Date: 2026-03-31T05:46:15+00:00

Actual source code: ex6.c

      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";

      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];

     16:   PetscFunctionBeginUser;
     17:   PetscCall(PetscInitialize(&argc, &args, NULL, help));
     18:   PetscCall(PetscOptionsGetInt(NULL, NULL, "-N", &N, NULL));

     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));

     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) PetscCall(MatSetValues(A, 1, &i, 2, col + 1, value + 1, INSERT_VALUES));
     35:     else if (i == N - 1) PetscCall(MatSetValues(A, 1, &i, 2, col, value, INSERT_VALUES));
     36:     else PetscCall(MatSetValues(A, 1, &i, 3, col, value, INSERT_VALUES));
     37:   }
     38:   PetscCall(MatAssemblyBegin(A, MAT_FINAL_ASSEMBLY));
     39:   PetscCall(MatAssemblyEnd(A, MAT_FINAL_ASSEMBLY));
     40:   PetscCall(MatSetOption(A, MAT_NEW_NONZERO_LOCATION_ERR, PETSC_TRUE));

     42:   /* Create vectors */
     43:   PetscCall(MatCreateVecs(A, &x, &b));
     44:   PetscCall(VecDuplicate(x, &u));

     46:   /* Set exact solution; then compute right-hand-side vector. */
     47:   PetscCall(VecSet(u, 1.0));
     48:   PetscCall(MatMult(A, u, b));

     50:   /* Create the linear solver and set various options. */
     51:   PetscCall(KSPCreate(PETSC_COMM_WORLD, &ksp));
     52:   PetscCall(KSPGetPC(ksp, &pc));
     53:   PetscCall(PCSetType(pc, PCJACOBI));
     54:   PetscCall(KSPSetTolerances(ksp, 1.e-5, PETSC_CURRENT, PETSC_CURRENT, PETSC_CURRENT));
     55:   PetscCall(KSPSetOperators(ksp, A, A));
     56:   PetscCall(KSPSetFromOptions(ksp));

     58:   num_numfac = 1;
     59:   PetscCall(PetscOptionsGetInt(NULL, NULL, "-num_numfac", &num_numfac, NULL));
     60:   while (num_numfac--) {
     61:     /* An example on how to update matrix A for repeated numerical factorization and solve. */
     62:     PetscScalar one = 1.0;
     63:     PetscInt    i   = 0;
     64:     PetscCall(MatSetValues(A, 1, &i, 1, &i, &one, ADD_VALUES));
     65:     PetscCall(MatAssemblyBegin(A, MAT_FINAL_ASSEMBLY));
     66:     PetscCall(MatAssemblyEnd(A, MAT_FINAL_ASSEMBLY));
     67:     /* Update b */
     68:     PetscCall(MatMult(A, u, b));

     70:     /* Solve the linear system */
     71:     PetscCall(KSPSolve(ksp, b, x));

     73:     /* Check the solution and clean up */
     74:     PetscCall(VecAXPY(x, -1.0, u));
     75:     PetscCall(VecNorm(x, NORM_2, &norm));
     76:     PetscCall(KSPGetIterationNumber(ksp, &its));
     77:     if (norm > tol) PetscCall(PetscPrintf(PETSC_COMM_WORLD, "Norm of error %g, Iterations %" PetscInt_FMT "\n", (double)norm, its));
     78:   }

     80:   /* Free work space. */
     81:   PetscCall(VecDestroy(&x));
     82:   PetscCall(VecDestroy(&u));
     83:   PetscCall(VecDestroy(&b));
     84:   PetscCall(MatDestroy(&A));
     85:   PetscCall(KSPDestroy(&ksp));

     87:   PetscCall(PetscFinalize());
     88:   return 0;
     89: }

     91: /*TEST

     93:     test:
     94:       args: -num_numfac 2 -pc_type lu
     95:       output_file: output/empty.out

     97:     test:
     98:       suffix: 2
     99:       args: -num_numfac 2 -pc_type lu -pc_factor_mat_solver_type mumps
    100:       requires: mumps
    101:       output_file: output/empty.out

    103:     test:
    104:       suffix: 3
    105:       nsize: 3
    106:       args: -num_numfac 2 -pc_type lu -pc_factor_mat_solver_type mumps
    107:       requires: mumps
    108:       output_file: output/empty.out

    110: TEST*/