[petsc-users] Null space correction depends on solver?

[Jed Brown]

You seem to have the solution and right hand side vectors mixed up.
On Aug 30, 2012 8:25 AM, "Thomas Witkowski" <thomas.witkowski at tu-dresden.de>
wrote:

>  Am 28.08.2012 19:57, schrieb Jed Brown:
>
> On Tue, Aug 28, 2012 at 12:25 PM, Thomas Witkowski <
> thomas.witkowski at tu-dresden.de> wrote:
>
>>
>>        GMRES uses left preconditioning by default which forces the null
>>> space into the Krylov space at each iteration. FGMRES uses right
>>> preconditioning and doesn't  do anything to the null space because it is
>>> naturally in the Krylov space (since the result with fgmres contains the
>>> constants this is why I suspect the matrix actually doesn't have the null
>>> space you think it has). You can try running -ksp_type gmres -ksp_pc_side
>>> right      my guess is that you will not get near zero for the dot.
>>>
>>  Any idea how to debug this problem? Lets concentrate on the gmres/no
>> precon case first.
>
>
> Left preconditioning and anything using -pc_type none works correctly. It
> is only the case of right preconditioning that is incorrect (and needs to
> be fixed in PETSc).
>
> If everything is fine for left preconditioning, can you please explain me
> what's going wrong in this minimal example. I patched
> src/ksp/ksp/examples/tutorials/ex4.c in the following way (just to make
> some test output):
>
> --- ex4-o.c     2012-08-30 15:14:52.852519625 +0200
> +++ ex4.c       2012-08-30 15:16:33.304517903 +0200
> @@ -169,9 +169,22 @@
>      ierr = KSPSetOperators(ksp, A, A,
> DIFFERENT_NONZERO_PATTERN);CHKERRQ(ierr);
>      ierr = MatNullSpaceCreate(PETSC_COMM_WORLD, PETSC_TRUE, 0,
> PETSC_NULL, &nullsp);CHKERRQ(ierr);
>      ierr = KSPSetNullSpace(ksp, nullsp);CHKERRQ(ierr);
> +    ierr = MatNullSpaceRemove(nullsp, x, PETSC_NULL);CHKERRQ(ierr);
> +    Vec  c, d;
> +    ierr = VecDuplicate(x, &d);CHKERRQ(ierr);
> +    ierr = VecDuplicate(x, &c);CHKERRQ(ierr);
> +    ierr = VecSet(d, 1.0);CHKERRQ(ierr);
> +    ierr = MatMult(A, d, c);CHKERRQ(ierr);
> +    PetscScalar    dot;
> +    ierr = VecNorm(c, NORM_2, &dot);CHKERRQ(ierr);
> +    ierr = PetscPrintf(PETSC_COMM_WORLD, "Norm of mat-mult = %e\n", dot);
> +    ierr = VecDot(x, d, &dot);CHKERRQ(ierr);
> +    ierr = PetscPrintf(PETSC_COMM_WORLD, "Dot product rhs = %e\n", dot);
>      ierr = MatNullSpaceDestroy(&nullsp);CHKERRQ(ierr);
>      ierr = KSPSetFromOptions(ksp);CHKERRQ(ierr);
>      ierr = KSPSolve(ksp, b, x);CHKERRQ(ierr);
> +    ierr = VecDot(b, d, &dot);CHKERRQ(ierr);
> +    ierr = PetscPrintf(PETSC_COMM_WORLD, "Dot product sol = %e\n", dot);
>      ierr = VecDestroy(&x);CHKERRQ(ierr);
>      ierr = VecDestroy(&b);CHKERRQ(ierr);
>      /* Solve physical system:
>
>
> I run this example with the following command:
>
> mpiexec -np 1 ./ex4 -gpu no -cpu -view no -solve
> -ksp_monitor_true_residual -ksp_type gmres -pc_type none
>
> The output is the following:
>
> Norm of mat-mult = 0.000000e+00
> Dot product rhs = 0.000000e+00
>   0 KSP preconditioned resid norm 9.544889963521e-01 true resid norm
> 1.322454133866e+00 ||r(i)||/||b|| 1.000000000000e+00
>   1 KSP preconditioned resid norm 6.183073265542e-01 true resid norm
> 1.104599312915e+00 ||r(i)||/||b|| 8.352647435007e-01
>   2 KSP preconditioned resid norm 1.770056136651e-01 true resid norm
> 9.322910914997e-01 ||r(i)||/||b|| 7.049704542680e-01
>   3 KSP preconditioned resid norm 5.212633308436e-02 true resid norm
> 9.168166919410e-01 ||r(i)||/||b|| 6.932691792200e-01
>   4 KSP preconditioned resid norm 2.714317700314e-02 true resid norm
> 9.157360122211e-01 ||r(i)||/||b|| 6.924520017526e-01
>   5 KSP preconditioned resid norm 1.718946122098e-03 true resid norm
> 9.153352646963e-01 ||r(i)||/||b|| 6.921489685398e-01
>   6 KSP preconditioned resid norm 2.794230282044e-16 true resid norm
> 9.153336506547e-01 ||r(i)||/||b|| 6.921477480502e-01
> Dot product sol = 2.746001e+00
>
> As you see, the constant vector is a member of the nullspace (and it
> should span it), the right hand side is orthogonal to the null space, but
> not the solution vector. Also the solver does not converge in the true
> residual norm.
>
> Thomas
>
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