Actual source code: ex4.c
1: /*$Id: ex4.c,v 1.64 2001/08/07 21:30:50 bsmith Exp $*/
3: static char help[] = "Solves a linear system with KSP. The matrix uses simple\n\
4: bilinear elements on the unit square. Input arguments are:\n\
5: -m <size> : problem size\n\n";
7: #include petscksp.h
11: int FormElementStiffness(PetscReal H,PetscScalar *Ke)
12: {
13: Ke[0] = H/6.0; Ke[1] = -.125*H; Ke[2] = H/12.0; Ke[3] = -.125*H;
14: Ke[4] = -.125*H; Ke[5] = H/6.0; Ke[6] = -.125*H; Ke[7] = H/12.0;
15: Ke[8] = H/12.0; Ke[9] = -.125*H; Ke[10] = H/6.0; Ke[11] = -.125*H;
16: Ke[12] = -.125*H; Ke[13] = H/12.0; Ke[14] = -.125*H; Ke[15] = H/6.0;
17: return 0;
18: }
21: int FormElementRhs(PetscReal x,PetscReal y,PetscReal H,PetscScalar *r)
22: {
23: r[0] = 0.; r[1] = 0.; r[2] = 0.; r[3] = 0.0;
24: return 0;
25: }
29: int main(int argc,char **args)
30: {
31: Mat C;
32: int i,m = 2,N,M,its,ierr,idx[4],count,*rows;
33: PetscScalar val,zero = 0.0,one = 1.0,none = -1.0,Ke[16],r[4];
34: PetscReal x,y,h,norm;
35: Vec u,ustar,b;
36: KSP ksp;
37: IS is;
39: PetscInitialize(&argc,&args,(char *)0,help);
40: PetscOptionsGetInt(PETSC_NULL,"-m",&m,PETSC_NULL);
41: N = (m+1)*(m+1); /* dimension of matrix */
42: M = m*m; /* number of elements */
43: h = 1.0/m; /* mesh width */
45: /* create stiffness matrix */
46: MatCreateSeqAIJ(PETSC_COMM_SELF,N,N,9,PETSC_NULL,&C);
48: /* forms the element stiffness for the Laplacian */
49: FormElementStiffness(h*h,Ke);
50: for (i=0; i<M; i++) {
51: /* location of lower left corner of element */
52: x = h*(i % m); y = h*(i/m);
53: /* node numbers for the four corners of element */
54: idx[0] = (m+1)*(i/m) + (i % m);
55: idx[1] = idx[0]+1; idx[2] = idx[1] + m + 1; idx[3] = idx[2] - 1;
56: MatSetValues(C,4,idx,4,idx,Ke,ADD_VALUES);
57: }
58: MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
59: MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);
61: /* create right hand side and solution */
63: VecCreateSeq(PETSC_COMM_SELF,N,&u);
64: VecDuplicate(u,&b);
65: VecDuplicate(b,&ustar);
66: VecSet(&zero,u);
67: VecSet(&zero,b);
69: for (i=0; i<M; i++) {
70: /* location of lower left corner of element */
71: x = h*(i % m); y = h*(i/m);
72: /* node numbers for the four corners of element */
73: idx[0] = (m+1)*(i/m) + (i % m);
74: idx[1] = idx[0]+1; idx[2] = idx[1] + m + 1; idx[3] = idx[2] - 1;
75: FormElementRhs(x,y,h*h,r);
76: VecSetValues(b,4,idx,r,ADD_VALUES);
77: }
78: VecAssemblyBegin(b);
79: VecAssemblyEnd(b);
81: /* modify matrix and rhs for Dirichlet boundary conditions */
82: PetscMalloc((4*m+1)*sizeof(int),&rows);
83: for (i=0; i<m+1; i++) {
84: rows[i] = i; /* bottom */
85: rows[3*m - 1 +i] = m*(m+1) + i; /* top */
86: }
87: count = m+1; /* left side */
88: for (i=m+1; i<m*(m+1); i+= m+1) {
89: rows[count++] = i;
90: }
91: count = 2*m; /* left side */
92: for (i=2*m+1; i<m*(m+1); i+= m+1) {
93: rows[count++] = i;
94: }
95: ISCreateGeneral(PETSC_COMM_SELF,4*m,rows,&is);
96: for (i=0; i<4*m; i++) {
97: x = h*(rows[i] % (m+1)); y = h*(rows[i]/(m+1));
98: val = y;
99: VecSetValues(u,1,&rows[i],&val,INSERT_VALUES);
100: VecSetValues(b,1,&rows[i],&val,INSERT_VALUES);
101: }
102: PetscFree(rows);
103: VecAssemblyBegin(u);
104: VecAssemblyEnd(u);
105: VecAssemblyBegin(b);
106: VecAssemblyEnd(b);
108: MatZeroRows(C,is,&one);
109: ISDestroy(is);
111: /* solve linear system */
112: KSPCreate(PETSC_COMM_WORLD,&ksp);
113: KSPSetOperators(ksp,C,C,DIFFERENT_NONZERO_PATTERN);
114:
115: KSPSetFromOptions(ksp);
116: KSPSetInitialGuessNonzero(ksp,PETSC_TRUE);
117: KSPSetRhs(ksp,b);
118: KSPSetSolution(ksp,u);
119: KSPSolve(ksp);
121: /* check error */
122: for (i=0; i<N; i++) {
123: x = h*(i % (m+1)); y = h*(i/(m+1));
124: val = y;
125: VecSetValues(ustar,1,&i,&val,INSERT_VALUES);
126: }
127: VecAssemblyBegin(ustar);
128: VecAssemblyEnd(ustar);
130: VecAXPY(&none,ustar,u);
131: VecNorm(u,NORM_2,&norm);
132: KSPGetIterationNumber(ksp,&its);
133: PetscPrintf(PETSC_COMM_WORLD,"Norm of error %A Iterations %d\n",norm*h,its);
135: KSPDestroy(ksp);
136: VecDestroy(ustar);
137: VecDestroy(u);
138: VecDestroy(b);
139: MatDestroy(C);
140: PetscFinalize();
141: return 0;
142: }