Actual source code: ex54.c

  1: static char help[] = "Creates a matrix from quadrilateral finite elements in 2D, Laplacian \n\
  2:   -ne <size>       : problem size in number of elements (eg, -ne 31 gives 32^2 grid)\n\
  3:   -alpha <v>      : scaling of material coefficient in embedded circle\n\n";

  5: #include <petscksp.h>

  7: int main(int argc, char **args)
  8: {
  9:   Mat           Amat, Pmat;
 10:   PetscInt      i, m, M, its, Istart, Iend, j, Ii, ix, ne = 4;
 11:   PetscReal     x, y, h;
 12:   Vec           xx, bb;
 13:   KSP           ksp;
 14:   PetscReal     soft_alpha = 1.e-3;
 15:   MPI_Comm      comm;
 16:   PetscMPIInt   npe, mype;
 17:   PetscScalar   DD[4][4], DD2[4][4];
 18:   PetscLogStage stage;
 19: #define DIAG_S 0.0
 20:   PetscScalar DD1[4][4] = {
 21:     {5.0 + DIAG_S, -2.0,         -1.0,         -2.0        },
 22:     {-2.0,         5.0 + DIAG_S, -2.0,         -1.0        },
 23:     {-1.0,         -2.0,         5.0 + DIAG_S, -2.0        },
 24:     {-2.0,         -1.0,         -2.0,         5.0 + DIAG_S}
 25:   };

 27:   PetscFunctionBeginUser;
 28:   PetscCall(PetscInitialize(&argc, &args, (char *)0, help));
 29:   comm = PETSC_COMM_WORLD;
 30:   PetscCallMPI(MPI_Comm_rank(comm, &mype));
 31:   PetscCallMPI(MPI_Comm_size(comm, &npe));
 32:   PetscCall(PetscOptionsGetInt(NULL, NULL, "-ne", &ne, NULL));
 33:   h = 1. / ne;
 34:   /* ne*ne; number of global elements */
 35:   PetscCall(PetscOptionsGetReal(NULL, NULL, "-alpha", &soft_alpha, NULL));
 36:   M = (ne + 1) * (ne + 1); /* global number of nodes */

 38:   /* create stiffness matrix (2) */
 39:   PetscCall(MatCreate(comm, &Amat));
 40:   PetscCall(MatSetSizes(Amat, PETSC_DECIDE, PETSC_DECIDE, M, M));
 41:   PetscCall(MatSetType(Amat, MATAIJ));
 42:   PetscCall(MatSetOption(Amat, MAT_SPD, PETSC_TRUE));
 43:   PetscCall(MatSetOption(Amat, MAT_SPD_ETERNAL, PETSC_TRUE));
 44:   PetscCall(MatSetFromOptions(Amat));
 45:   PetscCall(MatSeqAIJSetPreallocation(Amat, 81, NULL));
 46:   PetscCall(MatMPIAIJSetPreallocation(Amat, 81, NULL, 57, NULL));

 48:   PetscCall(MatCreate(comm, &Pmat));
 49:   PetscCall(MatSetSizes(Pmat, PETSC_DECIDE, PETSC_DECIDE, M, M));
 50:   PetscCall(MatSetType(Pmat, MATMPIAIJ));
 51:   PetscCall(MatSetFromOptions(Pmat));
 52:   PetscCall(MatSeqAIJSetPreallocation(Pmat, 81, NULL));
 53:   PetscCall(MatMPIAIJSetPreallocation(Pmat, 81, NULL, 57, NULL));

 55:   /* vectors */
 56:   PetscCall(MatCreateVecs(Amat, &bb, &xx));
 57:   PetscCall(VecSet(bb, .0));
 58:   /* generate element matrices -- see ex56.c on how to use different data set */
 59:   {
 60:     DD1[0][0] = 0.66666666666666663;
 61:     DD1[0][1] = -0.16666666666666669;
 62:     DD1[0][2] = -0.33333333333333343;
 63:     DD1[0][3] = -0.16666666666666666;
 64:     DD1[1][0] = -0.16666666666666669;
 65:     DD1[1][1] = 0.66666666666666663;
 66:     DD1[1][2] = -0.16666666666666666;
 67:     DD1[1][3] = -0.33333333333333343;
 68:     DD1[2][0] = -0.33333333333333343;
 69:     DD1[2][1] = -0.16666666666666666;
 70:     DD1[2][2] = 0.66666666666666663;
 71:     DD1[2][3] = -0.16666666666666663;
 72:     DD1[3][0] = -0.16666666666666666;
 73:     DD1[3][1] = -0.33333333333333343;
 74:     DD1[3][2] = -0.16666666666666663;
 75:     DD1[3][3] = 0.66666666666666663;

 77:     /* BC version of element */
 78:     for (i = 0; i < 4; i++) {
 79:       for (j = 0; j < 4; j++) {
 80:         if (i < 2 || j < 2) {
 81:           if (i == j) DD2[i][j] = .1 * DD1[i][j];
 82:           else DD2[i][j] = 0.0;
 83:         } else DD2[i][j] = DD1[i][j];
 84:       }
 85:     }
 86:   }
 87:   {
 88:     PetscReal *coords;
 89:     PC         pc;
 90:     /* forms the element stiffness for the Laplacian and coordinates */
 91:     PetscCall(MatGetOwnershipRange(Amat, &Istart, &Iend));
 92:     m = Iend - Istart;
 93:     PetscCall(PetscMalloc1(2 * m, &coords));
 94:     for (Ii = Istart, ix = 0; Ii < Iend; Ii++, ix++) {
 95:       j = Ii / (ne + 1);
 96:       i = Ii % (ne + 1);
 97:       /* coords */
 98:       x                  = h * (Ii % (ne + 1));
 99:       y                  = h * (Ii / (ne + 1));
100:       coords[2 * ix]     = x;
101:       coords[2 * ix + 1] = y;
102:       if (i < ne && j < ne) {
103:         PetscInt jj, ii, idx[4];
104:         /* radius */
105:         PetscReal radius = PetscSqrtReal((x - .5 + h / 2) * (x - .5 + h / 2) + (y - .5 + h / 2) * (y - .5 + h / 2));
106:         PetscReal alpha  = 1.0;
107:         idx[0]           = Ii;
108:         idx[1]           = Ii + 1;
109:         idx[2]           = Ii + (ne + 1) + 1;
110:         idx[3]           = Ii + (ne + 1);
111:         if (radius < 0.25) alpha = soft_alpha;
112:         for (ii = 0; ii < 4; ii++) {
113:           for (jj = 0; jj < 4; jj++) DD[ii][jj] = alpha * DD1[ii][jj];
114:         }
115:         PetscCall(MatSetValues(Pmat, 4, idx, 4, idx, (const PetscScalar *)DD, ADD_VALUES));
116:         if (j > 0) {
117:           PetscCall(MatSetValues(Amat, 4, idx, 4, idx, (const PetscScalar *)DD, ADD_VALUES));
118:         } else {
119:           /* a BC */
120:           for (ii = 0; ii < 4; ii++) {
121:             for (jj = 0; jj < 4; jj++) DD[ii][jj] = alpha * DD2[ii][jj];
122:           }
123:           PetscCall(MatSetValues(Amat, 4, idx, 4, idx, (const PetscScalar *)DD, ADD_VALUES));
124:         }
125:       }
126:       if (j > 0) {
127:         PetscScalar v  = h * h;
128:         PetscInt    jj = Ii;
129:         PetscCall(VecSetValues(bb, 1, &jj, &v, INSERT_VALUES));
130:       }
131:     }
132:     PetscCall(MatAssemblyBegin(Amat, MAT_FINAL_ASSEMBLY));
133:     PetscCall(MatAssemblyEnd(Amat, MAT_FINAL_ASSEMBLY));
134:     PetscCall(MatAssemblyBegin(Pmat, MAT_FINAL_ASSEMBLY));
135:     PetscCall(MatAssemblyEnd(Pmat, MAT_FINAL_ASSEMBLY));
136:     PetscCall(VecAssemblyBegin(bb));
137:     PetscCall(VecAssemblyEnd(bb));

139:     /* Setup solver */
140:     PetscCall(KSPCreate(PETSC_COMM_WORLD, &ksp));
141:     PetscCall(KSPSetFromOptions(ksp));

143:     /* finish KSP/PC setup */
144:     PetscCall(KSPSetOperators(ksp, Amat, Amat));

146:     PetscCall(KSPGetPC(ksp, &pc));
147:     PetscCall(PCSetCoordinates(pc, 2, m, coords));
148:     PetscCall(PetscFree(coords));
149:   }

151:   if (!PETSC_TRUE) {
152:     PetscViewer viewer;
153:     PetscCall(PetscViewerASCIIOpen(comm, "Amat.m", &viewer));
154:     PetscCall(PetscViewerPushFormat(viewer, PETSC_VIEWER_ASCII_MATLAB));
155:     PetscCall(MatView(Amat, viewer));
156:     PetscCall(PetscViewerPopFormat(viewer));
157:     PetscCall(PetscViewerDestroy(&viewer));
158:   }

160:   /* solve */
161:   PetscCall(PetscLogStageRegister("Solve", &stage));
162:   PetscCall(PetscLogStagePush(stage));
163:   PetscCall(VecSet(xx, .0));

165:   PetscCall(KSPSetUp(ksp));

167:   PetscCall(KSPSolve(ksp, bb, xx));

169:   PetscCall(PetscLogStagePop());

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

173:   if (!PETSC_TRUE) {
174:     PetscReal   norm, norm2;
175:     PetscViewer viewer;
176:     Vec         res;
177:     PetscCall(PetscViewerASCIIOpen(comm, "rhs.m", &viewer));
178:     PetscCall(PetscViewerPushFormat(viewer, PETSC_VIEWER_ASCII_MATLAB));
179:     PetscCall(VecView(bb, viewer));
180:     PetscCall(PetscViewerPopFormat(viewer));
181:     PetscCall(PetscViewerDestroy(&viewer));
182:     PetscCall(VecNorm(bb, NORM_2, &norm2));

184:     PetscCall(PetscViewerASCIIOpen(comm, "solution.m", &viewer));
185:     PetscCall(PetscViewerPushFormat(viewer, PETSC_VIEWER_ASCII_MATLAB));
186:     PetscCall(VecView(xx, viewer));
187:     PetscCall(PetscViewerPopFormat(viewer));
188:     PetscCall(PetscViewerDestroy(&viewer));

190:     PetscCall(VecDuplicate(xx, &res));
191:     PetscCall(MatMult(Amat, xx, res));
192:     PetscCall(VecAXPY(bb, -1.0, res));
193:     PetscCall(VecDestroy(&res));
194:     PetscCall(VecNorm(bb, NORM_2, &norm));
195:     PetscCall(PetscPrintf(PETSC_COMM_WORLD, "[%d]%s |b-Ax|/|b|=%e, |b|=%e\n", 0, PETSC_FUNCTION_NAME, (double)(norm / norm2), (double)norm2));

197:     PetscCall(PetscViewerASCIIOpen(comm, "residual.m", &viewer));
198:     PetscCall(PetscViewerPushFormat(viewer, PETSC_VIEWER_ASCII_MATLAB));
199:     PetscCall(VecView(bb, viewer));
200:     PetscCall(PetscViewerPopFormat(viewer));
201:     PetscCall(PetscViewerDestroy(&viewer));
202:   }

204:   /* Free work space */
205:   PetscCall(KSPDestroy(&ksp));
206:   PetscCall(VecDestroy(&xx));
207:   PetscCall(VecDestroy(&bb));
208:   PetscCall(MatDestroy(&Amat));
209:   PetscCall(MatDestroy(&Pmat));

211:   PetscCall(PetscFinalize());
212:   return 0;
213: }

215: /*TEST

217:    build:
218:       requires: !complex

220:    test:
221:       nsize: 4
222:       args: -ne 19 -alpha 1.e-3 -ksp_type cg -pc_type gamg -mg_levels_ksp_max_it 2 -ksp_monitor -ksp_converged_reason -pc_gamg_esteig_ksp_max_it 5 -pc_gamg_esteig_ksp_type cg -mg_levels_ksp_chebyshev_esteig 0,0.25,0,1.1 -pc_gamg_aggressive_coarsening 0

224:    test:
225:       suffix: seqaijmkl
226:       nsize: 4
227:       requires: mkl_sparse
228:       args: -ne 19 -alpha 1.e-3 -ksp_type cg -pc_type gamg -mg_levels_ksp_max_it 2 -ksp_monitor -ksp_converged_reason -pc_gamg_esteig_ksp_max_it 5 -pc_gamg_esteig_ksp_type cg -mg_levels_ksp_chebyshev_esteig 0,0.25,0,1.1 -mat_seqaij_type seqaijmkl -pc_gamg_aggressive_coarsening 0

230:    test:
231:       suffix: Classical
232:       args: -ne 49 -alpha 1.e-3 -ksp_type cg -pc_type gamg -mg_levels_ksp_max_it 2 -pc_gamg_type classical -ksp_monitor -ksp_converged_reason -mg_levels_esteig_ksp_type cg -mg_levels_ksp_chebyshev_esteig 0,0.25,0,1.1 -mat_coarsen_type mis
233:       output_file: output/ex54_classical.out

235:    test:
236:       suffix: geo
237:       nsize: 4
238:       args: -ne 49 -alpha 1.e-3 -ksp_type cg -pc_type gamg -mg_levels_ksp_max_it 4 -pc_gamg_type geo -pc_gamg_coarse_eq_limit 200 -mg_levels_esteig_ksp_type cg -mg_levels_esteig_ksp_max_it 10 -mg_levels_ksp_chebyshev_esteig 0,0.1,0,1.05 -ksp_monitor_short -ksp_converged_reason -ksp_rtol 1e-3 -ksp_norm_type unpreconditioned
239:       requires: triangle
240:       output_file: output/ex54_0.out

242:    test:
243:       requires: !single !__float128
244:       nsize: 4
245:       suffix: hem
246:       args: -ne 39 -ksp_type cg -pc_type gamg -pc_gamg_type agg -ksp_rtol 1e-4 -pc_gamg_square_graph 0 -ksp_monitor_short -ksp_norm_type unpreconditioned -mat_coarsen_type hem -ksp_monitor_short -pc_gamg_aggressive_coarsening 0
247: TEST*/