1 static char help[] = "Solves a tridiagonal linear system with KSP. \n\
2 It illustrates how to do one symbolic factorization and multiple numeric factorizations using same matrix nonzero structure. \n\n";
3
4 #include <petscksp.h>
main(int argc,char ** args)5 int main(int argc, char **args)
6 {
7 Vec x, b, u; /* approx solution, RHS, exact solution */
8 Mat A; /* linear system matrix */
9 KSP ksp; /* linear solver context */
10 PC pc; /* preconditioner context */
11 PetscReal norm; /* norm of solution error */
12 PetscReal tol = PetscDefined(USE_REAL___FLOAT128) ? 1e-14 : 100. * PETSC_MACHINE_EPSILON;
13 PetscInt i, col[3], its, rstart, rend, N = 10, num_numfac;
14 PetscScalar value[3];
15
16 PetscFunctionBeginUser;
17 PetscCall(PetscInitialize(&argc, &args, NULL, help));
18 PetscCall(PetscOptionsGetInt(NULL, NULL, "-N", &N, NULL));
19
20 /* Create and assemble matrix. */
21 PetscCall(MatCreate(PETSC_COMM_WORLD, &A));
22 PetscCall(MatSetSizes(A, PETSC_DECIDE, PETSC_DECIDE, N, N));
23 PetscCall(MatSetFromOptions(A));
24 PetscCall(MatSetUp(A));
25 PetscCall(MatGetOwnershipRange(A, &rstart, &rend));
26
27 value[0] = -1.0;
28 value[1] = 2.0;
29 value[2] = -1.0;
30 for (i = rstart; i < rend; i++) {
31 col[0] = i - 1;
32 col[1] = i;
33 col[2] = i + 1;
34 if (i == 0) {
35 PetscCall(MatSetValues(A, 1, &i, 2, col + 1, value + 1, INSERT_VALUES));
36 } else if (i == N - 1) {
37 PetscCall(MatSetValues(A, 1, &i, 2, col, value, INSERT_VALUES));
38 } else {
39 PetscCall(MatSetValues(A, 1, &i, 3, col, value, INSERT_VALUES));
40 }
41 }
42 PetscCall(MatAssemblyBegin(A, MAT_FINAL_ASSEMBLY));
43 PetscCall(MatAssemblyEnd(A, MAT_FINAL_ASSEMBLY));
44 PetscCall(MatSetOption(A, MAT_NEW_NONZERO_LOCATION_ERR, PETSC_TRUE));
45
46 /* Create vectors */
47 PetscCall(MatCreateVecs(A, &x, &b));
48 PetscCall(VecDuplicate(x, &u));
49
50 /* Set exact solution; then compute right-hand-side vector. */
51 PetscCall(VecSet(u, 1.0));
52 PetscCall(MatMult(A, u, b));
53
54 /* Create the linear solver and set various options. */
55 PetscCall(KSPCreate(PETSC_COMM_WORLD, &ksp));
56 PetscCall(KSPGetPC(ksp, &pc));
57 PetscCall(PCSetType(pc, PCJACOBI));
58 PetscCall(KSPSetTolerances(ksp, 1.e-5, PETSC_CURRENT, PETSC_CURRENT, PETSC_CURRENT));
59 PetscCall(KSPSetOperators(ksp, A, A));
60 PetscCall(KSPSetFromOptions(ksp));
61
62 num_numfac = 1;
63 PetscCall(PetscOptionsGetInt(NULL, NULL, "-num_numfac", &num_numfac, NULL));
64 while (num_numfac--) {
65 /* An example on how to update matrix A for repeated numerical factorization and solve. */
66 PetscScalar one = 1.0;
67 PetscInt i = 0;
68 PetscCall(MatSetValues(A, 1, &i, 1, &i, &one, ADD_VALUES));
69 PetscCall(MatAssemblyBegin(A, MAT_FINAL_ASSEMBLY));
70 PetscCall(MatAssemblyEnd(A, MAT_FINAL_ASSEMBLY));
71 /* Update b */
72 PetscCall(MatMult(A, u, b));
73
74 /* Solve the linear system */
75 PetscCall(KSPSolve(ksp, b, x));
76
77 /* Check the solution and clean up */
78 PetscCall(VecAXPY(x, -1.0, u));
79 PetscCall(VecNorm(x, NORM_2, &norm));
80 PetscCall(KSPGetIterationNumber(ksp, &its));
81 if (norm > tol) PetscCall(PetscPrintf(PETSC_COMM_WORLD, "Norm of error %g, Iterations %" PetscInt_FMT "\n", (double)norm, its));
82 }
83
84 /* Free work space. */
85 PetscCall(VecDestroy(&x));
86 PetscCall(VecDestroy(&u));
87 PetscCall(VecDestroy(&b));
88 PetscCall(MatDestroy(&A));
89 PetscCall(KSPDestroy(&ksp));
90
91 PetscCall(PetscFinalize());
92 return 0;
93 }
94
95 /*TEST
96
97 test:
98 args: -num_numfac 2 -pc_type lu
99 output_file: output/empty.out
100
101 test:
102 suffix: 2
103 args: -num_numfac 2 -pc_type lu -pc_factor_mat_solver_type mumps
104 requires: mumps
105 output_file: output/empty.out
106
107 test:
108 suffix: 3
109 nsize: 3
110 args: -num_numfac 2 -pc_type lu -pc_factor_mat_solver_type mumps
111 requires: mumps
112 output_file: output/empty.out
113
114 TEST*/
115