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 simple\n\
4: bilinear elements on the unit square. Input arguments are:\n\
5: -m <size> : problem size\n\n";
7: #include petscsles.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: SLES sles;
37: KSP ksp;
38: IS is;
40: PetscInitialize(&argc,&args,(char *)0,help);
41: PetscOptionsGetInt(PETSC_NULL,"-m",&m,PETSC_NULL);
42: N = (m+1)*(m+1); /* dimension of matrix */
43: M = m*m; /* number of elements */
44: h = 1.0/m; /* mesh width */
46: /* create stiffness matrix */
47: MatCreateSeqAIJ(PETSC_COMM_SELF,N,N,9,PETSC_NULL,&C);
49: /* forms the element stiffness for the Laplacian */
50: FormElementStiffness(h*h,Ke);
51: for (i=0; i<M; i++) {
52: /* location of lower left corner of element */
53: x = h*(i % m); y = h*(i/m);
54: /* node numbers for the four corners of element */
55: idx[0] = (m+1)*(i/m) + (i % m);
56: idx[1] = idx[0]+1; idx[2] = idx[1] + m + 1; idx[3] = idx[2] - 1;
57: MatSetValues(C,4,idx,4,idx,Ke,ADD_VALUES);
58: }
59: MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
60: MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);
62: /* create right hand side and solution */
64: VecCreateSeq(PETSC_COMM_SELF,N,&u);
65: VecDuplicate(u,&b);
66: VecDuplicate(b,&ustar);
67: VecSet(&zero,u);
68: VecSet(&zero,b);
70: for (i=0; i<M; i++) {
71: /* location of lower left corner of element */
72: x = h*(i % m); y = h*(i/m);
73: /* node numbers for the four corners of element */
74: idx[0] = (m+1)*(i/m) + (i % m);
75: idx[1] = idx[0]+1; idx[2] = idx[1] + m + 1; idx[3] = idx[2] - 1;
76: FormElementRhs(x,y,h*h,r);
77: VecSetValues(b,4,idx,r,ADD_VALUES);
78: }
79: VecAssemblyBegin(b);
80: VecAssemblyEnd(b);
82: /* modify matrix and rhs for Dirichlet boundary conditions */
83: PetscMalloc((4*m+1)*sizeof(int),&rows);
84: for (i=0; i<m+1; i++) {
85: rows[i] = i; /* bottom */
86: rows[3*m - 1 +i] = m*(m+1) + i; /* top */
87: }
88: count = m+1; /* left side */
89: for (i=m+1; i<m*(m+1); i+= m+1) {
90: rows[count++] = i;
91: }
92: count = 2*m; /* left side */
93: for (i=2*m+1; i<m*(m+1); i+= m+1) {
94: rows[count++] = i;
95: }
96: ISCreateGeneral(PETSC_COMM_SELF,4*m,rows,&is);
97: for (i=0; i<4*m; i++) {
98: x = h*(rows[i] % (m+1)); y = h*(rows[i]/(m+1));
99: val = y;
100: VecSetValues(u,1,&rows[i],&val,INSERT_VALUES);
101: VecSetValues(b,1,&rows[i],&val,INSERT_VALUES);
102: }
103: PetscFree(rows);
104: VecAssemblyBegin(u);
105: VecAssemblyEnd(u);
106: VecAssemblyBegin(b);
107: VecAssemblyEnd(b);
109: MatZeroRows(C,is,&one);
110: ISDestroy(is);
112: /* solve linear system */
113: SLESCreate(PETSC_COMM_WORLD,&sles);
114: SLESSetOperators(sles,C,C,DIFFERENT_NONZERO_PATTERN);
115:
116: SLESSetFromOptions(sles);
117: SLESGetKSP(sles,&ksp);
118: KSPSetInitialGuessNonzero(ksp,PETSC_TRUE);
119: SLESSolve(sles,b,u,&its);
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: PetscPrintf(PETSC_COMM_WORLD,"Norm of error %A Iterations %d\n",norm*h,its);
134: SLESDestroy(sles);
135: VecDestroy(ustar);
136: VecDestroy(u);
137: VecDestroy(b);
138: MatDestroy(C);
139: PetscFinalize();
140: return 0;
141: }