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

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

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

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

 55:   /* Create KSP context; set operators and options; solve linear system */
 56:   KSPCreate(PETSC_COMM_WORLD,&ksp);
 57:   KSPSetOperators(ksp,A,A);

 59:   /* Insure that preconditioner has same null space as matrix */
 60:   /* currently does not do anything */
 61:   KSPGetPC(ksp,&pc);

 63:   KSPSetFromOptions(ksp);
 64:   KSPSolve(ksp,b,x);
 65:   /* KSPView(ksp,PETSC_VIEWER_STDOUT_WORLD); */

 67:   /* Check error */
 68:   VecAXPY(x,none,u);
 69:   VecNorm(x,NORM_2,&norm);
 70:   KSPGetIterationNumber(ksp,&its);
 71:   PetscPrintf(PETSC_COMM_WORLD,"Norm of error %g, Iterations %D\n",(double)norm,its);

 73:   /* Free work space */
 74:   VecDestroy(&x));PetscCall(VecDestroy(&u);
 75:   VecDestroy(&b));PetscCall(MatDestroy(&A);
 76:   KSPDestroy(&ksp);
 77:   PetscFinalize();
 78:   return 0;
 79: }