Actual source code: ex54.c
petsc-3.8.4 2018-03-24
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 */
38: /* create stiffness matrix */
39: MatCreateAIJ(comm,PETSC_DECIDE,PETSC_DECIDE,M,M,
40: 18,NULL,6,NULL,&Amat);
41: MatCreateAIJ(comm,PETSC_DECIDE,PETSC_DECIDE,M,M,
42: 18,NULL,6,NULL,&Pmat);
43: MatGetOwnershipRange(Amat,&Istart,&Iend);
44: m = Iend-Istart;
45: /* Generate vectors */
46: VecCreate(comm,&xx);
47: VecSetSizes(xx,m,M);
48: VecSetFromOptions(xx);
49: VecDuplicate(xx,&bb);
50: VecSet(bb,.0);
51: /* generate element matrices -- see ex56.c on how to use different data set */
52: {
53: DD1[0][0] = 0.66666666666666663;
54: DD1[0][1] = -0.16666666666666669;
55: DD1[0][2] = -0.33333333333333343;
56: DD1[0][3] = -0.16666666666666666;
57: DD1[1][0] = -0.16666666666666669;
58: DD1[1][1] = 0.66666666666666663;
59: DD1[1][2] = -0.16666666666666666;
60: DD1[1][3] = -0.33333333333333343;
61: DD1[2][0] = -0.33333333333333343;
62: DD1[2][1] = -0.16666666666666666;
63: DD1[2][2] = 0.66666666666666663;
64: DD1[2][3] = -0.16666666666666663;
65: DD1[3][0] = -0.16666666666666666;
66: DD1[3][1] = -0.33333333333333343;
67: DD1[3][2] = -0.16666666666666663;
68: DD1[3][3] = 0.66666666666666663;
70: /* BC version of element */
71: for (i=0;i<4;i++) {
72: for (j=0;j<4;j++) {
73: if (i<2 || j < 2) {
74: if (i==j) DD2[i][j] = .1*DD1[i][j];
75: else DD2[i][j] = 0.0;
76: } else DD2[i][j] = DD1[i][j];
77: }
78: }
79: }
80: {
81: PetscReal *coords;
82: PC pc;
83: PetscMalloc1(2*m,&coords);
84: /* forms the element stiffness for the Laplacian and coordinates */
85: for (Ii=Istart,ix=0; Ii<Iend; Ii++,ix++) {
86: j = Ii/(ne+1); i = Ii%(ne+1);
87: /* coords */
88: x = h*(Ii % (ne+1)); y = h*(Ii/(ne+1));
89: coords[2*ix] = x; coords[2*ix+1] = y;
90: if (i<ne && j<ne) {
91: PetscInt jj,ii,idx[4];
92: /* radius */
93: PetscReal radius = PetscSqrtReal((x-.5+h/2)*(x-.5+h/2) + (y-.5+h/2)*(y-.5+h/2));
94: PetscReal alpha = 1.0;
96: idx[0] = Ii; idx[1] = Ii+1; idx[2] = Ii + (ne+1) + 1; idx[3] = Ii + (ne+1);
97: if (radius < 0.25) alpha = soft_alpha;
100: for (ii=0; ii<4; ii++) {
101: for (jj=0; jj<4; jj++) DD[ii][jj] = alpha*DD1[ii][jj];
102: }
103: MatSetValues(Pmat,4,idx,4,idx,(const PetscScalar*)DD,ADD_VALUES);
104: if (j>0) {
105: MatSetValues(Amat,4,idx,4,idx,(const PetscScalar*)DD,ADD_VALUES);
106: } else {
107: /* a BC */
108: for (ii=0;ii<4;ii++) {
109: for (jj=0;jj<4;jj++) DD[ii][jj] = alpha*DD2[ii][jj];
110: }
111: MatSetValues(Amat,4,idx,4,idx,(const PetscScalar*)DD,ADD_VALUES);
112: }
113: }
114: if (j>0) {
115: PetscScalar v = h*h;
116: PetscInt jj = Ii;
117: VecSetValues(bb,1,&jj,&v,INSERT_VALUES);
118: }
119: }
120: MatAssemblyBegin(Amat,MAT_FINAL_ASSEMBLY);
121: MatAssemblyEnd(Amat,MAT_FINAL_ASSEMBLY);
122: MatAssemblyBegin(Pmat,MAT_FINAL_ASSEMBLY);
123: MatAssemblyEnd(Pmat,MAT_FINAL_ASSEMBLY);
124: VecAssemblyBegin(bb);
125: VecAssemblyEnd(bb);
127: /* Setup solver */
128: KSPCreate(PETSC_COMM_WORLD,&ksp);
129: KSPSetFromOptions(ksp);
131: /* finish KSP/PC setup */
132: KSPSetOperators(ksp, Amat, Amat);
134: KSPGetPC(ksp,&pc);
135: PCSetCoordinates(pc, 2, m, coords);
136: PetscFree(coords);
137: }
139: if (!PETSC_TRUE) {
140: PetscViewer viewer;
141: PetscViewerASCIIOpen(comm, "Amat.m", &viewer);
142: PetscViewerPushFormat(viewer, PETSC_VIEWER_ASCII_MATLAB);
143: MatView(Amat,viewer);
144: PetscViewerPopFormat(viewer);
145: PetscViewerDestroy(&viewer);
146: }
148: /* solve */
149: #if defined(PETSC_USE_LOG)
150: PetscLogStageRegister("Solve", &stage);
151: PetscLogStagePush(stage);
152: #endif
153: VecSet(xx,.0);
155: KSPSetUp(ksp);
157: KSPSolve(ksp,bb,xx);
159: #if defined(PETSC_USE_LOG)
160: PetscLogStagePop();
161: #endif
163: KSPGetIterationNumber(ksp,&its);
165: if (!PETSC_TRUE) {
166: PetscReal norm,norm2;
167: PetscViewer viewer;
168: Vec res;
169: PetscViewerASCIIOpen(comm, "rhs.m", &viewer);
170: PetscViewerPushFormat(viewer, PETSC_VIEWER_ASCII_MATLAB);
171: VecView(bb,viewer);
172: PetscViewerPopFormat(viewer);
173: PetscViewerDestroy(&viewer);
174: VecNorm(bb, NORM_2, &norm2);
176: PetscViewerASCIIOpen(comm, "solution.m", &viewer);
177: PetscViewerPushFormat(viewer, PETSC_VIEWER_ASCII_MATLAB);
178: VecView(xx,viewer);
179: PetscViewerPopFormat(viewer);
180: PetscViewerDestroy(&viewer);
182: VecDuplicate(xx, &res);
183: MatMult(Amat, xx, res);
184: VecAXPY(bb, -1.0, res);
185: VecDestroy(&res);
186: VecNorm(bb,NORM_2,&norm);
187: PetscPrintf(PETSC_COMM_WORLD,"[%d]%s |b-Ax|/|b|=%e, |b|=%e\n",0,PETSC_FUNCTION_NAME,norm/norm2,norm2);
189: PetscViewerASCIIOpen(comm, "residual.m", &viewer);
190: PetscViewerPushFormat(viewer, PETSC_VIEWER_ASCII_MATLAB);
191: VecView(bb,viewer);
192: PetscViewerPopFormat(viewer);
193: PetscViewerDestroy(&viewer);
194: }
196: /* Free work space */
197: KSPDestroy(&ksp);
198: VecDestroy(&xx);
199: VecDestroy(&bb);
200: MatDestroy(&Amat);
201: MatDestroy(&Pmat);
203: PetscFinalize();
204: return ierr;
205: }