res);
587: }
588: }
589: VecViewFromOptions(u, NULL, "-sol_vec_view");
591: MatNullSpaceDestroy(&nullSpace);
592: if (A != J) {MatDestroy(&A);}
593: MatDestroy(&J);
594: VecDestroy(&u);
595: VecDestroy(&r);
596: SNESDestroy(&snes);
597: DMDestroy(&dm);
598: PetscFree(user.exactFuncs);
599: PetscFinalize();
600: return 0;
601: }