Actual source code: ex15.c

  1: static char help[] = "KSP linear solver on an operator with a null space.\n\n";

  3: #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;     /* KSP context */
 10:   PetscInt    i, n = 10, col[3], its, i1, i2;
 11:   PetscScalar none = -1.0, value[3], avalue;
 12:   PetscReal   norm;
 13:   PC          pc;

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

 19:   /* Create vectors */
 20:   PetscCall(VecCreate(PETSC_COMM_WORLD, &x));
 21:   PetscCall(VecSetSizes(x, PETSC_DECIDE, n));
 22:   PetscCall(VecSetFromOptions(x));
 23:   PetscCall(VecDuplicate(x, &b));
 24:   PetscCall(VecDuplicate(x, &u));

 26:   /* create a solution that is orthogonal to the constants */
 27:   PetscCall(VecGetOwnershipRange(u, &i1, &i2));
 28:   for (i = i1; i < i2; i++) {
 29:     avalue = i;
 30:     VecSetValues(u, 1, &i, &avalue, INSERT_VALUES);
 31:   }
 32:   PetscCall(VecAssemblyBegin(u));
 33:   PetscCall(VecAssemblyEnd(u));
 34:   PetscCall(VecSum(u, &avalue));
 35:   avalue = -avalue / (PetscReal)n;
 36:   PetscCall(VecShift(u, avalue));

 38:   /* Create and assemble matrix */
 39:   PetscCall(MatCreate(PETSC_COMM_WORLD, &A));
 40:   PetscCall(MatSetSizes(A, PETSC_DECIDE, PETSC_DECIDE, n, n));
 41:   PetscCall(MatSetFromOptions(A));
 42:   value[0] = -1.0;
 43:   value[1] = 2.0;
 44:   value[2] = -1.0;
 45:   for (i = 1; i < n - 1; i++) {
 46:     col[0] = i - 1;
 47:     col[1] = i;
 48:     col[2] = i + 1;
 49:     PetscCall(MatSetValues(A, 1, &i, 3, col, value, INSERT_VALUES));
 50:   }
 51:   i        = n - 1;
 52:   col[0]   = n - 2;
 53:   col[1]   = n - 1;
 54:   value[1] = 1.0;
 55:   PetscCall(MatSetValues(A, 1, &i, 2, col, value, INSERT_VALUES));
 56:   i        = 0;
 57:   col[0]   = 0;
 58:   col[1]   = 1;
 59:   value[0] = 1.0;
 60:   value[1] = -1.0;
 61:   PetscCall(MatSetValues(A, 1, &i, 2, col, value, INSERT_VALUES));
 62:   PetscCall(MatAssemblyBegin(A, MAT_FINAL_ASSEMBLY));
 63:   PetscCall(MatAssemblyEnd(A, MAT_FINAL_ASSEMBLY));
 64:   PetscCall(MatMult(A, u, b));

 66:   /* Create KSP context; set operators and options; solve linear system */
 67:   PetscCall(KSPCreate(PETSC_COMM_WORLD, &ksp));
 68:   PetscCall(KSPSetOperators(ksp, A, A));

 70:   /* Insure that preconditioner has same null space as matrix */
 71:   /* currently does not do anything */
 72:   PetscCall(KSPGetPC(ksp, &pc));

 74:   PetscCall(KSPSetFromOptions(ksp));
 75:   PetscCall(KSPSolve(ksp, b, x));
 76:   /* PetscCall(KSPView(ksp,PETSC_VIEWER_STDOUT_WORLD)); */

 78:   /* Check error */
 79:   PetscCall(VecAXPY(x, none, u));
 80:   PetscCall(VecNorm(x, NORM_2, &norm));
 81:   PetscCall(KSPGetIterationNumber(ksp, &its));
 82:   PetscCall(PetscPrintf(PETSC_COMM_WORLD, "Norm of error %g, Iterations %" PetscInt_FMT "\n", (double)norm, its));

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