Actual source code: ex54.c
petsc-3.4.5 2014-06-29
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>
10: int main(int argc,char **args)
11: {
12: Mat Amat,Pmat;
14: PetscInt i,m,M,its,Istart,Iend,j,Ii,bs,ix,ne=4;
15: PetscReal x,y,h;
16: Vec xx,bb;
17: KSP ksp;
18: PetscReal soft_alpha = 1.e-3;
19: MPI_Comm comm;
20: PetscMPIInt npe,mype;
21: PC pc;
22: PetscScalar DD[4][4],DD2[4][4];
23: #if defined(PETSC_USE_LOG)
24: PetscLogStage stage;
25: #endif
26: #define DIAG_S 0.0
27: PetscScalar DD1[4][4] = { {5.0+DIAG_S, -2.0, -1.0, -2.0},
28: {-2.0, 5.0+DIAG_S, -2.0, -1.0},
29: {-1.0, -2.0, 5.0+DIAG_S, -2.0},
30: {-2.0, -1.0, -2.0, 5.0+DIAG_S} };
32: PetscInitialize(&argc,&args,(char*)0,help);
33: comm = PETSC_COMM_WORLD;
34: MPI_Comm_rank(comm, &mype);
35: MPI_Comm_size(comm, &npe);
36: PetscOptionsGetInt(NULL,"-ne",&ne,NULL);
37: h = 1./ne;
38: /* ne*ne; number of global elements */
39: PetscOptionsGetReal(NULL,"-alpha",&soft_alpha,NULL);
40: M = (ne+1)*(ne+1); /* global number of nodes */
41: /* create stiffness matrix */
42: MatCreateAIJ(comm,PETSC_DECIDE,PETSC_DECIDE,M,M,
43: 18,NULL,6,NULL,&Amat);
44: MatCreateAIJ(comm,PETSC_DECIDE,PETSC_DECIDE,M,M,
45: 18,NULL,6,NULL,&Pmat);
46: MatGetOwnershipRange(Amat,&Istart,&Iend);
47: m = Iend-Istart;
48: bs = 1;
49: /* Generate vectors */
50: VecCreate(comm,&xx);
51: VecSetSizes(xx,m,M);
52: VecSetFromOptions(xx);
53: VecDuplicate(xx,&bb);
54: VecSet(bb,.0);
55: /* generate element matrices */
56: {
57: FILE *file;
58: char fname[] = "data/elem_2d_therm.txt";
59: file = fopen(fname, "r");
60: if (file == 0) {
61: DD1[0][0] = 0.66666666666666663;
62: DD1[0][1] = -0.16666666666666669;
63: DD1[0][2] = -0.33333333333333343;
64: DD1[0][3] = -0.16666666666666666;
65: DD1[1][0] = -0.16666666666666669;
66: DD1[1][1] = 0.66666666666666663;
67: DD1[1][2] = -0.16666666666666666;
68: DD1[1][3] = -0.33333333333333343;
69: DD1[2][0] = -0.33333333333333343;
70: DD1[2][1] = -0.16666666666666666;
71: DD1[2][2] = 0.66666666666666663;
72: DD1[2][3] = -0.16666666666666663;
73: DD1[3][0] = -0.16666666666666666;
74: DD1[3][1] = -0.33333333333333343;
75: DD1[3][2] = -0.16666666666666663;
76: DD1[3][3] = 0.66666666666666663;
77: } else {
78: for (i=0;i<4;i++) {
79: for (j=0;j<4;j++) {
80: fscanf(file, "%le", &DD1[i][j]);
81: }
82: }
83: }
84: /* BC version of element */
85: for (i=0;i<4;i++) {
86: for (j=0;j<4;j++) {
87: if (i<2 || j < 2) {
88: if (i==j) DD2[i][j] = .1*DD1[i][j];
89: else DD2[i][j] = 0.0;
90: } else DD2[i][j] = DD1[i][j];
91: }
92: }
93: }
94: {
95: PetscReal coords[2*m];
96: /* forms the element stiffness for the Laplacian and coordinates */
97: for (Ii=Istart,ix=0; Ii<Iend; Ii++,ix++) {
98: j = Ii/(ne+1); i = Ii%(ne+1);
99: /* coords */
100: x = h*(Ii % (ne+1)); y = h*(Ii/(ne+1));
101: coords[2*ix] = x; coords[2*ix+1] = y;
102: if (i<ne && j<ne) {
103: PetscInt jj,ii,idx[4] = {Ii, Ii+1, Ii + (ne+1) + 1, Ii + (ne+1)};
104: /* radius */
105: PetscReal radius = PetscSqrtScalar((x-.5+h/2)*(x-.5+h/2) + (y-.5+h/2)*(y-.5+h/2));
106: PetscReal alpha = 1.0;
107: if (radius < 0.25) alpha = soft_alpha;
110: for (ii=0; ii<4; ii++) {
111: for (jj=0; jj<4; jj++) DD[ii][jj] = alpha*DD1[ii][jj];
112: }
113: MatSetValues(Pmat,4,idx,4,idx,(const PetscScalar*)DD,ADD_VALUES);
114: if (j>0) {
115: MatSetValues(Amat,4,idx,4,idx,(const PetscScalar*)DD,ADD_VALUES);
116: } else {
117: /* a BC */
118: for (ii=0;ii<4;ii++) {
119: for (jj=0;jj<4;jj++) DD[ii][jj] = alpha*DD2[ii][jj];
120: }
121: MatSetValues(Amat,4,idx,4,idx,(const PetscScalar*)DD,ADD_VALUES);
122: }
123: }
124: if (j>0) {
125: PetscScalar v = h*h;
126: PetscInt jj = Ii;
127: VecSetValues(bb,1,&jj,&v,INSERT_VALUES);
128: }
129: }
130: MatAssemblyBegin(Amat,MAT_FINAL_ASSEMBLY);
131: MatAssemblyEnd(Amat,MAT_FINAL_ASSEMBLY);
132: MatAssemblyBegin(Pmat,MAT_FINAL_ASSEMBLY);
133: MatAssemblyEnd(Pmat,MAT_FINAL_ASSEMBLY);
134: VecAssemblyBegin(bb);
135: VecAssemblyEnd(bb);
137: /* Setup solver */
138: KSPCreate(PETSC_COMM_WORLD,&ksp);
139: KSPSetType(ksp, KSPCG);
140: KSPGetPC(ksp,&pc);
141: PCSetType(pc,PCGAMG);
142: KSPSetFromOptions(ksp);
144: /* PCGAMGSetType(pc,"agg"); */
146: /* finish KSP/PC setup */
147: KSPSetOperators(ksp, Amat, Amat, SAME_NONZERO_PATTERN);
148: PCSetCoordinates(pc, 2, m, coords);
149: }
151: if (!PETSC_TRUE) {
152: PetscViewer viewer;
153: PetscViewerASCIIOpen(comm, "Amat.m", &viewer);
154: PetscViewerSetFormat(viewer, PETSC_VIEWER_ASCII_MATLAB);
155: MatView(Amat,viewer);
156: PetscViewerDestroy(&viewer);
157: }
159: /* solve */
160: #if defined(PETSC_USE_LOG)
161: PetscLogStageRegister("Solve", &stage);
162: PetscLogStagePush(stage);
163: #endif
164: VecSet(xx,.0);
166: KSPSolve(ksp,bb,xx);
168: #if defined(PETSC_USE_LOG)
169: PetscLogStagePop();
170: #endif
172: KSPGetIterationNumber(ksp,&its);
174: if (!PETSC_TRUE) {
175: PetscReal norm,norm2;
176: PetscViewer viewer;
177: Vec res;
178: PetscViewerASCIIOpen(comm, "rhs.m", &viewer);
179: PetscViewerSetFormat(viewer, PETSC_VIEWER_ASCII_MATLAB);
180: VecView(bb,viewer);
181: PetscViewerDestroy(&viewer);
182: VecNorm(bb, NORM_2, &norm2);
184: PetscViewerASCIIOpen(comm, "solution.m", &viewer);
185: PetscViewerSetFormat(viewer, PETSC_VIEWER_ASCII_MATLAB);
186: VecView(xx,viewer);
187: PetscViewerDestroy(&viewer);
189: VecDuplicate(xx, &res);
190: MatMult(Amat, xx, res);
191: VecAXPY(bb, -1.0, res);
192: VecDestroy(&res);
193: VecNorm(bb,NORM_2,&norm);
194: PetscPrintf(PETSC_COMM_WORLD,"[%d]%s |b-Ax|/|b|=%e, |b|=%e\n",0,__FUNCT__,norm/norm2,norm2);
196: PetscViewerASCIIOpen(comm, "residual.m", &viewer);
197: PetscViewerSetFormat(viewer, PETSC_VIEWER_ASCII_MATLAB);
198: VecView(bb,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 0;
211: }