Actual source code: ex54.c
2: static char help[] = "Creates a matrix from quadrilateral finite elements in 2D, Laplacian \n\
3: -ne <size> : problem size in number of elements (eg, -ne 31 gives 32^2 grid)\n\
4: -alpha <v> : scaling of material coeficient in embedded circle\n\n";
6: #include <petscksp.h>
8: int main(int argc,char **args)
9: {
10: Mat Amat,Pmat;
12: PetscInt i,m,M,its,Istart,Iend,j,Ii,ix,ne=4;
13: PetscReal x,y,h;
14: Vec xx,bb;
15: KSP ksp;
16: PetscReal soft_alpha = 1.e-3;
17: MPI_Comm comm;
18: PetscMPIInt npe,mype;
19: PetscScalar DD[4][4],DD2[4][4];
20: #if defined(PETSC_USE_LOG)
21: PetscLogStage stage;
22: #endif
23: #define DIAG_S 0.0
24: PetscScalar DD1[4][4] = { {5.0+DIAG_S, -2.0, -1.0, -2.0},
25: {-2.0, 5.0+DIAG_S, -2.0, -1.0},
26: {-1.0, -2.0, 5.0+DIAG_S, -2.0},
27: {-2.0, -1.0, -2.0, 5.0+DIAG_S} };
29: PetscInitialize(&argc,&args,(char*)0,help);if (ierr) return ierr;
30: comm = PETSC_COMM_WORLD;
31: MPI_Comm_rank(comm, &mype);
32: MPI_Comm_size(comm, &npe);
33: PetscOptionsGetInt(NULL,NULL,"-ne",&ne,NULL);
34: h = 1./ne;
35: /* ne*ne; number of global elements */
36: PetscOptionsGetReal(NULL,NULL,"-alpha",&soft_alpha,NULL);
37: M = (ne+1)*(ne+1); /* global number of nodes */
39: /* create stiffness matrix (2) */
40: MatCreate(comm,&Amat);
41: MatSetSizes(Amat,PETSC_DECIDE,PETSC_DECIDE,M,M);
42: MatSetType(Amat,MATAIJ);
43: MatSetOption(Amat,MAT_SPD,PETSC_TRUE);
44: MatSetFromOptions(Amat);
45: MatSeqAIJSetPreallocation(Amat,81,NULL);
46: MatMPIAIJSetPreallocation(Amat,81,NULL,57,NULL);
48: MatCreate(comm,&Pmat);
49: MatSetSizes(Pmat,PETSC_DECIDE,PETSC_DECIDE,M,M);
50: MatSetType(Pmat,MATMPIAIJ);
51: MatSetFromOptions(Pmat);
52: MatSeqAIJSetPreallocation(Pmat,81,NULL);
53: MatMPIAIJSetPreallocation(Pmat,81,NULL,57,NULL);
55: /* vectors */
56: MatCreateVecs(Amat,&bb,&xx);
57: 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: MatGetOwnershipRange(Amat,&Istart,&Iend);
92: m = Iend-Istart;
93: PetscMalloc1(2*m,&coords);
94: for (Ii=Istart,ix=0; Ii<Iend; Ii++,ix++) {
95: j = Ii/(ne+1); i = Ii%(ne+1);
96: /* coords */
97: x = h*(Ii % (ne+1)); y = h*(Ii/(ne+1));
98: coords[2*ix] = x; coords[2*ix+1] = y;
99: if (i<ne && j<ne) {
100: PetscInt jj,ii,idx[4];
101: /* radius */
102: PetscReal radius = PetscSqrtReal((x-.5+h/2)*(x-.5+h/2) + (y-.5+h/2)*(y-.5+h/2));
103: PetscReal alpha = 1.0;
104: idx[0] = Ii; idx[1] = Ii+1; idx[2] = Ii + (ne+1) + 1; idx[3] = Ii + (ne+1);
105: if (radius < 0.25) alpha = soft_alpha;
106: for (ii=0; ii<4; ii++) {
107: for (jj=0; jj<4; jj++) DD[ii][jj] = alpha*DD1[ii][jj];
108: }
109: MatSetValues(Pmat,4,idx,4,idx,(const PetscScalar*)DD,ADD_VALUES);
110: if (j>0) {
111: MatSetValues(Amat,4,idx,4,idx,(const PetscScalar*)DD,ADD_VALUES);
112: } else {
113: /* a BC */
114: for (ii=0;ii<4;ii++) {
115: for (jj=0;jj<4;jj++) DD[ii][jj] = alpha*DD2[ii][jj];
116: }
117: MatSetValues(Amat,4,idx,4,idx,(const PetscScalar*)DD,ADD_VALUES);
118: }
119: }
120: if (j>0) {
121: PetscScalar v = h*h;
122: PetscInt jj = Ii;
123: VecSetValues(bb,1,&jj,&v,INSERT_VALUES);
124: }
125: }
126: MatAssemblyBegin(Amat,MAT_FINAL_ASSEMBLY);
127: MatAssemblyEnd(Amat,MAT_FINAL_ASSEMBLY);
128: MatAssemblyBegin(Pmat,MAT_FINAL_ASSEMBLY);
129: MatAssemblyEnd(Pmat,MAT_FINAL_ASSEMBLY);
130: VecAssemblyBegin(bb);
131: VecAssemblyEnd(bb);
133: /* Setup solver */
134: KSPCreate(PETSC_COMM_WORLD,&ksp);
135: KSPSetFromOptions(ksp);
137: /* finish KSP/PC setup */
138: KSPSetOperators(ksp, Amat, Amat);
140: KSPGetPC(ksp,&pc);
141: PCSetCoordinates(pc, 2, m, coords);
142: PetscFree(coords);
143: }
145: if (!PETSC_TRUE) {
146: PetscViewer viewer;
147: PetscViewerASCIIOpen(comm, "Amat.m", &viewer);
148: PetscViewerPushFormat(viewer, PETSC_VIEWER_ASCII_MATLAB);
149: MatView(Amat,viewer);
150: PetscViewerPopFormat(viewer);
151: PetscViewerDestroy(&viewer);
152: }
154: /* solve */
155: #if defined(PETSC_USE_LOG)
156: PetscLogStageRegister("Solve", &stage);
157: PetscLogStagePush(stage);
158: #endif
159: VecSet(xx,.0);
161: KSPSetUp(ksp);
163: KSPSolve(ksp,bb,xx);
165: #if defined(PETSC_USE_LOG)
166: PetscLogStagePop();
167: #endif
169: KSPGetIterationNumber(ksp,&its);
171: if (!PETSC_TRUE) {
172: PetscReal norm,norm2;
173: PetscViewer viewer;
174: Vec res;
175: PetscViewerASCIIOpen(comm, "rhs.m", &viewer);
176: PetscViewerPushFormat(viewer, PETSC_VIEWER_ASCII_MATLAB);
177: VecView(bb,viewer);
178: PetscViewerPopFormat(viewer);
179: PetscViewerDestroy(&viewer);
180: VecNorm(bb, NORM_2, &norm2);
182: PetscViewerASCIIOpen(comm, "solution.m", &viewer);
183: PetscViewerPushFormat(viewer, PETSC_VIEWER_ASCII_MATLAB);
184: VecView(xx,viewer);
185: PetscViewerPopFormat(viewer);
186: PetscViewerDestroy(&viewer);
188: VecDuplicate(xx, &res);
189: MatMult(Amat, xx, res);
190: VecAXPY(bb, -1.0, res);
191: VecDestroy(&res);
192: VecNorm(bb,NORM_2,&norm);
193: PetscPrintf(PETSC_COMM_WORLD,"[%d]%s |b-Ax|/|b|=%e, |b|=%e\n",0,PETSC_FUNCTION_NAME,norm/norm2,norm2);
195: PetscViewerASCIIOpen(comm, "residual.m", &viewer);
196: PetscViewerPushFormat(viewer, PETSC_VIEWER_ASCII_MATLAB);
197: VecView(bb,viewer);
198: PetscViewerPopFormat(viewer);
199: PetscViewerDestroy(&viewer);
200: }
202: /* Free work space */
203: KSPDestroy(&ksp);
204: VecDestroy(&xx);
205: VecDestroy(&bb);
206: MatDestroy(&Amat);
207: MatDestroy(&Pmat);
209: PetscFinalize();
210: return ierr;
211: }
215: /*TEST
217: build:
218: requires: !complex
220: test:
221: nsize: 4
222: args: -ne 19 -alpha 1.e-3 -pc_type gamg -pc_gamg_agg_nsmooths 1 -mg_levels_ksp_max_it 3 -ksp_monitor -ksp_converged_reason -ksp_type cg
224: test:
225: suffix: seqaijmkl
226: nsize: 4
227: requires: mkl_sparse
228: args: -ne 19 -alpha 1.e-3 -pc_type gamg -pc_gamg_agg_nsmooths 1 -mg_levels_ksp_max_it 3 -ksp_monitor -ksp_converged_reason -ksp_type cg -mat_seqaij_type seqaijmkl
230: test:
231: suffix: Classical
232: args: -ne 49 -alpha 1.e-3 -ksp_type cg -pc_type gamg -pc_gamg_type classical -mg_levels_ksp_chebyshev_esteig 0,0.05,0,1.05 -ksp_converged_reason
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 -pc_gamg_type geo -pc_gamg_coarse_eq_limit 200 -mg_levels_pc_type jacobi -mg_levels_ksp_chebyshev_esteig 0,0.05,0,1.05 -ksp_monitor_short -mg_levels_ksp_max_it 3
239: requires: triangle
240: output_file: output/ex54_0.out
242: TEST*/