Actual source code: ex54.c
petsc-3.7.5 2017-01-01
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,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: PetscScalar DD[4][4],DD2[4][4];
22: #if defined(PETSC_USE_LOG)
23: PetscLogStage stage;
24: #endif
25: #define DIAG_S 0.0
26: PetscScalar DD1[4][4] = { {5.0+DIAG_S, -2.0, -1.0, -2.0},
27: {-2.0, 5.0+DIAG_S, -2.0, -1.0},
28: {-1.0, -2.0, 5.0+DIAG_S, -2.0},
29: {-2.0, -1.0, -2.0, 5.0+DIAG_S} };
31: PetscInitialize(&argc,&args,(char*)0,help);
32: comm = PETSC_COMM_WORLD;
33: MPI_Comm_rank(comm, &mype);
34: MPI_Comm_size(comm, &npe);
35: PetscOptionsGetInt(NULL,NULL,"-ne",&ne,NULL);
36: h = 1./ne;
37: /* ne*ne; number of global elements */
38: PetscOptionsGetReal(NULL,NULL,"-alpha",&soft_alpha,NULL);
39: M = (ne+1)*(ne+1); /* global number of nodes */
40: /* create stiffness matrix */
41: MatCreateAIJ(comm,PETSC_DECIDE,PETSC_DECIDE,M,M,
42: 18,NULL,6,NULL,&Amat);
43: MatCreateAIJ(comm,PETSC_DECIDE,PETSC_DECIDE,M,M,
44: 18,NULL,6,NULL,&Pmat);
45: MatGetOwnershipRange(Amat,&Istart,&Iend);
46: m = Iend-Istart;
47: /* Generate vectors */
48: VecCreate(comm,&xx);
49: VecSetSizes(xx,m,M);
50: VecSetFromOptions(xx);
51: VecDuplicate(xx,&bb);
52: VecSet(bb,.0);
53: /* generate element matrices -- see ex56.c on how to use different data set */
54: {
55: DD1[0][0] = 0.66666666666666663;
56: DD1[0][1] = -0.16666666666666669;
57: DD1[0][2] = -0.33333333333333343;
58: DD1[0][3] = -0.16666666666666666;
59: DD1[1][0] = -0.16666666666666669;
60: DD1[1][1] = 0.66666666666666663;
61: DD1[1][2] = -0.16666666666666666;
62: DD1[1][3] = -0.33333333333333343;
63: DD1[2][0] = -0.33333333333333343;
64: DD1[2][1] = -0.16666666666666666;
65: DD1[2][2] = 0.66666666666666663;
66: DD1[2][3] = -0.16666666666666663;
67: DD1[3][0] = -0.16666666666666666;
68: DD1[3][1] = -0.33333333333333343;
69: DD1[3][2] = -0.16666666666666663;
70: DD1[3][3] = 0.66666666666666663;
72: /* BC version of element */
73: for (i=0;i<4;i++) {
74: for (j=0;j<4;j++) {
75: if (i<2 || j < 2) {
76: if (i==j) DD2[i][j] = .1*DD1[i][j];
77: else DD2[i][j] = 0.0;
78: } else DD2[i][j] = DD1[i][j];
79: }
80: }
81: }
82: {
83: PetscReal *coords;
84: PC pc;
85: PetscMalloc1(2*m,&coords);
86: /* forms the element stiffness for the Laplacian and coordinates */
87: for (Ii=Istart,ix=0; Ii<Iend; Ii++,ix++) {
88: j = Ii/(ne+1); i = Ii%(ne+1);
89: /* coords */
90: x = h*(Ii % (ne+1)); y = h*(Ii/(ne+1));
91: coords[2*ix] = x; coords[2*ix+1] = y;
92: if (i<ne && j<ne) {
93: PetscInt jj,ii,idx[4];
94: /* radius */
95: PetscReal radius = PetscSqrtReal((x-.5+h/2)*(x-.5+h/2) + (y-.5+h/2)*(y-.5+h/2));
96: PetscReal alpha = 1.0;
98: idx[0] = Ii; idx[1] = Ii+1; idx[2] = Ii + (ne+1) + 1; idx[3] = Ii + (ne+1);
99: if (radius < 0.25) alpha = soft_alpha;
102: for (ii=0; ii<4; ii++) {
103: for (jj=0; jj<4; jj++) DD[ii][jj] = alpha*DD1[ii][jj];
104: }
105: MatSetValues(Pmat,4,idx,4,idx,(const PetscScalar*)DD,ADD_VALUES);
106: if (j>0) {
107: MatSetValues(Amat,4,idx,4,idx,(const PetscScalar*)DD,ADD_VALUES);
108: } else {
109: /* a BC */
110: for (ii=0;ii<4;ii++) {
111: for (jj=0;jj<4;jj++) DD[ii][jj] = alpha*DD2[ii][jj];
112: }
113: MatSetValues(Amat,4,idx,4,idx,(const PetscScalar*)DD,ADD_VALUES);
114: }
115: }
116: if (j>0) {
117: PetscScalar v = h*h;
118: PetscInt jj = Ii;
119: VecSetValues(bb,1,&jj,&v,INSERT_VALUES);
120: }
121: }
122: MatAssemblyBegin(Amat,MAT_FINAL_ASSEMBLY);
123: MatAssemblyEnd(Amat,MAT_FINAL_ASSEMBLY);
124: MatAssemblyBegin(Pmat,MAT_FINAL_ASSEMBLY);
125: MatAssemblyEnd(Pmat,MAT_FINAL_ASSEMBLY);
126: VecAssemblyBegin(bb);
127: VecAssemblyEnd(bb);
129: /* Setup solver */
130: KSPCreate(PETSC_COMM_WORLD,&ksp);
131: KSPSetFromOptions(ksp);
133: /* finish KSP/PC setup */
134: KSPSetOperators(ksp, Amat, Amat);
136: KSPGetPC(ksp,&pc);
137: PCSetCoordinates(pc, 2, m, coords);
138: PetscFree(coords);
139: }
141: if (!PETSC_TRUE) {
142: PetscViewer viewer;
143: PetscViewerASCIIOpen(comm, "Amat.m", &viewer);
144: PetscViewerPushFormat(viewer, PETSC_VIEWER_ASCII_MATLAB);
145: MatView(Amat,viewer);
146: PetscViewerPopFormat(viewer);
147: PetscViewerDestroy(&viewer);
148: }
150: /* solve */
151: #if defined(PETSC_USE_LOG)
152: PetscLogStageRegister("Solve", &stage);
153: PetscLogStagePush(stage);
154: #endif
155: VecSet(xx,.0);
157: KSPSetUp(ksp);
159: KSPSolve(ksp,bb,xx);
161: #if defined(PETSC_USE_LOG)
162: PetscLogStagePop();
163: #endif
165: KSPGetIterationNumber(ksp,&its);
167: if (!PETSC_TRUE) {
168: PetscReal norm,norm2;
169: PetscViewer viewer;
170: Vec res;
171: PetscViewerASCIIOpen(comm, "rhs.m", &viewer);
172: PetscViewerPushFormat(viewer, PETSC_VIEWER_ASCII_MATLAB);
173: VecView(bb,viewer);
174: PetscViewerPopFormat(viewer);
175: PetscViewerDestroy(&viewer);
176: VecNorm(bb, NORM_2, &norm2);
178: PetscViewerASCIIOpen(comm, "solution.m", &viewer);
179: PetscViewerPushFormat(viewer, PETSC_VIEWER_ASCII_MATLAB);
180: VecView(xx,viewer);
181: PetscViewerPopFormat(viewer);
182: PetscViewerDestroy(&viewer);
184: VecDuplicate(xx, &res);
185: MatMult(Amat, xx, res);
186: VecAXPY(bb, -1.0, res);
187: VecDestroy(&res);
188: VecNorm(bb,NORM_2,&norm);
189: PetscPrintf(PETSC_COMM_WORLD,"[%d]%s |b-Ax|/|b|=%e, |b|=%e\n",0,__FUNCT__,norm/norm2,norm2);
191: PetscViewerASCIIOpen(comm, "residual.m", &viewer);
192: PetscViewerPushFormat(viewer, PETSC_VIEWER_ASCII_MATLAB);
193: VecView(bb,viewer);
194: PetscViewerPopFormat(viewer);
195: PetscViewerDestroy(&viewer);
196: }
198: /* Free work space */
199: KSPDestroy(&ksp);
200: VecDestroy(&xx);
201: VecDestroy(&bb);
202: MatDestroy(&Amat);
203: MatDestroy(&Pmat);
205: PetscFinalize();
206: return 0;
207: }