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 KSP. 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 petscksp.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: KSP ksp;
42: IS is;
44: PetscInitialize(&argc,&args,(char *)0,help);
45: PetscOptionsGetInt(PETSC_NULL,"-m",&m,PETSC_NULL);
46: N = (m+1)*(m+1); /* dimension of matrix */
47: M = m*m; /* number of elements */
48: h = 1.0/m; /* mesh width */
49: MPI_Comm_rank(PETSC_COMM_WORLD,&rank);
50: MPI_Comm_size(PETSC_COMM_WORLD,&size);
52: /* Create stiffness matrix */
53: MatCreate(PETSC_COMM_WORLD,PETSC_DECIDE,PETSC_DECIDE,N,N,&C);
54: MatSetFromOptions(C);
55: start = rank*(M/size) + ((M%size) < rank ? (M%size) : rank);
56: end = start + M/size + ((M%size) > rank);
58: /* Assemble matrix */
59: FormElementStiffness(h*h,Ke); /* element stiffness for Laplacian */
60: for (i=start; i<end; i++) {
61: /* location of lower left corner of element */
62: x = h*(i % m); y = h*(i/m);
63: /* node numbers for the four corners of element */
64: idx[0] = (m+1)*(i/m) + (i % m);
65: idx[1] = idx[0]+1; idx[2] = idx[1] + m + 1; idx[3] = idx[2] - 1;
66: MatSetValues(C,4,idx,4,idx,Ke,ADD_VALUES);
67: }
68: MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
69: MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);
71: /* Create right-hand-side and solution vectors */
72: VecCreate(PETSC_COMM_WORLD,&u);
73: VecSetSizes(u,PETSC_DECIDE,N);
74: VecSetFromOptions(u);
75: PetscObjectSetName((PetscObject)u,"Approx. Solution");
76: VecDuplicate(u,&b);
77: PetscObjectSetName((PetscObject)b,"Right hand side");
78: VecDuplicate(b,&ustar);
79: VecSet(&zero,u);
80: VecSet(&zero,b);
82: /* Assemble right-hand-side vector */
83: for (i=start; i<end; i++) {
84: /* location of lower left corner of element */
85: x = h*(i % m); y = h*(i/m);
86: /* node numbers for the four corners of element */
87: idx[0] = (m+1)*(i/m) + (i % m);
88: idx[1] = idx[0]+1; idx[2] = idx[1] + m + 1; idx[3] = idx[2] - 1;
89: FormElementRhs(x,y,h*h,r);
90: VecSetValues(b,4,idx,r,ADD_VALUES);
91: }
92: VecAssemblyBegin(b);
93: VecAssemblyEnd(b);
95: /* Modify matrix and right-hand-side for Dirichlet boundary conditions */
96: PetscMalloc(4*m*sizeof(int),&rows);
97: for (i=0; i<m+1; i++) {
98: rows[i] = i; /* bottom */
99: rows[3*m - 1 +i] = m*(m+1) + i; /* top */
100: }
101: count = m+1; /* left side */
102: for (i=m+1; i<m*(m+1); i+= m+1) {
103: rows[count++] = i;
104: }
105: count = 2*m; /* left side */
106: for (i=2*m+1; i<m*(m+1); i+= m+1) {
107: rows[count++] = i;
108: }
109: ISCreateGeneral(PETSC_COMM_SELF,4*m,rows,&is);
110: for (i=0; i<4*m; i++) {
111: x = h*(rows[i] % (m+1)); y = h*(rows[i]/(m+1));
112: val = y;
113: VecSetValues(u,1,&rows[i],&val,INSERT_VALUES);
114: VecSetValues(b,1,&rows[i],&val,INSERT_VALUES);
115: }
116: PetscFree(rows);
117: VecAssemblyBegin(u);
118: VecAssemblyEnd(u);
119: VecAssemblyBegin(b);
120: VecAssemblyEnd(b);
122: MatZeroRows(C,is,&one);
123: ISDestroy(is);
126: { Mat A;
127: MatConvert(C,MATSAME,&A);
128: MatDestroy(C);
129: MatConvert(A,MATSAME,&C);
130: MatDestroy(A);
131: }
133: /* Solve linear system */
134: KSPCreate(PETSC_COMM_WORLD,&ksp);
135: KSPSetOperators(ksp,C,C,DIFFERENT_NONZERO_PATTERN);
136: KSPSetFromOptions(ksp);
137: KSPSetInitialGuessNonzero(ksp,PETSC_TRUE);
138: KSPSetRhs(ksp,b);
139: KSPSetSolution(ksp,u);
140: KSPSolve(ksp);
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: KSPGetIterationNumber(ksp,&its);
154: PetscPrintf(PETSC_COMM_WORLD,"Norm of error %A Iterations %d\n",norm*h,its);
156: /* Free work space */
157: KSPDestroy(ksp);
158: VecDestroy(ustar);
159: VecDestroy(u);
160: VecDestroy(b);
161: MatDestroy(C);
162: PetscFinalize();
163: return 0;
164: }