Actual source code: ex3.c
2: static char help[] = "This example solves a linear system in parallel with KSP. The matrix\n\
3: uses simple bilinear elements on the unit square. To test the parallel\n\
4: matrix assembly, the matrix is intentionally laid out across processors\n\
5: differently from the way it is assembled. Input arguments are:\n\
6: -m <size> : problem size\n\n";
8: #include petscksp.h
12: int FormElementStiffness(PetscReal H,PetscScalar *Ke)
13: {
15: Ke[0] = H/6.0; Ke[1] = -.125*H; Ke[2] = H/12.0; Ke[3] = -.125*H;
16: Ke[4] = -.125*H; Ke[5] = H/6.0; Ke[6] = -.125*H; Ke[7] = H/12.0;
17: Ke[8] = H/12.0; Ke[9] = -.125*H; Ke[10] = H/6.0; Ke[11] = -.125*H;
18: Ke[12] = -.125*H; Ke[13] = H/12.0; Ke[14] = -.125*H; Ke[15] = H/6.0;
19: return(0);
20: }
23: int FormElementRhs(PetscReal x,PetscReal y,PetscReal H,PetscScalar *r)
24: {
26: r[0] = 0.; r[1] = 0.; r[2] = 0.; r[3] = 0.0;
27: return(0);
28: }
32: int main(int argc,char **args)
33: {
34: Mat C;
35: PetscMPIInt rank,size;
36: PetscInt i,m = 5,N,start,end,M,its;
37: PetscScalar val,Ke[16],r[4];
38: PetscReal x,y,h,norm;
40: PetscInt idx[4],count,*rows;
41: Vec u,ustar,b;
42: KSP ksp;
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,&C);
54: MatSetSizes(C,PETSC_DECIDE,PETSC_DECIDE,N,N);
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(u,0.0);
81: VecSet(b,0.0);
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(PetscInt),&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: 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: MatZeroRows(C,4*m,rows,1.0);
118: PetscFree(rows);
119: VecAssemblyBegin(u);
120: VecAssemblyEnd(u);
121: VecAssemblyBegin(b);
122: VecAssemblyEnd(b);
124: { Mat A;
125: MatConvert(C,MATSAME,MAT_INITIAL_MATRIX,&A);
126: MatDestroy(C);
127: MatConvert(A,MATSAME,MAT_INITIAL_MATRIX,&C);
128: MatDestroy(A);
129: }
131: /* Solve linear system */
132: KSPCreate(PETSC_COMM_WORLD,&ksp);
133: KSPSetOperators(ksp,C,C,DIFFERENT_NONZERO_PATTERN);
134: KSPSetFromOptions(ksp);
135: KSPSetInitialGuessNonzero(ksp,PETSC_TRUE);
136: KSPSolve(ksp,b,u);
138: /* Check error */
139: VecGetOwnershipRange(ustar,&start,&end);
140: for (i=start; i<end; i++) {
141: x = h*(i % (m+1)); y = h*(i/(m+1));
142: val = y;
143: VecSetValues(ustar,1,&i,&val,INSERT_VALUES);
144: }
145: VecAssemblyBegin(ustar);
146: VecAssemblyEnd(ustar);
147: VecAXPY(u,-1.0,ustar);
148: VecNorm(u,NORM_2,&norm);
149: KSPGetIterationNumber(ksp,&its);
150: PetscPrintf(PETSC_COMM_WORLD,"Norm of error %A Iterations %D\n",norm*h,its);
152: /* Free work space */
153: KSPDestroy(ksp);
154: VecDestroy(ustar);
155: VecDestroy(u);
156: VecDestroy(b);
157: MatDestroy(C);
158: PetscFinalize();
159: return 0;
160: }