Actual source code: ex15.c


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

  4: #include <petscksp.h>

  6: int main(int argc, char **args)
  7: {
  8:   Vec         x, b, u; /* approx solution, RHS, exact solution */
  9:   Mat         A;       /* linear system matrix */
 10:   KSP         ksp;     /* KSP context */
 11:   PetscInt    i, n = 10, col[3], its, i1, i2;
 12:   PetscScalar none = -1.0, value[3], avalue;
 13:   PetscReal   norm;
 14:   PC          pc;

 16:   PetscFunctionBeginUser;
 17:   PetscCall(PetscInitialize(&argc, &args, (char *)0, help));
 18:   PetscCall(PetscOptionsGetInt(NULL, NULL, "-n", &n, NULL));

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

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

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

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

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

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

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

 85:   /* Free work space */
 86:   PetscCall(VecDestroy(&x));
 87:   PetscCall(VecDestroy(&u));
 88:   PetscCall(VecDestroy(&b));
 89:   PetscCall(MatDestroy(&A));
 90:   PetscCall(KSPDestroy(&ksp));
 91:   PetscCall(PetscFinalize());
 92:   return 0;
 93: }