1 static char help[] = "Poiseuille Flow in 2d and 3d channels with finite elements.\n\
2 We solve the Poiseuille flow problem in a rectangular\n\
3 domain, using a parallel unstructured mesh (DMPLEX) to discretize it.\n\n\n";
4
5 /*F
6 A Poiseuille flow is a steady-state isoviscous Stokes flow in a pipe of constant cross-section. We discretize using the
7 finite element method on an unstructured mesh. The weak form equations are
8 \begin{align*}
9 < \nabla v, \nu (\nabla u + {\nabla u}^T) > - < \nabla\cdot v, p > + < v, \Delta \hat n >_{\Gamma_o} = 0
10 < q, \nabla\cdot u > = 0
11 \end{align*}
12 where $\nu$ is the kinematic viscosity, $\Delta$ is the pressure drop per unit length, assuming that pressure is 0 on
13 the left edge, and $\Gamma_o$ is the outlet boundary at the right edge of the pipe. The normal velocity will be zero at
14 the wall, but we will allow a fixed tangential velocity $u_0$.
15
16 In order to test our global to local basis transformation, we will allow the pipe to be at an angle $\alpha$ to the
17 coordinate axes.
18
19 For visualization, use
20
21 -dm_view hdf5:$PWD/sol.h5 -sol_vec_view hdf5:$PWD/sol.h5::append -exact_vec_view hdf5:$PWD/sol.h5::append
22 F*/
23
24 #include <petscdmplex.h>
25 #include <petscsnes.h>
26 #include <petscds.h>
27 #include <petscbag.h>
28
29 typedef struct {
30 PetscReal Delta; /* Pressure drop per unit length */
31 PetscReal nu; /* Kinematic viscosity */
32 PetscReal u_0; /* Tangential velocity at the wall */
33 PetscReal alpha; /* Angle of pipe wall to x-axis */
34 } Parameter;
35
36 typedef struct {
37 /* Domain and mesh definition */
38 PetscInt dim; /* The topological mesh dimension */
39 PetscBool simplex; /* Use simplices or tensor product cells */
40 PetscInt cells[3]; /* The initial domain division */
41 /* Problem definition */
42 PetscBag bag; /* Holds problem parameters */
43 PetscErrorCode (**exactFuncs)(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nf, PetscScalar *u, void *ctx);
44 } AppCtx;
45
46 /*
47 In 2D, plane Poiseuille flow has exact solution:
48
49 u = \Delta/(2 \nu) y (1 - y) + u_0
50 v = 0
51 p = -\Delta x
52 f = 0
53
54 so that
55
56 -\nu \Delta u + \nabla p + f = <\Delta, 0> + <-\Delta, 0> + <0, 0> = 0
57 \nabla \cdot u = 0 + 0 = 0
58
59 In 3D we use exact solution:
60
61 u = \Delta/(4 \nu) (y (1 - y) + z (1 - z)) + u_0
62 v = 0
63 w = 0
64 p = -\Delta x
65 f = 0
66
67 so that
68
69 -\nu \Delta u + \nabla p + f = <Delta, 0, 0> + <-Delta, 0, 0> + <0, 0, 0> = 0
70 \nabla \cdot u = 0 + 0 + 0 = 0
71
72 Note that these functions use coordinates X in the global (rotated) frame
73 */
quadratic_u(PetscInt dim,PetscReal time,const PetscReal X[],PetscInt Nf,PetscScalar * u,void * ctx)74 PetscErrorCode quadratic_u(PetscInt dim, PetscReal time, const PetscReal X[], PetscInt Nf, PetscScalar *u, void *ctx)
75 {
76 Parameter *param = (Parameter *) ctx;
77 PetscReal Delta = param->Delta;
78 PetscReal nu = param->nu;
79 PetscReal u_0 = param->u_0;
80 PetscReal fac = (PetscReal) (dim - 1);
81 PetscInt d;
82
83 u[0] = u_0;
84 for (d = 1; d < dim; ++d) u[0] += Delta/(fac * 2.0*nu) * X[d] * (1.0 - X[d]);
85 for (d = 1; d < dim; ++d) u[d] = 0.0;
86 return 0;
87 }
88
linear_p(PetscInt dim,PetscReal time,const PetscReal X[],PetscInt Nf,PetscScalar * p,void * ctx)89 PetscErrorCode linear_p(PetscInt dim, PetscReal time, const PetscReal X[], PetscInt Nf, PetscScalar *p, void *ctx)
90 {
91 Parameter *param = (Parameter *) ctx;
92 PetscReal Delta = param->Delta;
93
94 p[0] = -Delta * X[0];
95 return 0;
96 }
97
wall_velocity(PetscInt dim,PetscReal time,const PetscReal X[],PetscInt Nf,PetscScalar * u,void * ctx)98 PetscErrorCode wall_velocity(PetscInt dim, PetscReal time, const PetscReal X[], PetscInt Nf, PetscScalar *u, void *ctx)
99 {
100 Parameter *param = (Parameter *) ctx;
101 PetscReal u_0 = param->u_0;
102 PetscInt d;
103
104 u[0] = u_0;
105 for (d = 1; d < dim; ++d) u[d] = 0.0;
106 return 0;
107 }
108
109 /* 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}
110 u[Ncomp] = {p} */
f1_u(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[])111 void f1_u(PetscInt dim, PetscInt Nf, PetscInt NfAux,
112 const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
113 const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
114 PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f1[])
115 {
116 const PetscReal nu = PetscRealPart(constants[1]);
117 const PetscInt Nc = dim;
118 PetscInt c, d;
119
120 for (c = 0; c < Nc; ++c) {
121 for (d = 0; d < dim; ++d) {
122 /* f1[c*dim+d] = 0.5*nu*(u_x[c*dim+d] + u_x[d*dim+c]); */
123 f1[c*dim+d] = nu*u_x[c*dim+d];
124 }
125 f1[c*dim+c] -= u[uOff[1]];
126 }
127 }
128
129 /* 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} */
f0_p(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 void f0_p(PetscInt dim, PetscInt Nf, PetscInt NfAux,
131 const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
132 const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
133 PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f0[])
134 {
135 PetscInt d;
136 for (d = 0, f0[0] = 0.0; d < dim; ++d) f0[0] += u_x[d*dim+d];
137 }
138
139 /* Residual functions are in reference coordinates */
f0_bd_u(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[],const PetscReal n[],PetscInt numConstants,const PetscScalar constants[],PetscScalar f0[])140 static void f0_bd_u(PetscInt dim, PetscInt Nf, PetscInt NfAux,
141 const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
142 const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
143 PetscReal t, const PetscReal x[], const PetscReal n[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f0[])
144 {
145 const PetscReal Delta = PetscRealPart(constants[0]);
146 PetscReal alpha = PetscRealPart(constants[3]);
147 PetscReal X = PetscCosReal(alpha)*x[0] + PetscSinReal(alpha)*x[1];
148 PetscInt d;
149
150 for (d = 0; d < dim; ++d) {
151 f0[d] = -Delta * X * n[d];
152 }
153 }
154
155 /* < q, \nabla\cdot u >
156 NcompI = 1, NcompJ = dim */
g1_pu(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 g1[])157 void g1_pu(PetscInt dim, PetscInt Nf, PetscInt NfAux,
158 const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
159 const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
160 PetscReal t, PetscReal u_tShift, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar g1[])
161 {
162 PetscInt d;
163 for (d = 0; d < dim; ++d) g1[d*dim+d] = 1.0; /* \frac{\partial\phi^{u_d}}{\partial x_d} */
164 }
165
166 /* -< \nabla\cdot v, p >
167 NcompI = dim, NcompJ = 1 */
g2_up(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 g2[])168 void g2_up(PetscInt dim, PetscInt Nf, PetscInt NfAux,
169 const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
170 const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
171 PetscReal t, PetscReal u_tShift, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar g2[])
172 {
173 PetscInt d;
174 for (d = 0; d < dim; ++d) g2[d*dim+d] = -1.0; /* \frac{\partial\psi^{u_d}}{\partial x_d} */
175 }
176
177 /* < \nabla v, \nabla u + {\nabla u}^T >
178 This just gives \nabla u, give the perdiagonal for the transpose */
g3_uu(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[])179 void g3_uu(PetscInt dim, PetscInt Nf, PetscInt NfAux,
180 const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
181 const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
182 PetscReal t, PetscReal u_tShift, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar g3[])
183 {
184 const PetscReal nu = PetscRealPart(constants[1]);
185 const PetscInt Nc = dim;
186 PetscInt c, d;
187
188 for (c = 0; c < Nc; ++c) {
189 for (d = 0; d < dim; ++d) {
190 g3[((c*Nc+c)*dim+d)*dim+d] = nu;
191 }
192 }
193 }
194
ProcessOptions(MPI_Comm comm,AppCtx * options)195 PetscErrorCode ProcessOptions(MPI_Comm comm, AppCtx *options)
196 {
197 PetscInt n = 3;
198 PetscErrorCode ierr;
199
200 PetscFunctionBeginUser;
201 options->dim = 2;
202 options->simplex = PETSC_TRUE;
203 options->cells[0] = 3;
204 options->cells[1] = 3;
205 options->cells[2] = 3;
206
207 ierr = PetscOptionsBegin(comm, "", "Poiseuille Flow Options", "DMPLEX");CHKERRQ(ierr);
208 ierr = PetscOptionsInt("-dim", "The topological mesh dimension", "ex62.c", options->dim, &options->dim, NULL);CHKERRQ(ierr);
209 ierr = PetscOptionsBool("-simplex", "Use simplices or tensor product cells", "ex62.c", options->simplex, &options->simplex, NULL);CHKERRQ(ierr);
210 ierr = PetscOptionsIntArray("-cells", "The initial mesh division", "ex62.c", options->cells, &n, NULL);CHKERRQ(ierr);
211 ierr = PetscOptionsEnd();
212 PetscFunctionReturn(0);
213 }
214
SetupParameters(AppCtx * user)215 static PetscErrorCode SetupParameters(AppCtx *user)
216 {
217 PetscBag bag;
218 Parameter *p;
219 PetscErrorCode ierr;
220
221 PetscFunctionBeginUser;
222 /* setup PETSc parameter bag */
223 ierr = PetscBagGetData(user->bag, (void **) &p);CHKERRQ(ierr);
224 ierr = PetscBagSetName(user->bag, "par", "Poiseuille flow parameters");CHKERRQ(ierr);
225 bag = user->bag;
226 ierr = PetscBagRegisterReal(bag, &p->Delta, 1.0, "Delta", "Pressure drop per unit length");CHKERRQ(ierr);
227 ierr = PetscBagRegisterReal(bag, &p->nu, 1.0, "nu", "Kinematic viscosity");CHKERRQ(ierr);
228 ierr = PetscBagRegisterReal(bag, &p->u_0, 0.0, "u_0", "Tangential velocity at the wall");CHKERRQ(ierr);
229 ierr = PetscBagRegisterReal(bag, &p->alpha, 0.0, "alpha", "Angle of pipe wall to x-axis");CHKERRQ(ierr);
230 PetscFunctionReturn(0);
231 }
232
CreateMesh(MPI_Comm comm,AppCtx * user,DM * dm)233 PetscErrorCode CreateMesh(MPI_Comm comm, AppCtx *user, DM *dm)
234 {
235 PetscInt dim = user->dim;
236 PetscErrorCode ierr;
237
238 PetscFunctionBeginUser;
239 ierr = DMPlexCreateBoxMesh(comm, dim, user->simplex, user->cells, NULL, NULL, NULL, PETSC_TRUE, dm);CHKERRQ(ierr);
240 {
241 Parameter *param;
242 Vec coordinates;
243 PetscScalar *coords;
244 PetscReal alpha;
245 PetscInt cdim, N, bs, i;
246
247 ierr = DMGetCoordinateDim(*dm, &cdim);CHKERRQ(ierr);
248 ierr = DMGetCoordinates(*dm, &coordinates);CHKERRQ(ierr);
249 ierr = VecGetLocalSize(coordinates, &N);CHKERRQ(ierr);
250 ierr = VecGetBlockSize(coordinates, &bs);CHKERRQ(ierr);
251 if (bs != cdim) SETERRQ2(comm, PETSC_ERR_ARG_WRONG, "Invalid coordinate blocksize %D != embedding dimension %D", bs, cdim);
252 ierr = VecGetArray(coordinates, &coords);CHKERRQ(ierr);
253 ierr = PetscBagGetData(user->bag, (void **) ¶m);CHKERRQ(ierr);
254 alpha = param->alpha;
255 for (i = 0; i < N; i += cdim) {
256 PetscScalar x = coords[i+0];
257 PetscScalar y = coords[i+1];
258
259 coords[i+0] = PetscCosReal(alpha)*x - PetscSinReal(alpha)*y;
260 coords[i+1] = PetscSinReal(alpha)*x + PetscCosReal(alpha)*y;
261 }
262 ierr = VecRestoreArray(coordinates, &coords);CHKERRQ(ierr);
263 ierr = DMSetCoordinates(*dm, coordinates);CHKERRQ(ierr);
264 }
265 {
266 DM pdm = NULL;
267 PetscPartitioner part;
268
269 ierr = DMPlexGetPartitioner(*dm, &part);CHKERRQ(ierr);
270 ierr = PetscPartitionerSetFromOptions(part);CHKERRQ(ierr);
271 ierr = DMPlexDistribute(*dm, 0, NULL, &pdm);CHKERRQ(ierr);
272 if (pdm) {
273 ierr = DMDestroy(dm);CHKERRQ(ierr);
274 *dm = pdm;
275 }
276 }
277 ierr = DMSetFromOptions(*dm);CHKERRQ(ierr);
278 ierr = DMViewFromOptions(*dm, NULL, "-dm_view");CHKERRQ(ierr);
279 PetscFunctionReturn(0);
280 }
281
SetupProblem(DM dm,AppCtx * user)282 PetscErrorCode SetupProblem(DM dm, AppCtx *user)
283 {
284 PetscDS prob;
285 Parameter *ctx;
286 PetscInt id;
287 PetscErrorCode ierr;
288
289 PetscFunctionBeginUser;
290 ierr = DMGetDS(dm, &prob);CHKERRQ(ierr);
291 ierr = PetscDSSetResidual(prob, 0, NULL, f1_u);CHKERRQ(ierr);
292 ierr = PetscDSSetResidual(prob, 1, f0_p, NULL);CHKERRQ(ierr);
293 ierr = PetscDSSetBdResidual(prob, 0, f0_bd_u, NULL);CHKERRQ(ierr);
294 ierr = PetscDSSetJacobian(prob, 0, 0, NULL, NULL, NULL, g3_uu);CHKERRQ(ierr);
295 ierr = PetscDSSetJacobian(prob, 0, 1, NULL, NULL, g2_up, NULL);CHKERRQ(ierr);
296 ierr = PetscDSSetJacobian(prob, 1, 0, NULL, g1_pu, NULL, NULL);CHKERRQ(ierr);
297 /* Setup constants */
298 {
299 Parameter *param;
300 PetscScalar constants[4];
301
302 ierr = PetscBagGetData(user->bag, (void **) ¶m);CHKERRQ(ierr);
303
304 constants[0] = param->Delta;
305 constants[1] = param->nu;
306 constants[2] = param->u_0;
307 constants[3] = param->alpha;
308 ierr = PetscDSSetConstants(prob, 4, constants);CHKERRQ(ierr);
309 }
310 /* Setup Boundary Conditions */
311 ierr = PetscBagGetData(user->bag, (void **) &ctx);CHKERRQ(ierr);
312 id = 3;
313 ierr = DMAddBoundary(dm, DM_BC_ESSENTIAL, "top wall", "marker", 0, 0, NULL, (void (*)(void)) wall_velocity, NULL, 1, &id, ctx);CHKERRQ(ierr);
314 id = 1;
315 ierr = DMAddBoundary(dm, DM_BC_ESSENTIAL, "bottom wall", "marker", 0, 0, NULL, (void (*)(void)) wall_velocity, NULL, 1, &id, ctx);CHKERRQ(ierr);
316 id = 2;
317 ierr = DMAddBoundary(dm, DM_BC_NATURAL, "right wall", "marker", 0, 0, NULL, (void (*)(void)) NULL, NULL, 1, &id, ctx);CHKERRQ(ierr);
318 /* Setup exact solution */
319 user->exactFuncs[0] = quadratic_u;
320 user->exactFuncs[1] = linear_p;
321 ierr = PetscDSSetExactSolution(prob, 0, user->exactFuncs[0], ctx);CHKERRQ(ierr);
322 ierr = PetscDSSetExactSolution(prob, 1, user->exactFuncs[1], ctx);CHKERRQ(ierr);
323 PetscFunctionReturn(0);
324 }
325
SetupDiscretization(DM dm,AppCtx * user)326 PetscErrorCode SetupDiscretization(DM dm, AppCtx *user)
327 {
328 DM cdm = dm;
329 const PetscInt dim = user->dim;
330 PetscFE fe[2];
331 Parameter *param;
332 MPI_Comm comm;
333 PetscErrorCode ierr;
334
335 PetscFunctionBeginUser;
336 /* Create finite element */
337 ierr = PetscObjectGetComm((PetscObject) dm, &comm);CHKERRQ(ierr);
338 ierr = PetscFECreateDefault(comm, dim, dim, user->simplex, "vel_", PETSC_DEFAULT, &fe[0]);CHKERRQ(ierr);
339 ierr = PetscObjectSetName((PetscObject) fe[0], "velocity");CHKERRQ(ierr);
340 ierr = PetscFECreateDefault(comm, dim, 1, user->simplex, "pres_", PETSC_DEFAULT, &fe[1]);CHKERRQ(ierr);
341 ierr = PetscFECopyQuadrature(fe[0], fe[1]);CHKERRQ(ierr);
342 ierr = PetscObjectSetName((PetscObject) fe[1], "pressure");CHKERRQ(ierr);
343 /* Set discretization and boundary conditions for each mesh */
344 ierr = DMSetField(dm, 0, NULL, (PetscObject) fe[0]);CHKERRQ(ierr);
345 ierr = DMSetField(dm, 1, NULL, (PetscObject) fe[1]);CHKERRQ(ierr);
346 ierr = DMCreateDS(dm);CHKERRQ(ierr);
347 ierr = SetupProblem(dm, user);CHKERRQ(ierr);
348 ierr = PetscBagGetData(user->bag, (void **) ¶m);CHKERRQ(ierr);
349 while (cdm) {
350 ierr = DMCopyDisc(dm, cdm);CHKERRQ(ierr);
351 ierr = DMPlexCreateBasisRotation(cdm, param->alpha, 0.0, 0.0);CHKERRQ(ierr);
352 ierr = DMGetCoarseDM(cdm, &cdm);CHKERRQ(ierr);
353 }
354 ierr = PetscFEDestroy(&fe[0]);CHKERRQ(ierr);
355 ierr = PetscFEDestroy(&fe[1]);CHKERRQ(ierr);
356 PetscFunctionReturn(0);
357 }
358
main(int argc,char ** argv)359 int main(int argc, char **argv)
360 {
361 SNES snes; /* nonlinear solver */
362 DM dm; /* problem definition */
363 Vec u, r; /* solution and residual */
364 AppCtx user; /* user-defined work context */
365 PetscErrorCode ierr;
366
367 ierr = PetscInitialize(&argc, &argv, NULL,help);if (ierr) return ierr;
368 ierr = ProcessOptions(PETSC_COMM_WORLD, &user);CHKERRQ(ierr);
369 ierr = PetscBagCreate(PETSC_COMM_WORLD, sizeof(Parameter), &user.bag);CHKERRQ(ierr);
370 ierr = SetupParameters(&user);CHKERRQ(ierr);
371 ierr = SNESCreate(PETSC_COMM_WORLD, &snes);CHKERRQ(ierr);
372 ierr = CreateMesh(PETSC_COMM_WORLD, &user, &dm);CHKERRQ(ierr);
373 ierr = SNESSetDM(snes, dm);CHKERRQ(ierr);
374 ierr = DMSetApplicationContext(dm, &user);CHKERRQ(ierr);
375 /* Setup problem */
376 ierr = PetscMalloc(2 * sizeof(void (*)(const PetscReal[], PetscScalar *, void *)), &user.exactFuncs);CHKERRQ(ierr);
377 ierr = SetupDiscretization(dm, &user);CHKERRQ(ierr);
378 ierr = DMPlexCreateClosureIndex(dm, NULL);CHKERRQ(ierr);
379
380 ierr = DMCreateGlobalVector(dm, &u);CHKERRQ(ierr);
381 ierr = VecDuplicate(u, &r);CHKERRQ(ierr);
382
383 ierr = DMPlexSetSNESLocalFEM(dm,&user,&user,&user);CHKERRQ(ierr);
384
385 ierr = SNESSetFromOptions(snes);CHKERRQ(ierr);
386
387 {
388 Parameter *param;
389 void *ctxs[2];
390
391 ierr = PetscBagGetData(user.bag, (void **) ¶m);CHKERRQ(ierr);
392 ctxs[0] = ctxs[1] = param;
393 ierr = DMProjectFunction(dm, 0.0, user.exactFuncs, ctxs, INSERT_ALL_VALUES, u);CHKERRQ(ierr);
394 ierr = PetscObjectSetName((PetscObject) u, "Exact Solution");CHKERRQ(ierr);
395 ierr = VecViewFromOptions(u, NULL, "-exact_vec_view");CHKERRQ(ierr);
396 }
397 ierr = DMSNESCheckFromOptions(snes, u);CHKERRQ(ierr);
398 ierr = VecSet(u, 0.0);CHKERRQ(ierr);
399 ierr = PetscObjectSetName((PetscObject) u, "Solution");CHKERRQ(ierr);
400 ierr = SNESSolve(snes, NULL, u);CHKERRQ(ierr);
401 ierr = VecViewFromOptions(u, NULL, "-sol_vec_view");CHKERRQ(ierr);
402
403 ierr = VecDestroy(&u);CHKERRQ(ierr);
404 ierr = VecDestroy(&r);CHKERRQ(ierr);
405 ierr = PetscFree(user.exactFuncs);CHKERRQ(ierr);
406 ierr = DMDestroy(&dm);CHKERRQ(ierr);
407 ierr = SNESDestroy(&snes);CHKERRQ(ierr);
408 ierr = PetscBagDestroy(&user.bag);CHKERRQ(ierr);
409 ierr = PetscFinalize();
410 return ierr;
411 }
412
413 /*TEST
414
415 # Convergence
416 test:
417 suffix: 2d_quad_q1_p0_conv
418 requires: !single
419 args: -simplex 0 -dm_plex_separate_marker -dm_refine 1 \
420 -vel_petscspace_degree 1 -pres_petscspace_degree 0 \
421 -snes_convergence_estimate -convest_num_refine 2 -snes_error_if_not_converged \
422 -ksp_type fgmres -ksp_gmres_restart 10 -ksp_rtol 1.0e-9 -ksp_error_if_not_converged \
423 -pc_type fieldsplit -pc_fieldsplit_type schur -pc_fieldsplit_schur_factorization_type full \
424 -fieldsplit_velocity_pc_type lu \
425 -fieldsplit_pressure_ksp_rtol 1e-10 -fieldsplit_pressure_pc_type jacobi
426 test:
427 suffix: 2d_quad_q1_p0_conv_u0
428 requires: !single
429 args: -simplex 0 -dm_plex_separate_marker -dm_refine 1 -u_0 0.125 \
430 -vel_petscspace_degree 1 -pres_petscspace_degree 0 \
431 -snes_convergence_estimate -convest_num_refine 2 -snes_error_if_not_converged \
432 -ksp_type fgmres -ksp_gmres_restart 10 -ksp_rtol 1.0e-9 -ksp_error_if_not_converged \
433 -pc_type fieldsplit -pc_fieldsplit_type schur -pc_fieldsplit_schur_factorization_type full \
434 -fieldsplit_velocity_pc_type lu \
435 -fieldsplit_pressure_ksp_rtol 1e-10 -fieldsplit_pressure_pc_type jacobi
436 test:
437 suffix: 2d_quad_q1_p0_conv_u0_alpha
438 requires: !single
439 args: -simplex 0 -dm_plex_separate_marker -dm_refine 1 -u_0 0.125 -alpha 0.3927 \
440 -vel_petscspace_degree 1 -pres_petscspace_degree 0 \
441 -snes_convergence_estimate -convest_num_refine 2 -snes_error_if_not_converged \
442 -ksp_type fgmres -ksp_gmres_restart 10 -ksp_rtol 1.0e-9 -ksp_error_if_not_converged \
443 -pc_type fieldsplit -pc_fieldsplit_type schur -pc_fieldsplit_schur_factorization_type full \
444 -fieldsplit_velocity_pc_type lu \
445 -fieldsplit_pressure_ksp_rtol 1e-10 -fieldsplit_pressure_pc_type jacobi
446 test:
447 suffix: 2d_quad_q1_p0_conv_gmg_vanka
448 requires: !single long_runtime
449 args: -simplex 0 -dm_plex_separate_marker -cells 2,2 -dm_refine_hierarchy 1 \
450 -vel_petscspace_degree 1 -pres_petscspace_degree 0 \
451 -snes_convergence_estimate -convest_num_refine 1 -snes_error_if_not_converged \
452 -ksp_type fgmres -ksp_gmres_restart 10 -ksp_rtol 1.0e-9 -ksp_error_if_not_converged \
453 -pc_type fieldsplit -pc_fieldsplit_type schur -pc_fieldsplit_schur_factorization_type full \
454 -fieldsplit_velocity_pc_type mg \
455 -fieldsplit_velocity_mg_levels_pc_type patch -fieldsplit_velocity_mg_levels_pc_patch_exclude_subspaces 1 \
456 -fieldsplit_velocity_mg_levels_pc_patch_construct_codim 0 -fieldsplit_velocity_mg_levels_pc_patch_construct_type vanka \
457 -fieldsplit_pressure_ksp_rtol 1e-5 -fieldsplit_pressure_pc_type jacobi
458 test:
459 suffix: 2d_tri_p2_p1_conv
460 requires: triangle !single
461 args: -dm_plex_separate_marker -dm_refine 1 \
462 -vel_petscspace_degree 2 -pres_petscspace_degree 1 \
463 -dmsnes_check .001 -snes_error_if_not_converged \
464 -ksp_type fgmres -ksp_gmres_restart 10 -ksp_rtol 1.0e-9 -ksp_error_if_not_converged \
465 -pc_type fieldsplit -pc_fieldsplit_type schur -pc_fieldsplit_schur_factorization_type full \
466 -fieldsplit_velocity_pc_type lu \
467 -fieldsplit_pressure_ksp_rtol 1e-10 -fieldsplit_pressure_pc_type jacobi
468 test:
469 suffix: 2d_tri_p2_p1_conv_u0_alpha
470 requires: triangle !single
471 args: -dm_plex_separate_marker -dm_refine 0 -u_0 0.125 -alpha 0.3927 \
472 -vel_petscspace_degree 2 -pres_petscspace_degree 1 \
473 -dmsnes_check .001 -snes_error_if_not_converged \
474 -ksp_type fgmres -ksp_gmres_restart 10 -ksp_rtol 1.0e-9 -ksp_error_if_not_converged \
475 -pc_type fieldsplit -pc_fieldsplit_type schur -pc_fieldsplit_schur_factorization_type full \
476 -fieldsplit_velocity_pc_type lu \
477 -fieldsplit_pressure_ksp_rtol 1e-10 -fieldsplit_pressure_pc_type jacobi
478 test:
479 suffix: 2d_tri_p2_p1_conv_gmg_vcycle
480 requires: triangle !single
481 args: -dm_plex_separate_marker -cells 2,2 -dm_refine_hierarchy 1 \
482 -vel_petscspace_degree 2 -pres_petscspace_degree 1 \
483 -dmsnes_check .001 -snes_error_if_not_converged \
484 -ksp_type fgmres -ksp_gmres_restart 10 -ksp_rtol 1.0e-9 -ksp_error_if_not_converged \
485 -pc_type fieldsplit -pc_fieldsplit_type schur -pc_fieldsplit_schur_factorization_type full \
486 -fieldsplit_velocity_pc_type mg \
487 -fieldsplit_pressure_ksp_rtol 1e-10 -fieldsplit_pressure_pc_type jacobi
488 TEST*/
489