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 SLES. The matrix uses simplen
4: bilinear elements on the unit square. Input arguments are:n
5: -m <size> : problem sizenn";
7: #include petscsles.h
9: int FormElementStiffness(PetscReal H,PetscScalar *Ke)
10: {
11: Ke[0] = H/6.0; Ke[1] = -.125*H; Ke[2] = H/12.0; Ke[3] = -.125*H;
12: Ke[4] = -.125*H; Ke[5] = H/6.0; Ke[6] = -.125*H; Ke[7] = H/12.0;
13: Ke[8] = H/12.0; Ke[9] = -.125*H; Ke[10] = H/6.0; Ke[11] = -.125*H;
14: Ke[12] = -.125*H; Ke[13] = H/12.0; Ke[14] = -.125*H; Ke[15] = H/6.0;
15: return 0;
16: }
17: int FormElementRhs(PetscReal x,PetscReal y,PetscReal H,PetscScalar *r)
18: {
19: r[0] = 0.; r[1] = 0.; r[2] = 0.; r[3] = 0.0;
20: return 0;
21: }
23: int main(int argc,char **args)
24: {
25: Mat C;
26: int i,m = 2,N,M,its,ierr,idx[4],count,*rows;
27: PetscScalar val,zero = 0.0,one = 1.0,none = -1.0,Ke[16],r[4];
28: PetscReal x,y,h,norm;
29: Vec u,ustar,b;
30: SLES sles;
31: KSP ksp;
32: IS is;
34: PetscInitialize(&argc,&args,(char *)0,help);
35: PetscOptionsGetInt(PETSC_NULL,"-m",&m,PETSC_NULL);
36: N = (m+1)*(m+1); /* dimension of matrix */
37: M = m*m; /* number of elements */
38: h = 1.0/m; /* mesh width */
40: /* create stiffness matrix */
41: MatCreateSeqAIJ(PETSC_COMM_SELF,N,N,9,PETSC_NULL,&C);
43: /* forms the element stiffness for the Laplacian */
44: FormElementStiffness(h*h,Ke);
45: for (i=0; i<M; i++) {
46: /* location of lower left corner of element */
47: x = h*(i % m); y = h*(i/m);
48: /* node numbers for the four corners of element */
49: idx[0] = (m+1)*(i/m) + (i % m);
50: idx[1] = idx[0]+1; idx[2] = idx[1] + m + 1; idx[3] = idx[2] - 1;
51: MatSetValues(C,4,idx,4,idx,Ke,ADD_VALUES);
52: }
53: MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
54: MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);
56: /* create right hand side and solution */
58: VecCreateSeq(PETSC_COMM_SELF,N,&u);
59: VecDuplicate(u,&b);
60: VecDuplicate(b,&ustar);
61: VecSet(&zero,u);
62: VecSet(&zero,b);
64: for (i=0; i<M; i++) {
65: /* location of lower left corner of element */
66: x = h*(i % m); y = h*(i/m);
67: /* node numbers for the four corners of element */
68: idx[0] = (m+1)*(i/m) + (i % m);
69: idx[1] = idx[0]+1; idx[2] = idx[1] + m + 1; idx[3] = idx[2] - 1;
70: FormElementRhs(x,y,h*h,r);
71: VecSetValues(b,4,idx,r,ADD_VALUES);
72: }
73: VecAssemblyBegin(b);
74: VecAssemblyEnd(b);
76: /* modify matrix and rhs for Dirichlet boundary conditions */
77: PetscMalloc((4*m+1)*sizeof(int),&rows);
78: for (i=0; i<m+1; i++) {
79: rows[i] = i; /* bottom */
80: rows[3*m - 1 +i] = m*(m+1) + i; /* top */
81: }
82: count = m+1; /* left side */
83: for (i=m+1; i<m*(m+1); i+= m+1) {
84: rows[count++] = i;
85: }
86: count = 2*m; /* left side */
87: for (i=2*m+1; i<m*(m+1); i+= m+1) {
88: rows[count++] = i;
89: }
90: ISCreateGeneral(PETSC_COMM_SELF,4*m,rows,&is);
91: for (i=0; i<4*m; i++) {
92: x = h*(rows[i] % (m+1)); y = h*(rows[i]/(m+1));
93: val = y;
94: VecSetValues(u,1,&rows[i],&val,INSERT_VALUES);
95: VecSetValues(b,1,&rows[i],&val,INSERT_VALUES);
96: }
97: PetscFree(rows);
98: VecAssemblyBegin(u);
99: VecAssemblyEnd(u);
100: VecAssemblyBegin(b);
101: VecAssemblyEnd(b);
103: MatZeroRows(C,is,&one);
104: ISDestroy(is);
106: /* solve linear system */
107: SLESCreate(PETSC_COMM_WORLD,&sles);
108: SLESSetOperators(sles,C,C,DIFFERENT_NONZERO_PATTERN);
109:
110: SLESSetFromOptions(sles);
111: SLESGetKSP(sles,&ksp);
112: KSPSetInitialGuessNonzero(ksp,PETSC_TRUE);
113: SLESSolve(sles,b,u,&its);
115: /* check error */
116: for (i=0; i<N; i++) {
117: x = h*(i % (m+1)); y = h*(i/(m+1));
118: val = y;
119: VecSetValues(ustar,1,&i,&val,INSERT_VALUES);
120: }
121: VecAssemblyBegin(ustar);
122: VecAssemblyEnd(ustar);
124: VecAXPY(&none,ustar,u);
125: VecNorm(u,NORM_2,&norm);
126: PetscPrintf(PETSC_COMM_WORLD,"Norm of error %A Iterations %dn",norm*h,its);
128: SLESDestroy(sles);
129: VecDestroy(ustar);
130: VecDestroy(u);
131: VecDestroy(b);
132: MatDestroy(C);
133: PetscFinalize();
134: return 0;
135: }