xref: /petsc/src/snes/tutorials/ex56.c (revision 6a98f8dc3f2c9149905a87dc2e9d0fedaf64e09a)
1 static char help[] = "3D, tri-quadratic hexahedra (Q1), displacement finite element formulation\n\
2 of linear elasticity.  E=1.0, nu=1/3.\n\
3 Unit cube domain with Dirichlet boundary\n\n";
4 
5 #include <petscdmplex.h>
6 #include <petscsnes.h>
7 #include <petscds.h>
8 #include <petscdmforest.h>
9 
10 static PetscReal s_soft_alpha=1.e-3;
11 static PetscReal s_mu=0.4;
12 static PetscReal s_lambda=0.4;
13 
14 static void f0_bd_u_3d(PetscInt dim, PetscInt Nf, PetscInt NfAux,
15                        const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
16                        const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
17                        PetscReal t, const PetscReal x[], const PetscReal n[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f0[])
18 {
19   f0[0] = 1;     /* x direction pull */
20   f0[1] = -x[2]; /* add a twist around x-axis */
21   f0[2] =  x[1];
22 }
23 
24 static void f1_bd_u(PetscInt dim, PetscInt Nf, PetscInt NfAux,
25                     const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
26                     const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
27                     PetscReal t, const PetscReal x[], const PetscReal n[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f1[])
28 {
29   const PetscInt Ncomp = dim;
30   PetscInt       comp, d;
31   for (comp = 0; comp < Ncomp; ++comp) {
32     for (d = 0; d < dim; ++d) {
33       f1[comp*dim+d] = 0.0;
34     }
35   }
36 }
37 
38 /* gradU[comp*dim+d] = {u_x, u_y} or {u_x, u_y, u_z} */
39 static void f1_u_3d_alpha(PetscInt dim, PetscInt Nf, PetscInt NfAux,
40                           const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
41                           const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
42                           PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f1[])
43 {
44   PetscReal trace,mu=s_mu,lambda=s_lambda,rad;
45   PetscInt i,j;
46   for (i=0,rad=0.;i<dim;i++) {
47     PetscReal t=x[i];
48     rad += t*t;
49   }
50   rad = PetscSqrtReal(rad);
51   if (rad>0.25) {
52     mu *= s_soft_alpha;
53     lambda *= s_soft_alpha; /* we could keep the bulk the same like rubberish */
54   }
55   for (i=0,trace=0; i < dim; ++i) {
56     trace += PetscRealPart(u_x[i*dim+i]);
57   }
58   for (i=0; i < dim; ++i) {
59     for (j=0; j < dim; ++j) {
60       f1[i*dim+j] = mu*(u_x[i*dim+j]+u_x[j*dim+i]);
61     }
62     f1[i*dim+i] += lambda*trace;
63   }
64 }
65 
66 /* gradU[comp*dim+d] = {u_x, u_y} or {u_x, u_y, u_z} */
67 static void f1_u_3d(PetscInt dim, PetscInt Nf, PetscInt NfAux,
68                     const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
69                     const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
70                     PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f1[])
71 {
72   PetscReal trace,mu=s_mu,lambda=s_lambda;
73   PetscInt i,j;
74   for (i=0,trace=0; i < dim; ++i) {
75     trace += PetscRealPart(u_x[i*dim+i]);
76   }
77   for (i=0; i < dim; ++i) {
78     for (j=0; j < dim; ++j) {
79       f1[i*dim+j] = mu*(u_x[i*dim+j]+u_x[j*dim+i]);
80     }
81     f1[i*dim+i] += lambda*trace;
82   }
83 }
84 
85 /* 3D elasticity */
86 #define IDX(ii,jj,kk,ll) (27*ii+9*jj+3*kk+ll)
87 
88 void g3_uu_3d_private( PetscScalar g3[], const PetscReal mu, const PetscReal lambda)
89 {
90   if (1) {
91     g3[0] += lambda;
92     g3[0] += mu;
93     g3[0] += mu;
94     g3[4] += lambda;
95     g3[8] += lambda;
96     g3[10] += mu;
97     g3[12] += mu;
98     g3[20] += mu;
99     g3[24] += mu;
100     g3[28] += mu;
101     g3[30] += mu;
102     g3[36] += lambda;
103     g3[40] += lambda;
104     g3[40] += mu;
105     g3[40] += mu;
106     g3[44] += lambda;
107     g3[50] += mu;
108     g3[52] += mu;
109     g3[56] += mu;
110     g3[60] += mu;
111     g3[68] += mu;
112     g3[70] += mu;
113     g3[72] += lambda;
114     g3[76] += lambda;
115     g3[80] += lambda;
116     g3[80] += mu;
117     g3[80] += mu;
118   } else {
119     int        i,j,k,l;
120     static int cc=-1;
121     cc++;
122     for (i = 0; i < 3; ++i) {
123       for (j = 0; j < 3; ++j) {
124         for (k = 0; k < 3; ++k) {
125           for (l = 0; l < 3; ++l) {
126             if (k==l && i==j) g3[IDX(i,j,k,l)] += lambda;
127             if (i==k && j==l) g3[IDX(i,j,k,l)] += mu;
128             if (i==l && j==k) g3[IDX(i,j,k,l)] += mu;
129 	    if (k==l && i==j && !cc) (void) PetscPrintf(PETSC_COMM_WORLD,"g3[%d] += lambda;\n",IDX(i,j,k,l));
130 	    if (i==k && j==l && !cc) (void) PetscPrintf(PETSC_COMM_WORLD,"g3[%d] += mu;\n",IDX(i,j,k,l));
131 	    if (i==l && j==k && !cc) (void) PetscPrintf(PETSC_COMM_WORLD,"g3[%d] += mu;\n",IDX(i,j,k,l));
132           }
133         }
134       }
135     }
136   }
137 }
138 
139 static void g3_uu_3d_alpha(PetscInt dim, PetscInt Nf, PetscInt NfAux,
140                            const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
141                            const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
142                            PetscReal t, PetscReal u_tShift, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar g3[])
143 {
144   PetscReal mu=s_mu, lambda=s_lambda,rad;
145   PetscInt i;
146   for (i=0,rad=0.;i<dim;i++) {
147     PetscReal t=x[i];
148     rad += t*t;
149   }
150   rad = PetscSqrtReal(rad);
151   if (rad>0.25) {
152     mu *= s_soft_alpha;
153     lambda *= s_soft_alpha; /* we could keep the bulk the same like rubberish */
154   }
155   g3_uu_3d_private(g3,mu,lambda);
156 }
157 
158 static void g3_uu_3d(PetscInt dim, PetscInt Nf, PetscInt NfAux,
159                      const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
160                      const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
161                      PetscReal t, PetscReal u_tShift, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar g3[])
162 {
163   g3_uu_3d_private(g3,s_mu,s_lambda);
164 }
165 
166 static void f0_u(PetscInt dim, PetscInt Nf, PetscInt NfAux,
167                  const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
168                  const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
169                  PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f0[])
170 {
171   const    PetscInt Ncomp = dim;
172   PetscInt comp;
173 
174   for (comp = 0; comp < Ncomp; ++comp) f0[comp] = 0.0;
175 }
176 
177 /* PI_i (x_i^4 - x_i^2) */
178 static void f0_u_x4(PetscInt dim, PetscInt Nf, PetscInt NfAux,
179                     const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
180                     const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
181                     PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f0[])
182 {
183   const    PetscInt Ncomp = dim;
184   PetscInt comp,i;
185 
186   for (comp = 0; comp < Ncomp; ++comp) {
187     f0[comp] = 1e5;
188     for (i = 0; i < Ncomp; ++i) {
189       f0[comp] *= /* (comp+1)* */(x[i]*x[i]*x[i]*x[i] - x[i]*x[i]); /* assumes (0,1]^D domain */
190     }
191   }
192 }
193 
194 PetscErrorCode zero(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nf, PetscScalar *u, void *ctx)
195 {
196   const PetscInt Ncomp = dim;
197   PetscInt       comp;
198 
199   for (comp = 0; comp < Ncomp; ++comp) u[comp] = 0;
200   return 0;
201 }
202 
203 int main(int argc,char **args)
204 {
205   Mat            Amat;
206   PetscErrorCode ierr;
207   SNES           snes;
208   KSP            ksp;
209   MPI_Comm       comm;
210   PetscMPIInt    rank;
211   PetscLogStage  stage[17];
212   PetscBool      test_nonzero_cols=PETSC_FALSE,use_nearnullspace=PETSC_TRUE,attach_nearnullspace=PETSC_FALSE;
213   Vec            xx,bb;
214   PetscInt       iter,i,N,dim=3,cells[3]={1,1,1},max_conv_its,local_sizes[7],run_type=1;
215   DM             dm,distdm,basedm;
216   PetscBool      flg;
217   char           convType[256];
218   PetscReal      Lx,mdisp[10],err[10];
219   const char * const options[10] = {"-ex56_dm_refine 0",
220                                     "-ex56_dm_refine 1",
221                                     "-ex56_dm_refine 2",
222                                     "-ex56_dm_refine 3",
223                                     "-ex56_dm_refine 4",
224                                     "-ex56_dm_refine 5",
225                                     "-ex56_dm_refine 6",
226                                     "-ex56_dm_refine 7",
227                                     "-ex56_dm_refine 8",
228                                     "-ex56_dm_refine 9"};
229   PetscFunctionBeginUser;
230   ierr = PetscInitialize(&argc,&args,(char*)0,help);if (ierr) return ierr;
231   comm = PETSC_COMM_WORLD;
232   ierr = MPI_Comm_rank(comm, &rank);CHKERRQ(ierr);
233   /* options */
234   ierr = PetscOptionsBegin(comm,NULL,"3D bilinear Q1 elasticity options","");CHKERRQ(ierr);
235   {
236     i = 3;
237     ierr = PetscOptionsIntArray("-cells", "Number of (flux tube) processor in each dimension", "ex56.c", cells, &i, NULL);CHKERRQ(ierr);
238 
239     Lx = 1.; /* or ne for rod */
240     max_conv_its = 3;
241     ierr = PetscOptionsInt("-max_conv_its","Number of iterations in convergence study","",max_conv_its,&max_conv_its,NULL);CHKERRQ(ierr);
242     if (max_conv_its<=0 || max_conv_its>7) SETERRQ1(PETSC_COMM_WORLD, PETSC_ERR_USER, "Bad number of iterations for convergence test (%D)",max_conv_its);
243     ierr = PetscOptionsReal("-lx","Length of domain","",Lx,&Lx,NULL);CHKERRQ(ierr);
244     ierr = PetscOptionsReal("-alpha","material coefficient inside circle","",s_soft_alpha,&s_soft_alpha,NULL);CHKERRQ(ierr);
245     ierr = PetscOptionsBool("-test_nonzero_cols","nonzero test","",test_nonzero_cols,&test_nonzero_cols,NULL);CHKERRQ(ierr);
246     ierr = PetscOptionsBool("-use_mat_nearnullspace","MatNearNullSpace API test","",use_nearnullspace,&use_nearnullspace,NULL);CHKERRQ(ierr);
247     ierr = PetscOptionsBool("-attach_mat_nearnullspace","MatNearNullSpace API test (via MatSetNearNullSpace)","",attach_nearnullspace,&attach_nearnullspace,NULL);CHKERRQ(ierr);
248     ierr = PetscOptionsInt("-run_type","0: twisting load on cantalever, 1: 3rd order accurate convergence test","",run_type,&run_type,NULL);CHKERRQ(ierr);
249     i = 3;
250     ierr = PetscOptionsInt("-mat_block_size","","",i,&i,&flg);CHKERRQ(ierr);
251     if (!flg || i!=3) SETERRQ2(PETSC_COMM_WORLD, PETSC_ERR_USER, "'-mat_block_size 3' must be set (%D) and = 3 (%D)",flg,flg? i : 3);
252   }
253   ierr = PetscOptionsEnd();CHKERRQ(ierr);
254   ierr = PetscLogStageRegister("Mesh Setup", &stage[16]);CHKERRQ(ierr);
255   for (iter=0 ; iter<max_conv_its ; iter++) {
256     char str[] = "Solve 0";
257     str[6] += iter;
258     ierr = PetscLogStageRegister(str, &stage[iter]);CHKERRQ(ierr);
259   }
260   /* create DM, Plex calls DMSetup */
261   ierr = PetscLogStagePush(stage[16]);CHKERRQ(ierr);
262   ierr = DMPlexCreateBoxMesh(comm, dim, PETSC_FALSE, cells, NULL, NULL, NULL, PETSC_TRUE, &dm);CHKERRQ(ierr);
263   {
264     DMLabel         label;
265     IS              is;
266     ierr = DMCreateLabel(dm, "boundary");CHKERRQ(ierr);
267     ierr = DMGetLabel(dm, "boundary", &label);CHKERRQ(ierr);
268     ierr = DMPlexMarkBoundaryFaces(dm, 1, label);CHKERRQ(ierr);
269     if (!run_type) {
270       ierr = DMGetStratumIS(dm, "boundary", 1,  &is);CHKERRQ(ierr);
271       ierr = DMCreateLabel(dm,"Faces");CHKERRQ(ierr);
272       if (is) {
273         PetscInt        d, f, Nf;
274         const PetscInt *faces;
275         PetscInt        csize;
276         PetscSection    cs;
277         Vec             coordinates ;
278         DM              cdm;
279         ierr = ISGetLocalSize(is, &Nf);CHKERRQ(ierr);
280         ierr = ISGetIndices(is, &faces);CHKERRQ(ierr);
281         ierr = DMGetCoordinatesLocal(dm, &coordinates);CHKERRQ(ierr);
282         ierr = DMGetCoordinateDM(dm, &cdm);CHKERRQ(ierr);
283         ierr = DMGetLocalSection(cdm, &cs);CHKERRQ(ierr);
284         /* Check for each boundary face if any component of its centroid is either 0.0 or 1.0 */
285         for (f = 0; f < Nf; ++f) {
286           PetscReal   faceCoord;
287           PetscInt    b,v;
288           PetscScalar *coords = NULL;
289           PetscInt    Nv;
290           ierr = DMPlexVecGetClosure(cdm, cs, coordinates, faces[f], &csize, &coords);CHKERRQ(ierr);
291           Nv   = csize/dim; /* Calculate mean coordinate vector */
292           for (d = 0; d < dim; ++d) {
293             faceCoord = 0.0;
294             for (v = 0; v < Nv; ++v) faceCoord += PetscRealPart(coords[v*dim+d]);
295             faceCoord /= Nv;
296             for (b = 0; b < 2; ++b) {
297               if (PetscAbs(faceCoord - b) < PETSC_SMALL) { /* domain have not been set yet, still [0,1]^3 */
298                 ierr = DMSetLabelValue(dm, "Faces", faces[f], d*2+b+1);CHKERRQ(ierr);
299               }
300             }
301           }
302           ierr = DMPlexVecRestoreClosure(cdm, cs, coordinates, faces[f], &csize, &coords);CHKERRQ(ierr);
303         }
304         ierr = ISRestoreIndices(is, &faces);CHKERRQ(ierr);
305       }
306       ierr = ISDestroy(&is);CHKERRQ(ierr);
307       ierr = DMGetLabel(dm, "Faces", &label);CHKERRQ(ierr);
308       ierr = DMPlexLabelComplete(dm, label);CHKERRQ(ierr);
309     }
310   }
311   {
312     PetscInt    dimEmbed, i;
313     PetscInt    nCoords;
314     PetscScalar *coords,bounds[] = {0,1,-.5,.5,-.5,.5,}; /* x_min,x_max,y_min,y_max */
315     Vec         coordinates;
316     bounds[1] = Lx;
317     if (run_type==1) {
318       for (i = 0; i < 2*dim; i++) bounds[i] = (i%2) ? 1 : 0;
319     }
320     ierr = DMGetCoordinatesLocal(dm,&coordinates);CHKERRQ(ierr);
321     ierr = DMGetCoordinateDim(dm,&dimEmbed);CHKERRQ(ierr);
322     if (dimEmbed != dim) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"dimEmbed != dim %D",dimEmbed);
323     ierr = VecGetLocalSize(coordinates,&nCoords);CHKERRQ(ierr);
324     if (nCoords % dimEmbed) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Coordinate vector the wrong size");
325     ierr = VecGetArray(coordinates,&coords);CHKERRQ(ierr);
326     for (i = 0; i < nCoords; i += dimEmbed) {
327       PetscInt    j;
328       PetscScalar *coord = &coords[i];
329       for (j = 0; j < dimEmbed; j++) {
330         coord[j] = bounds[2 * j] + coord[j] * (bounds[2 * j + 1] - bounds[2 * j]);
331       }
332     }
333     ierr = VecRestoreArray(coordinates,&coords);CHKERRQ(ierr);
334     ierr = DMSetCoordinatesLocal(dm,coordinates);CHKERRQ(ierr);
335   }
336 
337   /* convert to p4est, and distribute */
338 
339   ierr = PetscOptionsBegin(comm, "", "Mesh conversion options", "DMPLEX");CHKERRQ(ierr);
340   ierr = PetscOptionsFList("-dm_type","Convert DMPlex to another format (should not be Plex!)","ex56.c",DMList,DMPLEX,convType,256,&flg);CHKERRQ(ierr);
341   ierr = PetscOptionsEnd();
342   if (flg) {
343     DM newdm;
344     ierr = DMConvert(dm,convType,&newdm);CHKERRQ(ierr);
345     if (newdm) {
346       const char *prefix;
347       PetscBool isForest;
348       ierr = PetscObjectGetOptionsPrefix((PetscObject)dm,&prefix);CHKERRQ(ierr);
349       ierr = PetscObjectSetOptionsPrefix((PetscObject)newdm,prefix);CHKERRQ(ierr);
350       ierr = DMIsForest(newdm,&isForest);CHKERRQ(ierr);
351       if (!isForest) SETERRQ(PETSC_COMM_WORLD, PETSC_ERR_USER, "Converted to non Forest?");
352       ierr = DMDestroy(&dm);CHKERRQ(ierr);
353       dm   = newdm;
354     } else SETERRQ(PETSC_COMM_WORLD, PETSC_ERR_USER, "Convert failed?");
355   } else {
356     PetscPartitioner part;
357     /* Plex Distribute mesh over processes */
358     ierr = DMPlexGetPartitioner(dm,&part);CHKERRQ(ierr);
359     ierr = PetscPartitionerSetFromOptions(part);CHKERRQ(ierr);
360     ierr = DMPlexDistribute(dm, 0, NULL, &distdm);CHKERRQ(ierr);
361     if (distdm) {
362       const char *prefix;
363       ierr = PetscObjectGetOptionsPrefix((PetscObject)dm,&prefix);CHKERRQ(ierr);
364       ierr = PetscObjectSetOptionsPrefix((PetscObject)distdm,prefix);CHKERRQ(ierr);
365       ierr = DMDestroy(&dm);CHKERRQ(ierr);
366       dm   = distdm;
367     }
368   }
369   ierr = PetscLogStagePop();CHKERRQ(ierr);
370   basedm = dm; dm = NULL;
371 
372   for (iter=0 ; iter<max_conv_its ; iter++) {
373     ierr = PetscLogStagePush(stage[16]);CHKERRQ(ierr);
374     /* make new DM */
375     ierr = DMClone(basedm, &dm);CHKERRQ(ierr);
376     ierr = PetscObjectSetOptionsPrefix((PetscObject) dm, "ex56_");CHKERRQ(ierr);
377     ierr = PetscObjectSetName( (PetscObject)dm,"Mesh");CHKERRQ(ierr);
378     if (max_conv_its > 1) {
379       /* If max_conv_its == 1, then we are not doing a convergence study. In this case, do not overwrite the -ex56_dm_refine
380        * options with the values in the options[] array; instead, use the user-specified value. */
381       ierr = PetscOptionsClearValue(NULL,"-ex56_dm_refine");CHKERRQ(ierr);
382       ierr = PetscOptionsInsertString(NULL,options[iter]);CHKERRQ(ierr);
383     }
384     ierr = DMSetFromOptions(dm);CHKERRQ(ierr); /* refinement done here in Plex, p4est */
385     /* snes */
386     ierr = SNESCreate(comm, &snes);CHKERRQ(ierr);
387     ierr = SNESSetDM(snes, dm);CHKERRQ(ierr);
388     /* fem */
389     {
390       const PetscInt Ncomp = dim;
391       const PetscInt components[] = {0,1,2};
392       const PetscInt Nfid = 1, Npid = 1;
393       const PetscInt fid[] = {1}; /* The fixed faces (x=0) */
394       const PetscInt pid[] = {2}; /* The faces with loading (x=L_x) */
395       PetscFE        fe;
396       PetscDS        prob;
397       DM             cdm = dm;
398 
399       ierr = PetscFECreateDefault(PetscObjectComm((PetscObject) dm), dim, dim, PETSC_FALSE, NULL, PETSC_DECIDE, &fe);CHKERRQ(ierr); /* elasticity */
400       ierr = PetscObjectSetName((PetscObject) fe, "deformation");CHKERRQ(ierr);
401       /* FEM prob */
402       ierr = DMSetField(dm, 0, NULL, (PetscObject) fe);CHKERRQ(ierr);
403       ierr = DMCreateDS(dm);CHKERRQ(ierr);
404       ierr = DMGetDS(dm, &prob);CHKERRQ(ierr);
405       /* setup problem */
406       if (run_type==1) {
407         ierr = PetscDSSetJacobian(prob, 0, 0, NULL, NULL, NULL, g3_uu_3d);CHKERRQ(ierr);
408         ierr = PetscDSSetResidual(prob, 0, f0_u_x4, f1_u_3d);CHKERRQ(ierr);
409       } else {
410         ierr = PetscDSSetJacobian(prob, 0, 0, NULL, NULL, NULL, g3_uu_3d_alpha);CHKERRQ(ierr);
411         ierr = PetscDSSetResidual(prob, 0, f0_u, f1_u_3d_alpha);CHKERRQ(ierr);
412         ierr = PetscDSSetBdResidual(prob, 0, f0_bd_u_3d, f1_bd_u);CHKERRQ(ierr);
413       }
414       /* bcs */
415       if (run_type==1) {
416         PetscInt id = 1;
417         ierr = DMAddBoundary(dm, DM_BC_ESSENTIAL, "wall", "boundary", 0, 0, NULL, (void (*)(void)) zero, 1, &id, NULL);CHKERRQ(ierr);
418       } else {
419         ierr = PetscDSAddBoundary(prob, DM_BC_ESSENTIAL, "fixed", "Faces", 0, Ncomp, components, (void (*)(void)) zero, Nfid, fid, NULL);CHKERRQ(ierr);
420         ierr = PetscDSAddBoundary(prob, DM_BC_NATURAL, "traction", "Faces", 0, Ncomp, components, NULL, Npid, pid, NULL);CHKERRQ(ierr);
421       }
422       while (cdm) {
423         ierr = DMCopyDisc(dm, cdm);CHKERRQ(ierr);
424         ierr = DMGetCoarseDM(cdm, &cdm);CHKERRQ(ierr);
425       }
426       ierr = PetscFEDestroy(&fe);CHKERRQ(ierr);
427     }
428     /* vecs & mat */
429     ierr = DMCreateGlobalVector(dm,&xx);CHKERRQ(ierr);
430     ierr = VecDuplicate(xx, &bb);CHKERRQ(ierr);
431     ierr = PetscObjectSetName((PetscObject) bb, "b");CHKERRQ(ierr);
432     ierr = PetscObjectSetName((PetscObject) xx, "u");CHKERRQ(ierr);
433     ierr = DMCreateMatrix(dm, &Amat);CHKERRQ(ierr);
434     ierr = MatSetOption(Amat,MAT_SYMMETRIC,PETSC_TRUE);CHKERRQ(ierr);        /* Some matrix kernels can take advantage of symmetry if we set this. */
435     ierr = MatSetOption(Amat,MAT_SYMMETRY_ETERNAL,PETSC_TRUE);CHKERRQ(ierr); /* Inform PETSc that Amat is always symmetric, so info set above isn't lost. */
436     ierr = VecGetSize(bb,&N);CHKERRQ(ierr);
437     local_sizes[iter] = N;
438     ierr = PetscInfo2(snes,"%D global equations, %D vertices\n",N,N/dim);CHKERRQ(ierr);
439     if ((use_nearnullspace || attach_nearnullspace) && N/dim > 1) {
440       /* Set up the near null space (a.k.a. rigid body modes) that will be used by the multigrid preconditioner */
441       DM           subdm;
442       MatNullSpace nearNullSpace;
443       PetscInt     fields = 0;
444       PetscObject  deformation;
445       ierr = DMCreateSubDM(dm, 1, &fields, NULL, &subdm);CHKERRQ(ierr);
446       ierr = DMPlexCreateRigidBody(subdm, &nearNullSpace);CHKERRQ(ierr);
447       ierr = DMGetField(dm, 0, NULL, &deformation);CHKERRQ(ierr);
448       ierr = PetscObjectCompose(deformation, "nearnullspace", (PetscObject) nearNullSpace);CHKERRQ(ierr);
449       ierr = DMDestroy(&subdm);CHKERRQ(ierr);
450       if (attach_nearnullspace) {
451         ierr = MatSetNearNullSpace(Amat,nearNullSpace);CHKERRQ(ierr);
452       }
453       ierr = MatNullSpaceDestroy(&nearNullSpace);CHKERRQ(ierr); /* created by DM and destroyed by Mat */
454     }
455     ierr = DMPlexSetSNESLocalFEM(dm,NULL,NULL,NULL);CHKERRQ(ierr);
456     ierr = SNESSetJacobian(snes, Amat, Amat, NULL, NULL);CHKERRQ(ierr);
457     ierr = SNESSetFromOptions(snes);CHKERRQ(ierr);
458     ierr = DMSetUp(dm);CHKERRQ(ierr);
459     ierr = PetscLogStagePop();CHKERRQ(ierr);
460     ierr = PetscLogStagePush(stage[16]);CHKERRQ(ierr);
461     /* ksp */
462     ierr = SNESGetKSP(snes, &ksp);CHKERRQ(ierr);
463     ierr = KSPSetComputeSingularValues(ksp,PETSC_TRUE);CHKERRQ(ierr);
464     /* test BCs */
465     ierr = VecZeroEntries(xx);CHKERRQ(ierr);
466     if (test_nonzero_cols) {
467       if (!rank) {
468         ierr = VecSetValue(xx,0,1.0,INSERT_VALUES);CHKERRQ(ierr);
469       }
470       ierr = VecAssemblyBegin(xx);CHKERRQ(ierr);
471       ierr = VecAssemblyEnd(xx);CHKERRQ(ierr);
472     }
473     ierr = VecZeroEntries(bb);CHKERRQ(ierr);
474     ierr = VecGetSize(bb,&i);CHKERRQ(ierr);
475     local_sizes[iter] = i;
476     ierr = PetscInfo2(snes,"%D equations in vector, %D vertices\n",i,i/dim);CHKERRQ(ierr);
477     ierr = PetscLogStagePop();CHKERRQ(ierr);
478     /* solve */
479     ierr = PetscLogStagePush(stage[iter]);CHKERRQ(ierr);
480     ierr = SNESSolve(snes, bb, xx);CHKERRQ(ierr);
481     ierr = PetscLogStagePop();CHKERRQ(ierr);
482     ierr = VecNorm(xx,NORM_INFINITY,&mdisp[iter]);CHKERRQ(ierr);
483     ierr = DMViewFromOptions(dm, NULL, "-dm_view");CHKERRQ(ierr);
484     {
485       PetscViewer       viewer = NULL;
486       PetscViewerFormat fmt;
487       ierr = PetscOptionsGetViewer(comm,NULL,"ex56_","-vec_view",&viewer,&fmt,&flg);CHKERRQ(ierr);
488       if (flg) {
489         ierr = PetscViewerPushFormat(viewer,fmt);CHKERRQ(ierr);
490         ierr = VecView(xx,viewer);CHKERRQ(ierr);
491         ierr = VecView(bb,viewer);CHKERRQ(ierr);
492         ierr = PetscViewerPopFormat(viewer);CHKERRQ(ierr);
493       }
494       ierr = PetscViewerDestroy(&viewer);CHKERRQ(ierr);
495     }
496     /* Free work space */
497     ierr = DMDestroy(&dm);CHKERRQ(ierr);
498     ierr = SNESDestroy(&snes);CHKERRQ(ierr);
499     ierr = VecDestroy(&xx);CHKERRQ(ierr);
500     ierr = VecDestroy(&bb);CHKERRQ(ierr);
501     ierr = MatDestroy(&Amat);CHKERRQ(ierr);
502   }
503   ierr = DMDestroy(&basedm);CHKERRQ(ierr);
504   if (run_type==1) err[0] = 59.975208 - mdisp[0]; /* error with what I think is the exact solution */
505   else             err[0] = 171.038 - mdisp[0];
506   for (iter=1 ; iter<max_conv_its ; iter++) {
507     if (run_type==1) err[iter] = 59.975208 - mdisp[iter];
508     else             err[iter] = 171.038 - mdisp[iter];
509     ierr = PetscPrintf(PETSC_COMM_WORLD,"[%d] %D) N=%12D, max displ=%9.7e, disp diff=%9.2e, error=%4.3e, rate=%3.2g\n",rank,iter,local_sizes[iter],(double)mdisp[iter],
510                        (double)(mdisp[iter]-mdisp[iter-1]),(double)err[iter],(double)(PetscLogReal(err[iter-1]/err[iter])/PetscLogReal(2.)));CHKERRQ(ierr);
511   }
512 
513   ierr = PetscFinalize();
514   return ierr;
515 }
516 
517 /*TEST
518 
519   test:
520     suffix: 0
521     nsize: 4
522     requires: !single
523     args: -cells 2,2,1 -max_conv_its 2 -petscspace_degree 2 -snes_max_it 2 -ksp_max_it 100 -ksp_type cg -ksp_rtol 1.e-11 -ksp_norm_type unpreconditioned -snes_rtol 1.e-10 -pc_type gamg -pc_gamg_type agg -pc_gamg_agg_nsmooths 1 -pc_gamg_coarse_eq_limit 1000 -pc_gamg_reuse_interpolation true -pc_gamg_square_graph 1 -pc_gamg_threshold 0.05 -pc_gamg_threshold_scale .0 -ksp_converged_reason -snes_monitor_short -ksp_monitor_short -snes_converged_reason -use_mat_nearnullspace true -mg_levels_ksp_max_it 1 -mg_levels_ksp_type chebyshev -pc_gamg_esteig_ksp_type cg -pc_gamg_esteig_ksp_max_it 10 -mg_levels_ksp_chebyshev_esteig 0,0.05,0,1.1 -mg_levels_pc_type jacobi -petscpartitioner_type simple -mat_block_size 3 -matptap_via scalable -ex56_dm_view -run_type 1
524     timeoutfactor: 2
525 
526   # HYPRE PtAP broken with complex numbers
527   test:
528     suffix: hypre
529     requires: hypre !single !complex
530     nsize: 4
531     args: -cells 2,2,1 -max_conv_its 2 -lx 1. -alpha .01 -ex56_dm_refine 1 -petscspace_degree 2 -ksp_type cg -ksp_monitor_short -ksp_rtol 1.e-8 -pc_type hypre -pc_hypre_type boomeramg -pc_hypre_boomeramg_no_CF true -pc_hypre_boomeramg_agg_nl 1 -pc_hypre_boomeramg_coarsen_type HMIS -pc_hypre_boomeramg_interp_type ext+i -ksp_converged_reason -use_mat_nearnullspace true -mat_block_size 3 -petscpartitioner_type simple
532 
533   test:
534     suffix: ml
535     requires: ml !single
536     nsize: 4
537     args: -cells 2,2,1 -max_conv_its 2 -lx 1. -alpha .01 -ex56_dm_refine 1 -petscspace_degree 2 -ksp_type cg -ksp_monitor_short -ksp_converged_reason -ksp_rtol 1.e-8 -pc_type ml -mg_levels_ksp_type chebyshev -mg_levels_ksp_max_it 3 -mg_levels_esteig_ksp_max_it 10 -mg_levels_ksp_chebyshev_esteig 0,0.05,0,1.05 -mg_levels_pc_type sor -mg_levels_esteig_ksp_type cg -mat_block_size 3 -petscpartitioner_type simple -use_mat_nearnullspace
538 
539   test:
540     suffix: hpddm
541     requires: hpddm slepc !single
542     nsize: 4
543     args: -cells 2,2,1 -max_conv_its 2 -lx 1. -alpha .01 -ex56_dm_refine 1 -petscspace_degree 2 -ksp_type fgmres -ksp_monitor_short -ksp_converged_reason -ksp_rtol 1.e-8 -pc_type hpddm -mat_block_size 3 -petscpartitioner_type simple -pc_hpddm_levels_1_sub_pc_type lu -pc_hpddm_levels_1_eps_nev 6 -pc_hpddm_coarse_p 1 -pc_hpddm_coarse_pc_type svd
544 
545   test:
546     nsize: 4
547     requires: parmetis !single
548     args: -cells 2,2,1 -max_conv_its 2 -petscspace_degree 2 -snes_max_it 2 -ksp_max_it 100 -ksp_type cg -ksp_rtol 1.e-11 -ksp_norm_type unpreconditioned -snes_rtol 1.e-10 -pc_type gamg -pc_gamg_type agg -pc_gamg_agg_nsmooths 1 -pc_gamg_coarse_eq_limit 10 -pc_gamg_reuse_interpolation true -pc_gamg_square_graph 1 -pc_gamg_threshold 0.05 -pc_gamg_threshold_scale .0 -snes_converged_reason -use_mat_nearnullspace true -mg_levels_ksp_max_it 1 -mg_levels_ksp_type chebyshev -pc_gamg_esteig_ksp_type cg -pc_gamg_esteig_ksp_max_it 10 -mg_levels_ksp_chebyshev_esteig 0,0.05,0,1.05 -mg_levels_pc_type jacobi -pc_gamg_mat_partitioning_type parmetis -mat_block_size 3 -run_type 1 -pc_gamg_repartition true
549 
550   test:
551     suffix: bddc
552     nsize: 4
553     requires: !single
554     args: -cells 2,2,1 -max_conv_its 2 -lx 1. -alpha .01 -ex56_dm_refine 1 -petscspace_degree 2 -ksp_type cg -ksp_monitor_short -ksp_rtol 1.e-8 -ksp_converged_reason -mat_block_size 3 -petscpartitioner_type simple -ex56_dm_mat_type is -matis_localmat_type {{sbaij baij aij}} -pc_type bddc
555 
556   testset:
557     nsize: 4
558     requires: !single
559     args: -cells 2,2,1 -max_conv_its 2 -lx 1. -alpha .01 -ex56_dm_refine 1 -petscspace_degree 2 -ksp_type cg -ksp_monitor_short -ksp_rtol 1.e-10 -ksp_converged_reason -mat_block_size 3 -petscpartitioner_type simple -ex56_dm_mat_type is -matis_localmat_type aij -pc_type bddc -attach_mat_nearnullspace {{0 1}separate output}
560     test:
561       suffix: bddc_approx_gamg
562       args: -pc_bddc_switch_static -prefix_push pc_bddc_dirichlet_ -approximate -pc_type gamg -pc_gamg_type agg -pc_gamg_agg_nsmooths 1 -pc_gamg_coarse_eq_limit 10 -pc_gamg_reuse_interpolation true -pc_gamg_square_graph 1 -pc_gamg_threshold 0.05 -pc_gamg_threshold_scale .0 -mg_levels_ksp_max_it 1 -mg_levels_ksp_type chebyshev -mg_levels_esteig_ksp_type cg -mg_levels_esteig_ksp_max_it 10 -pc_gamg_esteig_ksp_type cg -pc_gamg_esteig_ksp_max_it 10 -prefix_pop -prefix_push pc_bddc_neumann_ -approximate -pc_type gamg -pc_gamg_type agg -pc_gamg_agg_nsmooths 1 -pc_gamg_coarse_eq_limit 10 -pc_gamg_reuse_interpolation true -pc_gamg_square_graph 1 -pc_gamg_threshold 0.05 -pc_gamg_threshold_scale .0 -mg_levels_ksp_max_it 1 -mg_levels_ksp_type chebyshev -mg_levels_esteig_ksp_type cg -mg_levels_esteig_ksp_max_it 10 -pc_gamg_esteig_ksp_type cg -pc_gamg_esteig_ksp_max_it 10 -prefix_pop
563     # HYPRE PtAP broken with complex numbers
564     test:
565       requires: hypre !complex
566       suffix: bddc_approx_hypre
567       args: -pc_bddc_switch_static -prefix_push pc_bddc_dirichlet_ -pc_type hypre -pc_hypre_boomeramg_no_CF true -pc_hypre_boomeramg_strong_threshold 0.75 -pc_hypre_boomeramg_agg_nl 1 -pc_hypre_boomeramg_coarsen_type HMIS -pc_hypre_boomeramg_interp_type ext+i -prefix_pop -prefix_push pc_bddc_neumann_ -pc_type hypre -pc_hypre_boomeramg_no_CF true -pc_hypre_boomeramg_strong_threshold 0.75 -pc_hypre_boomeramg_agg_nl 1 -pc_hypre_boomeramg_coarsen_type HMIS -pc_hypre_boomeramg_interp_type ext+i -prefix_pop
568     test:
569       requires: ml
570       suffix: bddc_approx_ml
571       args: -pc_bddc_switch_static -prefix_push pc_bddc_dirichlet_ -approximate -pc_type ml -mg_levels_ksp_max_it 1 -mg_levels_ksp_type chebyshev -mg_levels_esteig_ksp_type cg -mg_levels_esteig_ksp_max_it 10 -prefix_pop -prefix_push pc_bddc_neumann_ -approximate -pc_type ml -mg_levels_ksp_max_it 1 -mg_levels_ksp_type chebyshev -mg_levels_esteig_ksp_type cg -mg_levels_esteig_ksp_max_it 10 -prefix_pop
572 
573   test:
574     suffix: fetidp
575     nsize: 4
576     requires: !single
577     args: -cells 2,2,1 -max_conv_its 2 -lx 1. -alpha .01 -ex56_dm_refine 1 -petscspace_degree 2 -ksp_type fetidp -fetidp_ksp_type cg -ksp_monitor_short -ksp_rtol 1.e-8 -ksp_converged_reason -mat_block_size 3 -petscpartitioner_type simple -ex56_dm_mat_type is -matis_localmat_type {{sbaij baij aij}}
578 
579   test:
580     suffix: bddc_elast
581     nsize: 4
582     requires: !single
583     args: -cells 2,2,1 -max_conv_its 2 -lx 1. -alpha .01 -ex56_dm_refine 1 -petscspace_degree 2 -ksp_type cg -ksp_monitor_short -ksp_rtol 1.e-8 -ksp_converged_reason -mat_block_size 3 -petscpartitioner_type simple -ex56_dm_mat_type is -matis_localmat_type sbaij -pc_type bddc -pc_bddc_monolithic -attach_mat_nearnullspace
584 
585   test:
586     suffix: fetidp_elast
587     nsize: 4
588     requires: !single
589     args: -cells 2,2,1 -max_conv_its 2 -lx 1. -alpha .01 -ex56_dm_refine 1 -petscspace_degree 2 -ksp_type fetidp -fetidp_ksp_type cg -ksp_monitor_short -ksp_rtol 1.e-8 -ksp_converged_reason -mat_block_size 3 -petscpartitioner_type simple -ex56_dm_mat_type is -matis_localmat_type sbaij -fetidp_bddc_pc_bddc_monolithic -attach_mat_nearnullspace
590 
591   test:
592     suffix: cuda
593     nsize: 2
594     requires: cuda !single
595     args: -cells 2,2,1 -max_conv_its 2 -petscspace_degree 2 -snes_max_it 2 -ksp_max_it 100 -ksp_type cg -ksp_rtol 1.e-11 -ksp_norm_type unpreconditioned -snes_rtol 1.e-10 -pc_type gamg -pc_gamg_type agg -pc_gamg_agg_nsmooths 1 -pc_gamg_coarse_eq_limit 10 -pc_gamg_reuse_interpolation true -pc_gamg_square_graph 1 -pc_gamg_threshold 0.05 -pc_gamg_threshold_scale .0 -snes_converged_reason -use_mat_nearnullspace true -mg_levels_ksp_max_it 1 -mg_levels_ksp_type chebyshev -pc_gamg_esteig_ksp_type cg -pc_gamg_esteig_ksp_max_it 10 -mg_levels_ksp_chebyshev_esteig 0,0.05,0,1.05 -mg_levels_pc_type jacobi -mat_block_size 3 -run_type 1 -ex56_dm_mat_type aijcusparse -ex56_dm_vec_type cuda -ksp_monitor_short
596 
597 TEST*/
598