Date: 2025-03-28T21:10:54+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:   PetscInt    i, col[3], its, rstart, rend, N = 10, num_numfac;
     13:   PetscScalar value[3];

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

     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));

     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));

     45:   /* Create vectors */
     46:   PetscCall(MatCreateVecs(A, &x, &b));
     47:   PetscCall(VecDuplicate(x, &u));

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

     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_CURRENT, PETSC_CURRENT, PETSC_CURRENT));
     58:   PetscCall(KSPSetOperators(ksp, A, A));
     59:   PetscCall(KSPSetFromOptions(ksp));

     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));

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

     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:   }

     83:   /* Free work space. */
     84:   PetscCall(VecDestroy(&x));
     85:   PetscCall(VecDestroy(&u));
     86:   PetscCall(VecDestroy(&b));
     87:   PetscCall(MatDestroy(&A));
     88:   PetscCall(KSPDestroy(&ksp));

     90:   PetscCall(PetscFinalize());
     91:   return 0;
     92: }

     94: /*TEST

     96:     test:
     97:       args: -num_numfac 2 -pc_type lu

     99:     test:
    100:       suffix: 2
    101:       args: -num_numfac 2 -pc_type lu -pc_factor_mat_solver_type mumps
    102:       requires: mumps

    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

    110: TEST*/