Actual source code: ex39.c
petsc-3.4.2 2013-07-02
1: /*
2: mpiexec -n 8 ./ex39 -ksp_type fbcgs -ksp_rtol 1.e-6 -sub_ksp_type bcgs -sub_ksp_rtol 1.e-3 -pc_type bjacobi -ksp_converged_reason -ksp_monitor -n1 32 -n2 32 -n3 32
4: Contributed by Jie Chen for testing flexible BiCGStab algorithm
5: */
7: static char help[] = "Solves the PDE (in 3D) - laplacian(u) + gamma x dot grad(u) + beta u = 1\n\
8: with zero Dirichlet condition. The discretization is standard centered\n\
9: difference. Input parameters include:\n\
10: -n1 : number of mesh points in 1st dimension (default 32)\n\
11: -n2 : number of mesh points in 2nd dimension (default 32)\n\
12: -n3 : number of mesh points in 3nd dimension (default 32)\n\
13: -h : spacing between mesh points (default 1/n1)\n\
14: -gamma : gamma (default 4/h)\n\
15: -beta : beta (default 0.01/h^2)\n\n";
17: #include <petscksp.h>
20: int main(int argc,char **args)
21: {
22: Vec x,b,u; /* approx solution, RHS, working vector */
23: Mat A; /* linear system matrix */
24: KSP ksp; /* linear solver context */
25: PetscInt n1, n2, n3; /* parameters */
26: PetscReal h, gamma, beta; /* parameters */
27: PetscInt i,j,k,Ii,J,Istart,Iend;
29: PetscScalar v, co1, co2;
31: PetscInitialize(&argc,&args,(char*)0,help);
32: n1 = 32;
33: n2 = 32;
34: n3 = 32;
35: PetscOptionsGetInt(NULL,"-n1",&n1,NULL);
36: PetscOptionsGetInt(NULL,"-n2",&n2,NULL);
37: PetscOptionsGetInt(NULL,"-n3",&n3,NULL);
39: h = 1.0/n1;
40: gamma = 4.0;
41: beta = 0.01;
42: PetscOptionsGetReal(NULL,"-h",&h,NULL);
43: PetscOptionsGetReal(NULL,"-gamma",&gamma,NULL);
44: PetscOptionsGetReal(NULL,"-beta",&beta,NULL);
45: gamma = gamma/h;
46: beta = beta/(h*h);
48: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
49: Compute the matrix and set right-hand-side vector.
50: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
51: MatCreate(PETSC_COMM_WORLD,&A);
52: MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,n1*n2*n3,n1*n2*n3);
53: MatSetFromOptions(A);
54: MatMPIAIJSetPreallocation(A,7,NULL,7,NULL);
55: MatSeqAIJSetPreallocation(A,7,NULL);
56: MatSetUp(A);
57: MatGetOwnershipRange(A,&Istart,&Iend);
59: /*
60: Set matrix elements for the 3-D, seven-point stencil in parallel.
61: - Each processor needs to insert only elements that it owns
62: locally (but any non-local elements will be sent to the
63: appropriate processor during matrix assembly).
64: - Always specify global rows and columns of matrix entries.
65: */
66: co1 = gamma * h * h / 2.0;
67: co2 = beta * h * h;
68: for (Ii=Istart; Ii<Iend; Ii++) {
69: i = Ii/(n2*n3); j = (Ii - i*n2*n3)/n3; k = Ii - i*n2*n3 - j*n3;
70: if (i>0) {
71: J = Ii - n2*n3; v = -1.0 + co1*(PetscScalar)i;
72: MatSetValues(A,1,&Ii,1,&J,&v,INSERT_VALUES);
73: }
74: if (i<n1-1) {
75: J = Ii + n2*n3; v = -1.0 + co1*(PetscScalar)i;
76: MatSetValues(A,1,&Ii,1,&J,&v,INSERT_VALUES);
77: }
78: if (j>0) {
79: J = Ii - n3; v = -1.0 + co1*(PetscScalar)j;
80: MatSetValues(A,1,&Ii,1,&J,&v,INSERT_VALUES);
81: }
82: if (j<n2-1) {
83: J = Ii + n3; v = -1.0 + co1*(PetscScalar)j;
84: MatSetValues(A,1,&Ii,1,&J,&v,INSERT_VALUES);
85: }
86: if (k>0) {
87: J = Ii - 1; v = -1.0 + co1*(PetscScalar)k;
88: MatSetValues(A,1,&Ii,1,&J,&v,INSERT_VALUES);
89: }
90: if (k<n3-1) {
91: J = Ii + 1; v = -1.0 + co1*(PetscScalar)k;
92: MatSetValues(A,1,&Ii,1,&J,&v,INSERT_VALUES);
93: }
94: v = 6.0 + co2;
95: MatSetValues(A,1,&Ii,1,&Ii,&v,INSERT_VALUES);
96: }
97: MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
98: MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
100: /* Create parallel vectors and Set right-hand side. */
101: VecCreate(PETSC_COMM_WORLD,&b);
102: VecSetSizes(b,PETSC_DECIDE,n1*n2*n3);
103: VecSetFromOptions(b);
104: VecDuplicate(b,&x);
105: VecDuplicate(b,&u);
106: VecSet(b,1.0);
108: /* Create linear solver context */
109: KSPCreate(PETSC_COMM_WORLD,&ksp);
110: KSPSetOperators(ksp,A,A,DIFFERENT_NONZERO_PATTERN);
111: KSPSetTolerances(ksp,1.e-6,1.e-50,PETSC_DEFAULT,200);
112: KSPSetFromOptions(ksp);
114: /* Solve the linear system */
115: KSPSolve(ksp,b,x);
117: /* Free work space. */
118: KSPDestroy(&ksp);
119: VecDestroy(&u); VecDestroy(&x);
120: VecDestroy(&b); MatDestroy(&A);
121: PetscFinalize();
122: return 0;
123: }