Actual source code: ex56.c

  1: static char help[] = "3D, tri-linear quadrilateral (Q1), displacement finite element formulation\n\
  2: of linear elasticity.  E=1.0, nu=0.25.\n\
  3: Unit square domain with Dirichelet boundary condition on the y=0 side only.\n\
  4: Load of 1.0 in x + 2y direction on all nodes (not a true uniform load).\n\
  5:   -ne <size>      : number of (square) quadrilateral elements in each dimension\n\
  6:   -alpha <v>      : scaling of material coefficient in embedded circle\n\n";

  8: #include <petscksp.h>

 10: static PetscBool log_stages = PETSC_TRUE;

 12: static PetscErrorCode MaybeLogStagePush(PetscLogStage stage)
 13: {
 14:   return log_stages ? PetscLogStagePush(stage) : PETSC_SUCCESS;
 15: }

 17: static PetscErrorCode MaybeLogStagePop(void)
 18: {
 19:   return log_stages ? PetscLogStagePop() : PETSC_SUCCESS;
 20: }

 22: PetscErrorCode elem_3d_elast_v_25(PetscScalar *);

 24: int main(int argc, char **args)
 25: {
 26:   Mat           Amat;
 27:   PetscInt      m, nn, M, Istart, Iend, i, j, k, ii, jj, kk, ic, ne = 4, id;
 28:   PetscReal     x, y, z, h, *coords, soft_alpha = 1.e-3;
 29:   PetscBool     two_solves = PETSC_FALSE, test_nonzero_cols = PETSC_FALSE, use_nearnullspace = PETSC_FALSE, test_late_bs = PETSC_FALSE;
 30:   Vec           xx, bb;
 31:   KSP           ksp;
 32:   MPI_Comm      comm;
 33:   PetscMPIInt   npe, mype;
 34:   PetscScalar   DD[24][24], DD2[24][24];
 35:   PetscLogStage stage[6];
 36:   PetscScalar   DD1[24][24];

 38:   PetscFunctionBeginUser;
 39:   PetscCall(PetscInitialize(&argc, &args, NULL, help));
 40:   comm = PETSC_COMM_WORLD;
 41:   PetscCallMPI(MPI_Comm_rank(comm, &mype));
 42:   PetscCallMPI(MPI_Comm_size(comm, &npe));

 44:   PetscOptionsBegin(comm, NULL, "3D bilinear Q1 elasticity options", "");
 45:   {
 46:     char nestring[256];
 47:     PetscCall(PetscSNPrintf(nestring, sizeof nestring, "number of elements in each direction, ne+1 must be a multiple of %" PetscInt_FMT " (sizes^{1/3})", (PetscInt)(PetscPowReal((PetscReal)npe, 1. / 3.) + .5)));
 48:     PetscCall(PetscOptionsInt("-ne", nestring, "", ne, &ne, NULL));
 49:     PetscCall(PetscOptionsBool("-log_stages", "Log stages of solve separately", "", log_stages, &log_stages, NULL));
 50:     PetscCall(PetscOptionsReal("-alpha", "material coefficient inside circle", "", soft_alpha, &soft_alpha, NULL));
 51:     PetscCall(PetscOptionsBool("-two_solves", "solve additional variant of the problem", "", two_solves, &two_solves, NULL));
 52:     PetscCall(PetscOptionsBool("-test_nonzero_cols", "nonzero test", "", test_nonzero_cols, &test_nonzero_cols, NULL));
 53:     PetscCall(PetscOptionsBool("-use_mat_nearnullspace", "MatNearNullSpace API test", "", use_nearnullspace, &use_nearnullspace, NULL));
 54:     PetscCall(PetscOptionsBool("-test_late_bs", "", "", test_late_bs, &test_late_bs, NULL));
 55:   }
 56:   PetscOptionsEnd();

 58:   if (log_stages) {
 59:     PetscCall(PetscLogStageRegister("Setup", &stage[0]));
 60:     PetscCall(PetscLogStageRegister("Solve", &stage[1]));
 61:     PetscCall(PetscLogStageRegister("2nd Setup", &stage[2]));
 62:     PetscCall(PetscLogStageRegister("2nd Solve", &stage[3]));
 63:     PetscCall(PetscLogStageRegister("3rd Setup", &stage[4]));
 64:     PetscCall(PetscLogStageRegister("3rd Solve", &stage[5]));
 65:   } else {
 66:     for (i = 0; i < (PetscInt)PETSC_STATIC_ARRAY_LENGTH(stage); i++) stage[i] = -1;
 67:   }

 69:   h  = 1. / ne;
 70:   nn = ne + 1;
 71:   /* ne*ne; number of global elements */
 72:   M = 3 * nn * nn * nn; /* global number of equations */
 73:   if (npe == 2) {
 74:     if (mype == 1) m = 0;
 75:     else m = nn * nn * nn;
 76:     npe = 1;
 77:   } else {
 78:     m = nn * nn * nn / npe;
 79:     if (mype == npe - 1) m = nn * nn * nn - (npe - 1) * m;
 80:   }
 81:   m *= 3; /* number of equations local*/
 82:   /* Setup solver */
 83:   PetscCall(KSPCreate(PETSC_COMM_WORLD, &ksp));
 84:   PetscCall(KSPSetComputeSingularValues(ksp, PETSC_TRUE));
 85:   PetscCall(KSPSetFromOptions(ksp));
 86:   {
 87:     /* configuration */
 88:     const PetscInt NP  = (PetscInt)(PetscPowReal((PetscReal)npe, 1. / 3.) + .5);
 89:     const PetscInt ipx = mype % NP, ipy = (mype % (NP * NP)) / NP, ipz = mype / (NP * NP);
 90:     const PetscInt Ni0 = ipx * (nn / NP), Nj0 = ipy * (nn / NP), Nk0 = ipz * (nn / NP);
 91:     const PetscInt Ni1 = Ni0 + (m > 0 ? (nn / NP) : 0), Nj1 = Nj0 + (nn / NP), Nk1 = Nk0 + (nn / NP);
 92:     const PetscInt NN = nn / NP, id0 = ipz * nn * nn * NN + ipy * nn * NN * NN + ipx * NN * NN * NN;
 93:     PetscInt      *d_nnz, *o_nnz, osz[4] = {0, 9, 15, 19}, nbc;
 94:     PetscScalar    vv[24], v2[24];
 95:     PetscCheck(npe == NP * NP * NP, comm, PETSC_ERR_ARG_WRONG, "npe=%d: npe^{1/3} must be integer", npe);
 96:     PetscCheck(nn == NP * (nn / NP), comm, PETSC_ERR_ARG_WRONG, "-ne %" PetscInt_FMT ": (ne+1)%%(npe^{1/3}) must equal zero", ne);

 98:     /* count nnz */
 99:     PetscCall(PetscMalloc1(m + 1, &d_nnz));
100:     PetscCall(PetscMalloc1(m + 1, &o_nnz));
101:     for (i = Ni0, ic = 0; i < Ni1; i++) {
102:       for (j = Nj0; j < Nj1; j++) {
103:         for (k = Nk0; k < Nk1; k++) {
104:           nbc = 0;
105:           if (i == Ni0 || i == Ni1 - 1) nbc++;
106:           if (j == Nj0 || j == Nj1 - 1) nbc++;
107:           if (k == Nk0 || k == Nk1 - 1) nbc++;
108:           for (jj = 0; jj < 3; jj++, ic++) {
109:             d_nnz[ic] = 3 * (27 - osz[nbc]);
110:             o_nnz[ic] = 3 * osz[nbc];
111:           }
112:         }
113:       }
114:     }
115:     PetscCheck(ic == m, PETSC_COMM_SELF, PETSC_ERR_PLIB, "ic %" PetscInt_FMT " does not equal m %" PetscInt_FMT, ic, m);

117:     /* create stiffness matrix */
118:     PetscCall(MatCreate(comm, &Amat));
119:     PetscCall(MatSetSizes(Amat, m, m, M, M));
120:     if (!test_late_bs) PetscCall(MatSetBlockSize(Amat, 3));
121:     PetscCall(MatSetType(Amat, MATAIJ));
122:     PetscCall(MatSetOption(Amat, MAT_SPD, PETSC_TRUE));
123:     PetscCall(MatSetOption(Amat, MAT_SPD_ETERNAL, PETSC_TRUE)); // this keeps CG after switch to negative
124:     PetscCall(MatSetFromOptions(Amat));
125:     PetscCall(MatSeqAIJSetPreallocation(Amat, 0, d_nnz));
126:     PetscCall(MatMPIAIJSetPreallocation(Amat, 0, d_nnz, 0, o_nnz));

128:     PetscCall(PetscFree(d_nnz));
129:     PetscCall(PetscFree(o_nnz));
130:     PetscCall(MatCreateVecs(Amat, &bb, &xx));

132:     PetscCall(MatGetOwnershipRange(Amat, &Istart, &Iend));

134:     PetscCheck(m == Iend - Istart, PETSC_COMM_SELF, PETSC_ERR_PLIB, "m %" PetscInt_FMT " does not equal Iend %" PetscInt_FMT " - Istart %" PetscInt_FMT, m, Iend, Istart);
135:     /* generate element matrices */
136:     {
137:       PetscBool hasData = PETSC_TRUE;
138:       if (!hasData) {
139:         PetscCall(PetscPrintf(PETSC_COMM_WORLD, "\t No data is provided\n"));
140:         for (i = 0; i < 24; i++) {
141:           for (j = 0; j < 24; j++) {
142:             if (i == j) DD1[i][j] = 1.0;
143:             else DD1[i][j] = -.25;
144:           }
145:         }
146:       } else {
147:         /* Get array data */
148:         PetscCall(elem_3d_elast_v_25((PetscScalar *)DD1));
149:       }

151:       /* BC version of element */
152:       for (i = 0; i < 24; i++) {
153:         for (j = 0; j < 24; j++) {
154:           if (i < 12 || (j < 12 && !test_nonzero_cols)) {
155:             if (i == j) DD2[i][j] = 0.1 * DD1[i][j];
156:             else DD2[i][j] = 0.0;
157:           } else DD2[i][j] = DD1[i][j];
158:         }
159:       }
160:       /* element residual/load vector */
161:       for (i = 0; i < 24; i++) {
162:         if (i % 3 == 0) vv[i] = h * h;
163:         else if (i % 3 == 1) vv[i] = 2.0 * h * h;
164:         else vv[i] = .0;
165:       }
166:       for (i = 0; i < 24; i++) {
167:         if (i % 3 == 0 && i >= 12) v2[i] = h * h;
168:         else if (i % 3 == 1 && i >= 12) v2[i] = 2.0 * h * h;
169:         else v2[i] = .0;
170:       }
171:     }

173:     PetscCall(PetscMalloc1(m + 1, &coords));
174:     coords[m] = -99.0;

176:     /* forms the element stiffness and coordinates */
177:     for (i = Ni0, ic = 0, ii = 0; i < Ni1; i++, ii++) {
178:       for (j = Nj0, jj = 0; j < Nj1; j++, jj++) {
179:         for (k = Nk0, kk = 0; k < Nk1; k++, kk++, ic++) {
180:           /* coords */
181:           x = coords[3 * ic] = h * (PetscReal)i;
182:           y = coords[3 * ic + 1] = h * (PetscReal)j;
183:           z = coords[3 * ic + 2] = h * (PetscReal)k;
184:           /* matrix */
185:           id = id0 + ii + NN * jj + NN * NN * kk;
186:           if (i < ne && j < ne && k < ne) {
187:             /* radius */
188:             PetscReal radius = PetscSqrtReal((x - .5 + h / 2) * (x - .5 + h / 2) + (y - .5 + h / 2) * (y - .5 + h / 2) + (z - .5 + h / 2) * (z - .5 + h / 2));
189:             PetscReal alpha  = 1.0;
190:             PetscInt  jx, ix, idx[8], idx3[24];
191:             idx[0] = id;
192:             idx[1] = id + 1;
193:             idx[2] = id + NN + 1;
194:             idx[3] = id + NN;
195:             idx[4] = id + NN * NN;
196:             idx[5] = id + 1 + NN * NN;
197:             idx[6] = id + NN + 1 + NN * NN;
198:             idx[7] = id + NN + NN * NN;

200:             /* correct indices */
201:             if (i == Ni1 - 1 && Ni1 != nn) {
202:               idx[1] += NN * (NN * NN - 1);
203:               idx[2] += NN * (NN * NN - 1);
204:               idx[5] += NN * (NN * NN - 1);
205:               idx[6] += NN * (NN * NN - 1);
206:             }
207:             if (j == Nj1 - 1 && Nj1 != nn) {
208:               idx[2] += NN * NN * (nn - 1);
209:               idx[3] += NN * NN * (nn - 1);
210:               idx[6] += NN * NN * (nn - 1);
211:               idx[7] += NN * NN * (nn - 1);
212:             }
213:             if (k == Nk1 - 1 && Nk1 != nn) {
214:               idx[4] += NN * (nn * nn - NN * NN);
215:               idx[5] += NN * (nn * nn - NN * NN);
216:               idx[6] += NN * (nn * nn - NN * NN);
217:               idx[7] += NN * (nn * nn - NN * NN);
218:             }

220:             if (radius < 0.25) alpha = soft_alpha;

222:             for (ix = 0; ix < 24; ix++) {
223:               for (jx = 0; jx < 24; jx++) DD[ix][jx] = alpha * DD1[ix][jx];
224:             }
225:             if (k > 0) {
226:               if (!test_late_bs) {
227:                 PetscCall(MatSetValuesBlocked(Amat, 8, idx, 8, idx, (const PetscScalar *)DD, ADD_VALUES));
228:                 PetscCall(VecSetValuesBlocked(bb, 8, idx, (const PetscScalar *)vv, ADD_VALUES));
229:               } else {
230:                 for (ix = 0; ix < 8; ix++) {
231:                   idx3[3 * ix]     = 3 * idx[ix];
232:                   idx3[3 * ix + 1] = 3 * idx[ix] + 1;
233:                   idx3[3 * ix + 2] = 3 * idx[ix] + 2;
234:                 }
235:                 PetscCall(MatSetValues(Amat, 24, idx3, 24, idx3, (const PetscScalar *)DD, ADD_VALUES));
236:                 PetscCall(VecSetValues(bb, 24, idx3, (const PetscScalar *)vv, ADD_VALUES));
237:               }
238:             } else {
239:               /* a BC */
240:               for (ix = 0; ix < 24; ix++) {
241:                 for (jx = 0; jx < 24; jx++) DD[ix][jx] = alpha * DD2[ix][jx];
242:               }
243:               if (!test_late_bs) {
244:                 PetscCall(MatSetValuesBlocked(Amat, 8, idx, 8, idx, (const PetscScalar *)DD, ADD_VALUES));
245:                 PetscCall(VecSetValuesBlocked(bb, 8, idx, (const PetscScalar *)v2, ADD_VALUES));
246:               } else {
247:                 for (ix = 0; ix < 8; ix++) {
248:                   idx3[3 * ix]     = 3 * idx[ix];
249:                   idx3[3 * ix + 1] = 3 * idx[ix] + 1;
250:                   idx3[3 * ix + 2] = 3 * idx[ix] + 2;
251:                 }
252:                 PetscCall(MatSetValues(Amat, 24, idx3, 24, idx3, (const PetscScalar *)DD, ADD_VALUES));
253:                 PetscCall(VecSetValues(bb, 24, idx3, (const PetscScalar *)v2, ADD_VALUES));
254:               }
255:             }
256:           }
257:         }
258:       }
259:     }
260:     PetscCall(MatAssemblyBegin(Amat, MAT_FINAL_ASSEMBLY));
261:     PetscCall(MatAssemblyEnd(Amat, MAT_FINAL_ASSEMBLY));
262:     PetscCall(VecAssemblyBegin(bb));
263:     PetscCall(VecAssemblyEnd(bb));
264:   }
265:   PetscCall(MatAssemblyBegin(Amat, MAT_FINAL_ASSEMBLY));
266:   PetscCall(MatAssemblyEnd(Amat, MAT_FINAL_ASSEMBLY));
267:   PetscCall(VecAssemblyBegin(bb));
268:   PetscCall(VecAssemblyEnd(bb));
269:   if (test_late_bs) {
270:     PetscCall(VecSetBlockSize(xx, 3));
271:     PetscCall(VecSetBlockSize(bb, 3));
272:     PetscCall(MatSetBlockSize(Amat, 3));
273:   }

275:   if (!PETSC_TRUE) {
276:     PetscViewer viewer;
277:     PetscCall(PetscViewerASCIIOpen(comm, "Amat.m", &viewer));
278:     PetscCall(PetscViewerPushFormat(viewer, PETSC_VIEWER_ASCII_MATLAB));
279:     PetscCall(MatView(Amat, viewer));
280:     PetscCall(PetscViewerPopFormat(viewer));
281:     PetscCall(PetscViewerDestroy(&viewer));
282:   }

284:   /* finish KSP/PC setup */
285:   PetscCall(KSPSetOperators(ksp, Amat, Amat));
286:   if (use_nearnullspace) {
287:     MatNullSpace matnull;
288:     Vec          vec_coords;
289:     PetscScalar *c;
290:     PC           pc;
291:     PetscCall(VecCreate(MPI_COMM_WORLD, &vec_coords));
292:     PetscCall(VecSetBlockSize(vec_coords, 3));
293:     PetscCall(VecSetSizes(vec_coords, m, PETSC_DECIDE));
294:     PetscCall(VecSetUp(vec_coords));
295:     PetscCall(VecGetArray(vec_coords, &c));
296:     for (i = 0; i < m; i++) c[i] = coords[i]; /* Copy since Scalar type might be Complex */
297:     PetscCall(VecRestoreArray(vec_coords, &c));
298:     PetscCall(MatNullSpaceCreateRigidBody(vec_coords, &matnull));
299:     PetscCall(MatSetNearNullSpace(Amat, matnull));
300:     PetscCall(MatNullSpaceDestroy(&matnull));
301:     PetscCall(VecDestroy(&vec_coords));
302:     PetscCall(KSPGetPC(ksp, &pc));
303:     PetscCall(PCJacobiSetRowl1Scale(pc, 0.5));
304:   } else {
305:     PC       pc;
306:     PetscInt idx[] = {1, 2};
307:     PetscCall(KSPGetPC(ksp, &pc));
308:     PetscCall(PCSetCoordinates(pc, 3, m / 3, coords));
309:     PetscCall(PCGAMGSetUseSAEstEig(pc, PETSC_FALSE));
310:     PetscCall(PCGAMGSetLowMemoryFilter(pc, PETSC_TRUE));
311:     PetscCall(PCGAMGMISkSetMinDegreeOrdering(pc, PETSC_TRUE));
312:     PetscCall(PCGAMGSetAggressiveSquareGraph(pc, PETSC_FALSE));
313:     PetscCall(PCGAMGSetInjectionIndex(pc, 2, idx)); // code coverage, same as command line
314:   }

316:   PetscCall(MaybeLogStagePush(stage[0]));

318:   /* PC setup basically */
319:   PetscCall(KSPSetUp(ksp));

321:   PetscCall(MaybeLogStagePop());
322:   PetscCall(MaybeLogStagePush(stage[1]));

324:   /* test BCs */
325:   if (test_nonzero_cols) {
326:     PetscCall(VecZeroEntries(xx));
327:     if (mype == 0) PetscCall(VecSetValue(xx, 0, 1.0, INSERT_VALUES));
328:     PetscCall(VecAssemblyBegin(xx));
329:     PetscCall(VecAssemblyEnd(xx));
330:     PetscCall(KSPSetInitialGuessNonzero(ksp, PETSC_TRUE));
331:   }

333:   /* 1st solve */
334:   PetscCall(KSPSolve(ksp, bb, xx));

336:   PetscCall(MaybeLogStagePop());

338:   /* 2nd solve */
339:   if (two_solves) {
340:     PetscReal emax, emin;
341:     PetscReal norm, norm2;
342:     Vec       res;

344:     PetscCall(MaybeLogStagePush(stage[2]));
345:     /* PC setup basically */
346:     PetscCall(MatScale(Amat, -100000.0));
347:     PetscCall(MatSetOption(Amat, MAT_SPD, PETSC_FALSE));
348:     PetscCall(KSPSetOperators(ksp, Amat, Amat));
349:     PetscCall(KSPSetUp(ksp));

351:     PetscCall(MaybeLogStagePop());
352:     PetscCall(MaybeLogStagePush(stage[3]));
353:     PetscCall(KSPSolve(ksp, bb, xx));
354:     PetscCall(KSPComputeExtremeSingularValues(ksp, &emax, &emin));

356:     PetscCall(MaybeLogStagePop());
357:     PetscCall(MaybeLogStagePush(stage[4]));

359:     PetscCall(MaybeLogStagePop());
360:     PetscCall(MaybeLogStagePush(stage[5]));

362:     /* 3rd solve */
363:     PetscCall(KSPSolve(ksp, bb, xx));

365:     PetscCall(MaybeLogStagePop());

367:     PetscCall(VecNorm(bb, NORM_2, &norm2));

369:     PetscCall(VecDuplicate(xx, &res));
370:     PetscCall(MatMult(Amat, xx, res));
371:     PetscCall(VecAXPY(bb, -1.0, res));
372:     PetscCall(VecDestroy(&res));
373:     PetscCall(VecNorm(bb, NORM_2, &norm));
374:     PetscCall(PetscPrintf(PETSC_COMM_WORLD, "[%d]%s |b-Ax|/|b|=%e, |b|=%e, emax=%e\n", 0, PETSC_FUNCTION_NAME, (double)(norm / norm2), (double)norm2, (double)emax));
375:   }

377:   /* Free work space */
378:   PetscCall(KSPDestroy(&ksp));
379:   PetscCall(VecDestroy(&xx));
380:   PetscCall(VecDestroy(&bb));
381:   PetscCall(MatDestroy(&Amat));
382:   PetscCall(PetscFree(coords));

384:   PetscCall(PetscFinalize());
385:   return 0;
386: }

388: /* Data was previously provided in the file data/elem_3d_elast_v_25.tx */
389: PetscErrorCode elem_3d_elast_v_25(PetscScalar *dd)
390: {
391:   PetscScalar DD[] = {
392:     0.18981481481481474,       5.27777777777777568E-002,  5.27777777777777568E-002,  -5.64814814814814659E-002, -1.38888888888889072E-002, -1.38888888888889089E-002, -8.24074074074073876E-002, -5.27777777777777429E-002, 1.38888888888888725E-002,
393:     4.90740740740740339E-002,  1.38888888888889124E-002,  4.72222222222222071E-002,  4.90740740740740339E-002,  4.72222222222221932E-002,  1.38888888888888968E-002,  -8.24074074074073876E-002, 1.38888888888888673E-002,  -5.27777777777777429E-002,
394:     -7.87037037037036785E-002, -4.72222222222221932E-002, -4.72222222222222071E-002, 1.20370370370370180E-002,  -1.38888888888888742E-002, -1.38888888888888829E-002, 5.27777777777777568E-002,  0.18981481481481474,       5.27777777777777568E-002,
395:     1.38888888888889124E-002,  4.90740740740740269E-002,  4.72222222222221932E-002,  -5.27777777777777637E-002, -8.24074074074073876E-002, 1.38888888888888725E-002,  -1.38888888888889037E-002, -5.64814814814814728E-002, -1.38888888888888985E-002,
396:     4.72222222222221932E-002,  4.90740740740740478E-002,  1.38888888888888968E-002,  -1.38888888888888673E-002, 1.20370370370370058E-002,  -1.38888888888888742E-002, -4.72222222222221932E-002, -7.87037037037036785E-002, -4.72222222222222002E-002,
397:     1.38888888888888742E-002,  -8.24074074074073598E-002, -5.27777777777777568E-002, 5.27777777777777568E-002,  5.27777777777777568E-002,  0.18981481481481474,       1.38888888888889055E-002,  4.72222222222222002E-002,  4.90740740740740269E-002,
398:     -1.38888888888888829E-002, -1.38888888888888829E-002, 1.20370370370370180E-002,  4.72222222222222002E-002,  1.38888888888888985E-002,  4.90740740740740339E-002,  -1.38888888888888985E-002, -1.38888888888888968E-002, -5.64814814814814520E-002,
399:     -5.27777777777777568E-002, 1.38888888888888777E-002,  -8.24074074074073876E-002, -4.72222222222222002E-002, -4.72222222222221932E-002, -7.87037037037036646E-002, 1.38888888888888794E-002,  -5.27777777777777568E-002, -8.24074074074073598E-002,
400:     -5.64814814814814659E-002, 1.38888888888889124E-002,  1.38888888888889055E-002,  0.18981481481481474,       -5.27777777777777568E-002, -5.27777777777777499E-002, 4.90740740740740269E-002,  -1.38888888888889072E-002, -4.72222222222221932E-002,
401:     -8.24074074074073876E-002, 5.27777777777777568E-002,  -1.38888888888888812E-002, -8.24074074074073876E-002, -1.38888888888888742E-002, 5.27777777777777499E-002,  4.90740740740740269E-002,  -4.72222222222221863E-002, -1.38888888888889089E-002,
402:     1.20370370370370162E-002,  1.38888888888888673E-002,  1.38888888888888742E-002,  -7.87037037037036785E-002, 4.72222222222222002E-002,  4.72222222222222071E-002,  -1.38888888888889072E-002, 4.90740740740740269E-002,  4.72222222222222002E-002,
403:     -5.27777777777777568E-002, 0.18981481481481480,       5.27777777777777568E-002,  1.38888888888889020E-002,  -5.64814814814814728E-002, -1.38888888888888951E-002, 5.27777777777777637E-002,  -8.24074074074073876E-002, 1.38888888888888881E-002,
404:     1.38888888888888742E-002,  1.20370370370370232E-002,  -1.38888888888888812E-002, -4.72222222222221863E-002, 4.90740740740740339E-002,  1.38888888888888933E-002,  -1.38888888888888812E-002, -8.24074074074073876E-002, -5.27777777777777568E-002,
405:     4.72222222222222071E-002,  -7.87037037037036924E-002, -4.72222222222222140E-002, -1.38888888888889089E-002, 4.72222222222221932E-002,  4.90740740740740269E-002,  -5.27777777777777499E-002, 5.27777777777777568E-002,  0.18981481481481477,
406:     -4.72222222222222071E-002, 1.38888888888888968E-002,  4.90740740740740131E-002,  1.38888888888888812E-002,  -1.38888888888888708E-002, 1.20370370370370267E-002,  5.27777777777777568E-002,  1.38888888888888812E-002,  -8.24074074074073876E-002,
407:     1.38888888888889124E-002,  -1.38888888888889055E-002, -5.64814814814814589E-002, -1.38888888888888812E-002, -5.27777777777777568E-002, -8.24074074074073737E-002, 4.72222222222222002E-002,  -4.72222222222222002E-002, -7.87037037037036924E-002,
408:     -8.24074074074073876E-002, -5.27777777777777637E-002, -1.38888888888888829E-002, 4.90740740740740269E-002,  1.38888888888889020E-002,  -4.72222222222222071E-002, 0.18981481481481480,       5.27777777777777637E-002,  -5.27777777777777637E-002,
409:     -5.64814814814814728E-002, -1.38888888888889037E-002, 1.38888888888888951E-002,  -7.87037037037036785E-002, -4.72222222222222002E-002, 4.72222222222221932E-002,  1.20370370370370128E-002,  -1.38888888888888725E-002, 1.38888888888888812E-002,
410:     4.90740740740740408E-002,  4.72222222222222002E-002,  -1.38888888888888951E-002, -8.24074074074073876E-002, 1.38888888888888812E-002,  5.27777777777777637E-002,  -5.27777777777777429E-002, -8.24074074074073876E-002, -1.38888888888888829E-002,
411:     -1.38888888888889072E-002, -5.64814814814814728E-002, 1.38888888888888968E-002,  5.27777777777777637E-002,  0.18981481481481480,       -5.27777777777777568E-002, 1.38888888888888916E-002,  4.90740740740740339E-002,  -4.72222222222222210E-002,
412:     -4.72222222222221932E-002, -7.87037037037036924E-002, 4.72222222222222002E-002,  1.38888888888888742E-002,  -8.24074074074073876E-002, 5.27777777777777429E-002,  4.72222222222222002E-002,  4.90740740740740269E-002,  -1.38888888888888951E-002,
413:     -1.38888888888888846E-002, 1.20370370370370267E-002,  1.38888888888888916E-002,  1.38888888888888725E-002,  1.38888888888888725E-002,  1.20370370370370180E-002,  -4.72222222222221932E-002, -1.38888888888888951E-002, 4.90740740740740131E-002,
414:     -5.27777777777777637E-002, -5.27777777777777568E-002, 0.18981481481481480,       -1.38888888888888968E-002, -4.72222222222221932E-002, 4.90740740740740339E-002,  4.72222222222221932E-002,  4.72222222222222071E-002,  -7.87037037037036646E-002,
415:     -1.38888888888888742E-002, 5.27777777777777499E-002,  -8.24074074074073737E-002, 1.38888888888888933E-002,  1.38888888888889020E-002,  -5.64814814814814589E-002, 5.27777777777777568E-002,  -1.38888888888888794E-002, -8.24074074074073876E-002,
416:     4.90740740740740339E-002,  -1.38888888888889037E-002, 4.72222222222222002E-002,  -8.24074074074073876E-002, 5.27777777777777637E-002,  1.38888888888888812E-002,  -5.64814814814814728E-002, 1.38888888888888916E-002,  -1.38888888888888968E-002,
417:     0.18981481481481480,       -5.27777777777777499E-002, 5.27777777777777707E-002,  1.20370370370370180E-002,  1.38888888888888812E-002,  -1.38888888888888812E-002, -7.87037037037036785E-002, 4.72222222222222002E-002,  -4.72222222222222071E-002,
418:     -8.24074074074073876E-002, -1.38888888888888742E-002, -5.27777777777777568E-002, 4.90740740740740616E-002,  -4.72222222222222002E-002, 1.38888888888888846E-002,  1.38888888888889124E-002,  -5.64814814814814728E-002, 1.38888888888888985E-002,
419:     5.27777777777777568E-002,  -8.24074074074073876E-002, -1.38888888888888708E-002, -1.38888888888889037E-002, 4.90740740740740339E-002,  -4.72222222222221932E-002, -5.27777777777777499E-002, 0.18981481481481480,       -5.27777777777777568E-002,
420:     -1.38888888888888673E-002, -8.24074074074073598E-002, 5.27777777777777429E-002,  4.72222222222222002E-002,  -7.87037037037036785E-002, 4.72222222222222002E-002,  1.38888888888888708E-002,  1.20370370370370128E-002,  1.38888888888888760E-002,
421:     -4.72222222222222002E-002, 4.90740740740740478E-002,  -1.38888888888888951E-002, 4.72222222222222071E-002,  -1.38888888888888985E-002, 4.90740740740740339E-002,  -1.38888888888888812E-002, 1.38888888888888881E-002,  1.20370370370370267E-002,
422:     1.38888888888888951E-002,  -4.72222222222222210E-002, 4.90740740740740339E-002,  5.27777777777777707E-002,  -5.27777777777777568E-002, 0.18981481481481477,       1.38888888888888829E-002,  5.27777777777777707E-002,  -8.24074074074073598E-002,
423:     -4.72222222222222140E-002, 4.72222222222222140E-002,  -7.87037037037036646E-002, -5.27777777777777707E-002, -1.38888888888888829E-002, -8.24074074074073876E-002, -1.38888888888888881E-002, 1.38888888888888881E-002,  -5.64814814814814589E-002,
424:     4.90740740740740339E-002,  4.72222222222221932E-002,  -1.38888888888888985E-002, -8.24074074074073876E-002, 1.38888888888888742E-002,  5.27777777777777568E-002,  -7.87037037037036785E-002, -4.72222222222221932E-002, 4.72222222222221932E-002,
425:     1.20370370370370180E-002,  -1.38888888888888673E-002, 1.38888888888888829E-002,  0.18981481481481469,       5.27777777777777429E-002,  -5.27777777777777429E-002, -5.64814814814814659E-002, -1.38888888888889055E-002, 1.38888888888889055E-002,
426:     -8.24074074074074153E-002, -5.27777777777777429E-002, -1.38888888888888760E-002, 4.90740740740740408E-002,  1.38888888888888968E-002,  -4.72222222222222071E-002, 4.72222222222221932E-002,  4.90740740740740478E-002,  -1.38888888888888968E-002,
427:     -1.38888888888888742E-002, 1.20370370370370232E-002,  1.38888888888888812E-002,  -4.72222222222222002E-002, -7.87037037037036924E-002, 4.72222222222222071E-002,  1.38888888888888812E-002,  -8.24074074074073598E-002, 5.27777777777777707E-002,
428:     5.27777777777777429E-002,  0.18981481481481477,       -5.27777777777777499E-002, 1.38888888888889107E-002,  4.90740740740740478E-002,  -4.72222222222221932E-002, -5.27777777777777568E-002, -8.24074074074074153E-002, -1.38888888888888812E-002,
429:     -1.38888888888888846E-002, -5.64814814814814659E-002, 1.38888888888888812E-002,  1.38888888888888968E-002,  1.38888888888888968E-002,  -5.64814814814814520E-002, 5.27777777777777499E-002,  -1.38888888888888812E-002, -8.24074074074073876E-002,
430:     4.72222222222221932E-002,  4.72222222222222002E-002,  -7.87037037037036646E-002, -1.38888888888888812E-002, 5.27777777777777429E-002,  -8.24074074074073598E-002, -5.27777777777777429E-002, -5.27777777777777499E-002, 0.18981481481481474,
431:     -1.38888888888888985E-002, -4.72222222222221863E-002, 4.90740740740740339E-002,  1.38888888888888829E-002,  1.38888888888888777E-002,  1.20370370370370249E-002,  -4.72222222222222002E-002, -1.38888888888888933E-002, 4.90740740740740339E-002,
432:     -8.24074074074073876E-002, -1.38888888888888673E-002, -5.27777777777777568E-002, 4.90740740740740269E-002,  -4.72222222222221863E-002, 1.38888888888889124E-002,  1.20370370370370128E-002,  1.38888888888888742E-002,  -1.38888888888888742E-002,
433:     -7.87037037037036785E-002, 4.72222222222222002E-002,  -4.72222222222222140E-002, -5.64814814814814659E-002, 1.38888888888889107E-002,  -1.38888888888888985E-002, 0.18981481481481474,       -5.27777777777777499E-002, 5.27777777777777499E-002,
434:     4.90740740740740339E-002,  -1.38888888888889055E-002, 4.72222222222221932E-002,  -8.24074074074074153E-002, 5.27777777777777499E-002,  1.38888888888888829E-002,  1.38888888888888673E-002,  1.20370370370370058E-002,  1.38888888888888777E-002,
435:     -4.72222222222221863E-002, 4.90740740740740339E-002,  -1.38888888888889055E-002, -1.38888888888888725E-002, -8.24074074074073876E-002, 5.27777777777777499E-002,  4.72222222222222002E-002,  -7.87037037037036785E-002, 4.72222222222222140E-002,
436:     -1.38888888888889055E-002, 4.90740740740740478E-002,  -4.72222222222221863E-002, -5.27777777777777499E-002, 0.18981481481481469,       -5.27777777777777499E-002, 1.38888888888889072E-002,  -5.64814814814814659E-002, 1.38888888888889003E-002,
437:     5.27777777777777429E-002,  -8.24074074074074153E-002, -1.38888888888888812E-002, -5.27777777777777429E-002, -1.38888888888888742E-002, -8.24074074074073876E-002, -1.38888888888889089E-002, 1.38888888888888933E-002,  -5.64814814814814589E-002,
438:     1.38888888888888812E-002,  5.27777777777777429E-002,  -8.24074074074073737E-002, -4.72222222222222071E-002, 4.72222222222222002E-002,  -7.87037037037036646E-002, 1.38888888888889055E-002,  -4.72222222222221932E-002, 4.90740740740740339E-002,
439:     5.27777777777777499E-002,  -5.27777777777777499E-002, 0.18981481481481474,       4.72222222222222002E-002,  -1.38888888888888985E-002, 4.90740740740740339E-002,  -1.38888888888888846E-002, 1.38888888888888812E-002,  1.20370370370370284E-002,
440:     -7.87037037037036785E-002, -4.72222222222221932E-002, -4.72222222222222002E-002, 1.20370370370370162E-002,  -1.38888888888888812E-002, -1.38888888888888812E-002, 4.90740740740740408E-002,  4.72222222222222002E-002,  1.38888888888888933E-002,
441:     -8.24074074074073876E-002, 1.38888888888888708E-002,  -5.27777777777777707E-002, -8.24074074074074153E-002, -5.27777777777777568E-002, 1.38888888888888829E-002,  4.90740740740740339E-002,  1.38888888888889072E-002,  4.72222222222222002E-002,
442:     0.18981481481481477,       5.27777777777777429E-002,  5.27777777777777568E-002,  -5.64814814814814659E-002, -1.38888888888888846E-002, -1.38888888888888881E-002, -4.72222222222221932E-002, -7.87037037037036785E-002, -4.72222222222221932E-002,
443:     1.38888888888888673E-002,  -8.24074074074073876E-002, -5.27777777777777568E-002, 4.72222222222222002E-002,  4.90740740740740269E-002,  1.38888888888889020E-002,  -1.38888888888888742E-002, 1.20370370370370128E-002,  -1.38888888888888829E-002,
444:     -5.27777777777777429E-002, -8.24074074074074153E-002, 1.38888888888888777E-002,  -1.38888888888889055E-002, -5.64814814814814659E-002, -1.38888888888888985E-002, 5.27777777777777429E-002,  0.18981481481481469,       5.27777777777777429E-002,
445:     1.38888888888888933E-002,  4.90740740740740339E-002,  4.72222222222222071E-002,  -4.72222222222222071E-002, -4.72222222222222002E-002, -7.87037037037036646E-002, 1.38888888888888742E-002,  -5.27777777777777568E-002, -8.24074074074073737E-002,
446:     -1.38888888888888951E-002, -1.38888888888888951E-002, -5.64814814814814589E-002, -5.27777777777777568E-002, 1.38888888888888760E-002,  -8.24074074074073876E-002, -1.38888888888888760E-002, -1.38888888888888812E-002, 1.20370370370370249E-002,
447:     4.72222222222221932E-002,  1.38888888888889003E-002,  4.90740740740740339E-002,  5.27777777777777568E-002,  5.27777777777777429E-002,  0.18981481481481474,       1.38888888888888933E-002,  4.72222222222222071E-002,  4.90740740740740339E-002,
448:     1.20370370370370180E-002,  1.38888888888888742E-002,  1.38888888888888794E-002,  -7.87037037037036785E-002, 4.72222222222222071E-002,  4.72222222222222002E-002,  -8.24074074074073876E-002, -1.38888888888888846E-002, 5.27777777777777568E-002,
449:     4.90740740740740616E-002,  -4.72222222222222002E-002, -1.38888888888888881E-002, 4.90740740740740408E-002,  -1.38888888888888846E-002, -4.72222222222222002E-002, -8.24074074074074153E-002, 5.27777777777777429E-002,  -1.38888888888888846E-002,
450:     -5.64814814814814659E-002, 1.38888888888888933E-002,  1.38888888888888933E-002,  0.18981481481481477,       -5.27777777777777568E-002, -5.27777777777777637E-002, -1.38888888888888742E-002, -8.24074074074073598E-002, -5.27777777777777568E-002,
451:     4.72222222222222002E-002,  -7.87037037037036924E-002, -4.72222222222222002E-002, 1.38888888888888812E-002,  1.20370370370370267E-002,  -1.38888888888888794E-002, -4.72222222222222002E-002, 4.90740740740740478E-002,  1.38888888888888881E-002,
452:     1.38888888888888968E-002,  -5.64814814814814659E-002, -1.38888888888888933E-002, 5.27777777777777499E-002,  -8.24074074074074153E-002, 1.38888888888888812E-002,  -1.38888888888888846E-002, 4.90740740740740339E-002,  4.72222222222222071E-002,
453:     -5.27777777777777568E-002, 0.18981481481481477,       5.27777777777777637E-002,  -1.38888888888888829E-002, -5.27777777777777568E-002, -8.24074074074073598E-002, 4.72222222222222071E-002,  -4.72222222222222140E-002, -7.87037037037036924E-002,
454:     5.27777777777777637E-002,  1.38888888888888916E-002,  -8.24074074074073876E-002, 1.38888888888888846E-002,  -1.38888888888888951E-002, -5.64814814814814589E-002, -4.72222222222222071E-002, 1.38888888888888812E-002,  4.90740740740740339E-002,
455:     1.38888888888888829E-002,  -1.38888888888888812E-002, 1.20370370370370284E-002,  -1.38888888888888881E-002, 4.72222222222222071E-002,  4.90740740740740339E-002,  -5.27777777777777637E-002, 5.27777777777777637E-002,  0.18981481481481477,
456:   };

458:   PetscFunctionBeginUser;
459:   PetscCall(PetscArraycpy(dd, DD, 576));
460:   PetscFunctionReturn(PETSC_SUCCESS);
461: }

463: /*TEST

465:    testset:
466:      requires: !complex
467:      args: -ne 11 -alpha 1.e-3 -ksp_type cg -pc_type gamg -pc_gamg_agg_nsmooths 1 -two_solves -ksp_converged_reason -use_mat_nearnullspace -mg_levels_ksp_max_it 1 -mg_levels_ksp_type chebyshev -mg_levels_ksp_chebyshev_esteig 0,0.2,0,1.05 -mg_levels_sub_pc_type lu -pc_gamg_asm_use_agg -mg_levels_pc_asm_overlap 0 -pc_gamg_parallel_coarse_grid_solver -mg_coarse_pc_type jacobi -mg_coarse_ksp_type cg -pc_gamg_mat_coarsen_type hem -pc_gamg_mat_coarsen_max_it 5 -ksp_rtol 1e-4 -ksp_norm_type unpreconditioned -pc_gamg_threshold .001 -pc_gamg_mat_coarsen_strength_index 1,2
468:      test:
469:        suffix: 1
470:        nsize: 1
471:        filter: sed -e "s/Linear solve converged due to CONVERGED_RTOL iterations 15/Linear solve converged due to CONVERGED_RTOL iterations 14/g"
472:      test:
473:        suffix: 2
474:        nsize: 8
475:        filter: sed -e "s/Linear solve converged due to CONVERGED_RTOL iterations 1[3|4]/Linear solve converged due to CONVERGED_RTOL iterations 15/g"

477:    testset:
478:      nsize: 8
479:      args: -ne 15 -alpha 1.e-3 -ksp_type cg -ksp_converged_reason -use_mat_nearnullspace -ksp_rtol 1e-4 -ksp_norm_type unpreconditioned -two_solves
480:      test:
481:        requires: hypre !complex !defined(PETSC_HAVE_HYPRE_DEVICE)
482:        suffix: hypre
483:        args: -pc_type hypre -pc_hypre_boomeramg_relax_type_all l1scaled-Jacobi
484:      test:
485:        suffix: gamg
486:        args: -pc_type gamg -mg_levels_ksp_type richardson -mg_levels_pc_type jacobi -mg_levels_pc_jacobi_type rowl1 -mg_levels_pc_jacobi_rowl1_scale .5 -mg_levels_pc_jacobi_fixdiagonal
487:      test:
488:        suffix: baij
489:        filter: grep -v variant
490:        args: -pc_type jacobi -pc_jacobi_type rowl1 -ksp_type cg -mat_type baij -ksp_view -ksp_rtol 1e-1 -two_solves false

492:    test:
493:       suffix: latebs
494:       filter: grep -v variant
495:       nsize: 8
496:       args: -test_late_bs 0 -ne 9 -alpha 1.e-3 -ksp_type cg -pc_type gamg -pc_gamg_agg_nsmooths 1 -pc_gamg_reuse_interpolation true -two_solves -ksp_converged_reason -use_mat_nearnullspace false -mg_levels_ksp_max_it 2 -mg_levels_ksp_type chebyshev -mg_levels_ksp_chebyshev_esteig 0,0.2,0,1.05 -pc_gamg_esteig_ksp_max_it 10 -pc_gamg_threshold -0.01 -pc_gamg_coarse_eq_limit 200 -pc_gamg_process_eq_limit 30 -pc_gamg_repartition false -pc_mg_cycle_type v -pc_gamg_parallel_coarse_grid_solver -mg_coarse_pc_type jacobi -mg_coarse_ksp_type cg -ksp_monitor_short -ksp_view -pc_gamg_injection_index 1,2 -mg_fine_ksp_type richardson -mg_fine_pc_type jacobi -mg_fine_pc_jacobi_type rowl1 -mg_fine_pc_jacobi_rowl1_scale .25

498:    test:
499:       suffix: latebs-2
500:       filter: grep -v variant
501:       nsize: 8
502:       args: -test_late_bs -ne 9 -alpha 1.e-3 -ksp_type cg -pc_type gamg -pc_gamg_agg_nsmooths 1 -pc_gamg_reuse_interpolation true -two_solves -ksp_converged_reason -use_mat_nearnullspace -mg_levels_ksp_max_it 2 -mg_levels_ksp_type chebyshev -mg_levels_ksp_chebyshev_esteig 0,0.2,0,1.05 -pc_gamg_esteig_ksp_max_it 10 -pc_gamg_threshold -0.01 -pc_gamg_coarse_eq_limit 200 -pc_gamg_process_eq_limit 30 -pc_gamg_repartition false -pc_mg_cycle_type v -pc_gamg_parallel_coarse_grid_solver -mg_coarse_pc_type jacobi -mg_coarse_ksp_type cg -ksp_monitor_short -ksp_view

504:    test:
505:       suffix: ml
506:       nsize: 8
507:       args: -ne 9 -alpha 1.e-3 -ksp_type cg -pc_type ml -mg_levels_ksp_type chebyshev -mg_levels_ksp_chebyshev_esteig 0,0.05,0,1.05 -mg_levels_pc_type sor -ksp_monitor_short
508:       requires: ml

510:    test:
511:       suffix: nns
512:       args: -ne 9 -alpha 1.e-3 -ksp_converged_reason -ksp_type cg -ksp_max_it 50 -pc_type gamg -pc_gamg_esteig_ksp_type cg -pc_gamg_esteig_ksp_max_it 10 -pc_gamg_type agg -pc_gamg_agg_nsmooths 1 -pc_gamg_coarse_eq_limit 1000 -mg_levels_ksp_type chebyshev -mg_levels_pc_type sor -pc_gamg_reuse_interpolation true -two_solves -use_mat_nearnullspace -pc_gamg_use_sa_esteig 0 -mg_levels_esteig_ksp_max_it 10

514:    test:
515:       suffix: nns_telescope
516:       nsize: 2
517:       args: -use_mat_nearnullspace -pc_type telescope -pc_telescope_reduction_factor 2 -telescope_pc_type gamg -telescope_pc_gamg_esteig_ksp_type cg -telescope_pc_gamg_esteig_ksp_max_it 10

519:    test:
520:       suffix: nns_gdsw
521:       filter: grep -v "variant HERMITIAN"
522:       nsize: 8
523:       args: -use_mat_nearnullspace -ksp_monitor_short -pc_type mg -pc_mg_levels 2 -pc_mg_adapt_interp_coarse_space gdsw -pc_mg_galerkin -mg_levels_pc_type bjacobi -ne 3 -ksp_view

525:    test:
526:       suffix: seqaijmkl
527:       nsize: 8
528:       requires: mkl_sparse
529:       args: -ne 9 -alpha 1.e-3 -ksp_type cg -pc_type gamg -pc_gamg_agg_nsmooths 1 -pc_gamg_reuse_interpolation true -two_solves -ksp_converged_reason -use_mat_nearnullspace -mg_levels_ksp_max_it 2 -mg_levels_ksp_type chebyshev -mg_levels_pc_type jacobi -mg_levels_ksp_chebyshev_esteig 0,0.2,0,1.05 -pc_gamg_esteig_ksp_max_it 10 -pc_gamg_threshold 0.01 -pc_gamg_coarse_eq_limit 2000 -pc_gamg_process_eq_limit 200 -pc_gamg_repartition false -pc_mg_cycle_type v -mat_seqaij_type seqaijmkl

531: TEST*/