Actual source code: ex55.c

  1: static char help[] = "2D, bi-linear quadrilateral (Q1), displacement finite element formulation\n\
  2: of plain strain 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 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: int main(int argc, char **args)
 11: {
 12:   Mat           Amat;
 13:   PetscInt      i, m, M, its, Istart, Iend, j, Ii, ix, ne = 4;
 14:   PetscReal     x, y, h;
 15:   Vec           xx, bb;
 16:   KSP           ksp;
 17:   PetscReal     soft_alpha = 1.e-3;
 18:   MPI_Comm      comm;
 19:   PetscBool     use_coords = PETSC_FALSE;
 20:   PetscMPIInt   npe, mype;
 21:   PetscScalar   DD[8][8], DD2[8][8];
 22:   PetscLogStage stage[2];
 23:   PetscScalar   DD1[8][8] = {
 24:     {5.333333333333333E-01,  2.0000E-01,             -3.333333333333333E-01, 0.0000E+00,             -2.666666666666667E-01, -2.0000E-01,            6.666666666666667E-02,  0.0000E-00            },
 25:     {2.0000E-01,             5.333333333333333E-01,  0.0000E-00,             6.666666666666667E-02,  -2.0000E-01,            -2.666666666666667E-01, 0.0000E-00,             -3.333333333333333E-01},
 26:     {-3.333333333333333E-01, 0.0000E-00,             5.333333333333333E-01,  -2.0000E-01,            6.666666666666667E-02,  0.0000E-00,             -2.666666666666667E-01, 2.0000E-01            },
 27:     {0.0000E+00,             6.666666666666667E-02,  -2.0000E-01,            5.333333333333333E-01,  0.0000E-00,             -3.333333333333333E-01, 2.0000E-01,             -2.666666666666667E-01},
 28:     {-2.666666666666667E-01, -2.0000E-01,            6.666666666666667E-02,  0.0000E-00,             5.333333333333333E-01,  2.0000E-01,             -3.333333333333333E-01, 0.0000E+00            },
 29:     {-2.0000E-01,            -2.666666666666667E-01, 0.0000E-00,             -3.333333333333333E-01, 2.0000E-01,             5.333333333333333E-01,  0.0000E-00,             6.666666666666667E-02 },
 30:     {6.666666666666667E-02,  0.0000E-00,             -2.666666666666667E-01, 2.0000E-01,             -3.333333333333333E-01, 0.0000E-00,             5.333333333333333E-01,  -2.0000E-01           },
 31:     {0.0000E-00,             -3.333333333333333E-01, 2.0000E-01,             -2.666666666666667E-01, 0.0000E-00,             6.666666666666667E-02,  -2.0000E-01,            5.333333333333333E-01 }
 32:   };

 34:   PetscFunctionBeginUser;
 35:   PetscCall(PetscInitialize(&argc, &args, NULL, help));
 36:   comm = PETSC_COMM_WORLD;
 37:   PetscCallMPI(MPI_Comm_rank(comm, &mype));
 38:   PetscCallMPI(MPI_Comm_size(comm, &npe));
 39:   PetscCall(PetscOptionsGetInt(NULL, NULL, "-ne", &ne, NULL));
 40:   h = 1. / ne;
 41:   /* ne*ne; number of global elements */
 42:   PetscCall(PetscOptionsGetReal(NULL, NULL, "-alpha", &soft_alpha, NULL));
 43:   PetscCall(PetscOptionsGetBool(NULL, NULL, "-use_coordinates", &use_coords, NULL));
 44:   M = 2 * (ne + 1) * (ne + 1); /* global number of equations */
 45:   m = (ne + 1) * (ne + 1) / npe;
 46:   if (mype == npe - 1) m = (ne + 1) * (ne + 1) - (npe - 1) * m;
 47:   m *= 2;
 48:   /* create stiffness matrix */
 49:   PetscCall(MatCreate(comm, &Amat));
 50:   PetscCall(MatSetSizes(Amat, m, m, M, M));
 51:   PetscCall(MatSetType(Amat, MATAIJ));
 52:   PetscCall(MatSetOption(Amat, MAT_SPD, PETSC_TRUE));
 53:   PetscCall(MatSetOption(Amat, MAT_SPD_ETERNAL, PETSC_TRUE));
 54:   PetscCall(MatSetFromOptions(Amat));
 55:   PetscCall(MatSetBlockSize(Amat, 2));
 56:   PetscCall(MatSeqAIJSetPreallocation(Amat, 18, NULL));
 57:   PetscCall(MatMPIAIJSetPreallocation(Amat, 18, NULL, 18, NULL));
 58: #if defined(PETSC_HAVE_HYPRE)
 59:   PetscCall(MatHYPRESetPreallocation(Amat, 18, NULL, 18, NULL));
 60: #endif

 62:   PetscCall(MatGetOwnershipRange(Amat, &Istart, &Iend));
 63:   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);
 64:   /* Generate vectors */
 65:   PetscCall(MatCreateVecs(Amat, &xx, &bb));
 66:   PetscCall(VecSet(bb, .0));
 67:   /* generate element matrices -- see ex56.c on how to use different data set */
 68:   {
 69:     DD[0][0] = 0.53333333333333321;
 70:     DD[0][1] = 0.20000000000000001;
 71:     DD[0][2] = -0.33333333333333331;
 72:     DD[0][3] = 0.0000000000000000;
 73:     DD[0][4] = -0.26666666666666666;
 74:     DD[0][5] = -0.20000000000000001;
 75:     DD[0][6] = 6.66666666666666796E-002;
 76:     DD[0][7] = 6.93889390390722838E-018;
 77:     DD[1][0] = 0.20000000000000001;
 78:     DD[1][1] = 0.53333333333333333;
 79:     DD[1][2] = 7.80625564189563192E-018;
 80:     DD[1][3] = 6.66666666666666935E-002;
 81:     DD[1][4] = -0.20000000000000001;
 82:     DD[1][5] = -0.26666666666666666;
 83:     DD[1][6] = -3.46944695195361419E-018;
 84:     DD[1][7] = -0.33333333333333331;
 85:     DD[2][0] = -0.33333333333333331;
 86:     DD[2][1] = 1.12757025938492461E-017;
 87:     DD[2][2] = 0.53333333333333333;
 88:     DD[2][3] = -0.20000000000000001;
 89:     DD[2][4] = 6.66666666666666935E-002;
 90:     DD[2][5] = -6.93889390390722838E-018;
 91:     DD[2][6] = -0.26666666666666666;
 92:     DD[2][7] = 0.19999999999999998;
 93:     DD[3][0] = 0.0000000000000000;
 94:     DD[3][1] = 6.66666666666666935E-002;
 95:     DD[3][2] = -0.20000000000000001;
 96:     DD[3][3] = 0.53333333333333333;
 97:     DD[3][4] = 4.33680868994201774E-018;
 98:     DD[3][5] = -0.33333333333333331;
 99:     DD[3][6] = 0.20000000000000001;
100:     DD[3][7] = -0.26666666666666666;
101:     DD[4][0] = -0.26666666666666666;
102:     DD[4][1] = -0.20000000000000001;
103:     DD[4][2] = 6.66666666666666935E-002;
104:     DD[4][3] = 8.67361737988403547E-019;
105:     DD[4][4] = 0.53333333333333333;
106:     DD[4][5] = 0.19999999999999998;
107:     DD[4][6] = -0.33333333333333331;
108:     DD[4][7] = -3.46944695195361419E-018;
109:     DD[5][0] = -0.20000000000000001;
110:     DD[5][1] = -0.26666666666666666;
111:     DD[5][2] = -1.04083408558608426E-017;
112:     DD[5][3] = -0.33333333333333331;
113:     DD[5][4] = 0.19999999999999998;
114:     DD[5][5] = 0.53333333333333333;
115:     DD[5][6] = 6.93889390390722838E-018;
116:     DD[5][7] = 6.66666666666666519E-002;
117:     DD[6][0] = 6.66666666666666796E-002;
118:     DD[6][1] = -6.93889390390722838E-018;
119:     DD[6][2] = -0.26666666666666666;
120:     DD[6][3] = 0.19999999999999998;
121:     DD[6][4] = -0.33333333333333331;
122:     DD[6][5] = 6.93889390390722838E-018;
123:     DD[6][6] = 0.53333333333333321;
124:     DD[6][7] = -0.20000000000000001;
125:     DD[7][0] = 6.93889390390722838E-018;
126:     DD[7][1] = -0.33333333333333331;
127:     DD[7][2] = 0.19999999999999998;
128:     DD[7][3] = -0.26666666666666666;
129:     DD[7][4] = 0.0000000000000000;
130:     DD[7][5] = 6.66666666666666519E-002;
131:     DD[7][6] = -0.20000000000000001;
132:     DD[7][7] = 0.53333333333333321;

134:     /* BC version of element */
135:     for (i = 0; i < 8; i++) {
136:       for (j = 0; j < 8; j++) {
137:         if (i < 4 || j < 4) {
138:           if (i == j) DD2[i][j] = .1 * DD1[i][j];
139:           else DD2[i][j] = 0.0;
140:         } else DD2[i][j] = DD1[i][j];
141:       }
142:     }
143:   }
144:   {
145:     PetscReal *coords;
146:     PetscCall(PetscMalloc1(m, &coords));
147:     /* forms the element stiffness and coordinates */
148:     for (Ii = Istart / 2, ix = 0; Ii < Iend / 2; Ii++, ix++) {
149:       j = Ii / (ne + 1);
150:       i = Ii % (ne + 1);
151:       /* coords */
152:       x                  = h * (Ii % (ne + 1));
153:       y                  = h * (Ii / (ne + 1));
154:       coords[2 * ix]     = x;
155:       coords[2 * ix + 1] = y;
156:       if (i < ne && j < ne) {
157:         PetscInt jj, ii, idx[4];
158:         /* radius */
159:         PetscReal radius = PetscSqrtReal((x - .5 + h / 2) * (x - .5 + h / 2) + (y - .5 + h / 2) * (y - .5 + h / 2));
160:         PetscReal alpha  = 1.0;
161:         if (radius < 0.25) alpha = soft_alpha;

163:         idx[0] = Ii;
164:         idx[1] = Ii + 1;
165:         idx[2] = Ii + (ne + 1) + 1;
166:         idx[3] = Ii + (ne + 1);
167:         for (ii = 0; ii < 8; ii++) {
168:           for (jj = 0; jj < 8; jj++) DD[ii][jj] = alpha * DD1[ii][jj];
169:         }
170:         if (j > 0) {
171:           PetscCall(MatSetValuesBlocked(Amat, 4, idx, 4, idx, (const PetscScalar *)DD, ADD_VALUES));
172:         } else {
173:           /* a BC */
174:           for (ii = 0; ii < 8; ii++) {
175:             for (jj = 0; jj < 8; jj++) DD[ii][jj] = alpha * DD2[ii][jj];
176:           }
177:           PetscCall(MatSetValuesBlocked(Amat, 4, idx, 4, idx, (const PetscScalar *)DD, ADD_VALUES));
178:         }
179:       }
180:       if (j > 0) {
181:         PetscScalar v  = h * h;
182:         PetscInt    jj = 2 * Ii; /* load in x direction */
183:         PetscCall(VecSetValues(bb, 1, &jj, &v, INSERT_VALUES));
184:       }
185:     }
186:     PetscCall(MatAssemblyBegin(Amat, MAT_FINAL_ASSEMBLY));
187:     PetscCall(MatAssemblyEnd(Amat, MAT_FINAL_ASSEMBLY));
188:     PetscCall(VecAssemblyBegin(bb));
189:     PetscCall(VecAssemblyEnd(bb));

191:     /* Setup solver */
192:     PetscCall(KSPCreate(PETSC_COMM_WORLD, &ksp));
193:     PetscCall(KSPSetFromOptions(ksp));

195:     /* finish KSP/PC setup */
196:     PetscCall(KSPSetOperators(ksp, Amat, Amat));
197:     if (use_coords) {
198:       PC pc;

200:       PetscCall(KSPGetPC(ksp, &pc));
201:       PetscCall(PCSetCoordinates(pc, 2, m / 2, coords));
202:     }
203:     PetscCall(PetscFree(coords));
204:   }

206:   if (!PETSC_TRUE) {
207:     PetscViewer viewer;
208:     PetscCall(PetscViewerASCIIOpen(comm, "Amat.m", &viewer));
209:     PetscCall(PetscViewerPushFormat(viewer, PETSC_VIEWER_ASCII_MATLAB));
210:     PetscCall(MatView(Amat, viewer));
211:     PetscCall(PetscViewerPopFormat(viewer));
212:     PetscCall(PetscViewerDestroy(&viewer));
213:   }

215:   /* solve */
216:   PetscCall(PetscLogStageRegister("Setup", &stage[0]));
217:   PetscCall(PetscLogStageRegister("Solve", &stage[1]));
218:   PetscCall(PetscLogStagePush(stage[0]));
219:   PetscCall(KSPSetUp(ksp));
220:   PetscCall(PetscLogStagePop());

222:   PetscCall(VecSet(xx, .0));

224:   PetscCall(PetscLogStagePush(stage[1]));
225:   PetscCall(KSPSolve(ksp, bb, xx));
226:   PetscCall(PetscLogStagePop());

228:   PetscCall(KSPGetIterationNumber(ksp, &its));

230:   if (0) {
231:     PetscReal   norm, norm2;
232:     PetscViewer viewer;
233:     Vec         res;

235:     PetscCall(PetscObjectGetComm((PetscObject)bb, &comm));
236:     PetscCall(VecNorm(bb, NORM_2, &norm2));

238:     PetscCall(VecDuplicate(xx, &res));
239:     PetscCall(MatMult(Amat, xx, res));
240:     PetscCall(VecAXPY(bb, -1.0, res));
241:     PetscCall(VecDestroy(&res));
242:     PetscCall(VecNorm(bb, NORM_2, &norm));
243:     PetscCall(PetscPrintf(PETSC_COMM_WORLD, "[%d]%s |b-Ax|/|b|=%e, |b|=%e\n", 0, PETSC_FUNCTION_NAME, (double)(norm / norm2), (double)norm2));
244:     PetscCall(PetscViewerASCIIOpen(comm, "residual.m", &viewer));
245:     PetscCall(PetscViewerPushFormat(viewer, PETSC_VIEWER_ASCII_MATLAB));
246:     PetscCall(VecView(bb, viewer));
247:     PetscCall(PetscViewerPopFormat(viewer));
248:     PetscCall(PetscViewerDestroy(&viewer));
249:   }

251:   /* Free work space */
252:   PetscCall(KSPDestroy(&ksp));
253:   PetscCall(VecDestroy(&xx));
254:   PetscCall(VecDestroy(&bb));
255:   PetscCall(MatDestroy(&Amat));

257:   PetscCall(PetscFinalize());
258:   return 0;
259: }

261: /*TEST

263:    test:
264:       suffix: 1
265:       nsize: 4
266:       args: -ne 29 -alpha 1.e-3 -ksp_type cg -pc_type gamg -pc_gamg_type agg -pc_gamg_agg_nsmooths 1 -use_coordinates -ksp_converged_reason -pc_gamg_esteig_ksp_max_it 5 -ksp_rtol 1.e-3 -ksp_monitor_short -mg_levels_ksp_chebyshev_esteig 0,0.05,0,1.2 -pc_gamg_aggressive_coarsening 0
267:       output_file: output/ex55_sa.out

269:    test:
270:       suffix: Classical
271:       nsize: 4
272:       requires: !complex
273:       args: -ne 29 -alpha 1.e-3 -ksp_type gmres -pc_type gamg -pc_gamg_type classical -mg_levels_ksp_max_it 5 -ksp_converged_reason -ksp_rtol 1e-3 -pc_gamg_mat_coarsen_misk_distance 2 -pc_gamg_threshold 0
274:       output_file: output/ex55_classical.out
275:       filter: sed -e "s/Linear solve converged due to CONVERGED_RTOL iterations 17/Linear solve converged due to CONVERGED_RTOL iterations 18/g"

277:    test:
278:       suffix: NC
279:       nsize: 4
280:       args: -ne 29 -alpha 1.e-3 -ksp_type cg -pc_type gamg -pc_gamg_type agg -pc_gamg_agg_nsmooths 1 -ksp_converged_reason -pc_gamg_esteig_ksp_max_it 10 -mg_levels_ksp_chebyshev_esteig 0,0.05,0,1.2 -pc_gamg_aggressive_coarsening 0 -pc_gamg_threshold 0
281:       filter: sed -e "s/Linear solve converged due to CONVERGED_RTOL iterations 12/Linear solve converged due to CONVERGED_RTOL iterations 11/g"

283:    test:
284:       suffix: geo
285:       nsize: 4
286:       args: -ne 29 -alpha 1.e-3 -ksp_type cg -pc_type gamg -pc_gamg_type geo -use_coordinates -ksp_monitor_short -ksp_type cg -ksp_norm_type unpreconditioned -mg_levels_ksp_max_it 3 -pc_gamg_threshold 0
287:       output_file: output/ex55_0.out
288:       requires: triangle

290:    test:
291:       suffix: hypre
292:       nsize: 4
293:       requires: hypre !complex !defined(PETSC_HAVE_HYPRE_DEVICE)
294:       args: -ne 29 -alpha 1.e-3 -ksp_type cg -pc_type hypre -pc_hypre_type boomeramg -ksp_monitor_short

296:    test:
297:       suffix: hypre_ilu
298:       nsize: 4
299:       requires: hypre !complex !defined(PETSC_HAVE_HYPRE_DEVICE)
300:       args: -ne 29 -alpha 1.e-3 -pc_type hypre -pc_hypre_type ilu -ksp_monitor_short

302:    test:
303:       suffix: kok
304:       nsize: 4
305:       requires: kokkos_kernels
306:       args: -ne 29 -ksp_type cg -pc_type pbjacobi -mat_type aijkokkos -ksp_converged_reason
307:       filter: grep -v CONVERGED_RTOL
308:       output_file: output/empty.out

310:    # command line options match GPU defaults
311:    test:
312:       suffix: hypre_device
313:       nsize: 4
314:       requires: hypre !complex
315:       args: -mat_type hypre -ksp_view -ne 29 -alpha 1.e-3 -ksp_type cg -pc_type hypre -pc_hypre_type boomeramg -ksp_monitor_short -pc_hypre_boomeramg_relax_type_all l1scaled-Jacobi -pc_hypre_boomeramg_interp_type ext+i -pc_hypre_boomeramg_coarsen_type PMIS -pc_hypre_boomeramg_no_CF -pc_mg_galerkin_mat_product_algorithm hypre

317: TEST*/