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