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> 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