Actual source code: ex3.c
1: /*$Id: ex3.c,v 1.73 2001/08/07 21:30:50 bsmith Exp $*/
3: static char help[] = "This example solves a linear system in parallel with SLES. The matrix\n\
4: uses simple bilinear elements on the unit square. To test the parallel\n\
5: matrix assembly, the matrix is intentionally laid out across processors\n\
6: differently from the way it is assembled. Input arguments are:\n\
7: -m <size> : problem size\n\n";
9: #include petscsles.h
13: int FormElementStiffness(PetscReal H,PetscScalar *Ke)
14: {
16: Ke[0] = H/6.0; Ke[1] = -.125*H; Ke[2] = H/12.0; Ke[3] = -.125*H;
17: Ke[4] = -.125*H; Ke[5] = H/6.0; Ke[6] = -.125*H; Ke[7] = H/12.0;
18: Ke[8] = H/12.0; Ke[9] = -.125*H; Ke[10] = H/6.0; Ke[11] = -.125*H;
19: Ke[12] = -.125*H; Ke[13] = H/12.0; Ke[14] = -.125*H; Ke[15] = H/6.0;
20: return(0);
21: }
24: int FormElementRhs(PetscReal x,PetscReal y,PetscReal H,PetscScalar *r)
25: {
27: r[0] = 0.; r[1] = 0.; r[2] = 0.; r[3] = 0.0;
28: return(0);
29: }
33: int main(int argc,char **args)
34: {
35: Mat C;
36: int i,m = 5,rank,size,N,start,end,M,its;
37: PetscScalar val,zero = 0.0,one = 1.0,none = -1.0,Ke[16],r[4];
38: PetscReal x,y,h,norm;
39: int ierr,idx[4],count,*rows;
40: Vec u,ustar,b;
41: SLES sles;
42: KSP ksp;
43: IS is;
45: PetscInitialize(&argc,&args,(char *)0,help);
46: PetscOptionsGetInt(PETSC_NULL,"-m",&m,PETSC_NULL);
47: N = (m+1)*(m+1); /* dimension of matrix */
48: M = m*m; /* number of elements */
49: h = 1.0/m; /* mesh width */
50: MPI_Comm_rank(PETSC_COMM_WORLD,&rank);
51: MPI_Comm_size(PETSC_COMM_WORLD,&size);
53: /* Create stiffness matrix */
54: MatCreate(PETSC_COMM_WORLD,PETSC_DECIDE,PETSC_DECIDE,N,N,&C);
55: MatSetFromOptions(C);
56: start = rank*(M/size) + ((M%size) < rank ? (M%size) : rank);
57: end = start + M/size + ((M%size) > rank);
59: /* Assemble matrix */
60: FormElementStiffness(h*h,Ke); /* element stiffness for Laplacian */
61: for (i=start; i<end; i++) {
62: /* location of lower left corner of element */
63: x = h*(i % m); y = h*(i/m);
64: /* node numbers for the four corners of element */
65: idx[0] = (m+1)*(i/m) + (i % m);
66: idx[1] = idx[0]+1; idx[2] = idx[1] + m + 1; idx[3] = idx[2] - 1;
67: MatSetValues(C,4,idx,4,idx,Ke,ADD_VALUES);
68: }
69: MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
70: MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);
72: /* Create right-hand-side and solution vectors */
73: VecCreate(PETSC_COMM_WORLD,&u);
74: VecSetSizes(u,PETSC_DECIDE,N);
75: VecSetFromOptions(u);
76: PetscObjectSetName((PetscObject)u,"Approx. Solution");
77: VecDuplicate(u,&b);
78: PetscObjectSetName((PetscObject)b,"Right hand side");
79: VecDuplicate(b,&ustar);
80: VecSet(&zero,u);
81: VecSet(&zero,b);
83: /* Assemble right-hand-side vector */
84: for (i=start; i<end; i++) {
85: /* location of lower left corner of element */
86: x = h*(i % m); y = h*(i/m);
87: /* node numbers for the four corners of element */
88: idx[0] = (m+1)*(i/m) + (i % m);
89: idx[1] = idx[0]+1; idx[2] = idx[1] + m + 1; idx[3] = idx[2] - 1;
90: FormElementRhs(x,y,h*h,r);
91: VecSetValues(b,4,idx,r,ADD_VALUES);
92: }
93: VecAssemblyBegin(b);
94: VecAssemblyEnd(b);
96: /* Modify matrix and right-hand-side for Dirichlet boundary conditions */
97: PetscMalloc(4*m*sizeof(int),&rows);
98: for (i=0; i<m+1; i++) {
99: rows[i] = i; /* bottom */
100: rows[3*m - 1 +i] = m*(m+1) + i; /* top */
101: }
102: count = m+1; /* left side */
103: for (i=m+1; i<m*(m+1); i+= m+1) {
104: rows[count++] = i;
105: }
106: count = 2*m; /* left side */
107: for (i=2*m+1; i<m*(m+1); i+= m+1) {
108: rows[count++] = i;
109: }
110: ISCreateGeneral(PETSC_COMM_SELF,4*m,rows,&is);
111: for (i=0; i<4*m; i++) {
112: x = h*(rows[i] % (m+1)); y = h*(rows[i]/(m+1));
113: val = y;
114: VecSetValues(u,1,&rows[i],&val,INSERT_VALUES);
115: VecSetValues(b,1,&rows[i],&val,INSERT_VALUES);
116: }
117: PetscFree(rows);
118: VecAssemblyBegin(u);
119: VecAssemblyEnd(u);
120: VecAssemblyBegin(b);
121: VecAssemblyEnd(b);
123: MatZeroRows(C,is,&one);
124: ISDestroy(is);
127: { Mat A;
128: MatConvert(C,MATSAME,&A);
129: MatDestroy(C);
130: MatConvert(A,MATSAME,&C);
131: MatDestroy(A);
132: }
134: /* Solve linear system */
135: SLESCreate(PETSC_COMM_WORLD,&sles);
136: SLESSetOperators(sles,C,C,DIFFERENT_NONZERO_PATTERN);
137: SLESSetFromOptions(sles);
138: SLESGetKSP(sles,&ksp);
139: KSPSetInitialGuessNonzero(ksp,PETSC_TRUE);
140: SLESSolve(sles,b,u,&its);
142: /* Check error */
143: VecGetOwnershipRange(ustar,&start,&end);
144: for (i=start; i<end; i++) {
145: x = h*(i % (m+1)); y = h*(i/(m+1));
146: val = y;
147: VecSetValues(ustar,1,&i,&val,INSERT_VALUES);
148: }
149: VecAssemblyBegin(ustar);
150: VecAssemblyEnd(ustar);
151: VecAXPY(&none,ustar,u);
152: VecNorm(u,NORM_2,&norm);
153: PetscPrintf(PETSC_COMM_WORLD,"Norm of error %A Iterations %d\n",norm*h,its);
155: /* Free work space */
156: SLESDestroy(sles);
157: VecDestroy(ustar);
158: VecDestroy(u);
159: VecDestroy(b);
160: MatDestroy(C);
161: PetscFinalize();
162: return 0;
163: }