[petsc-users] move from KSPSetNullSpace to MatSetNullSpace

[Matthew Knepley]

On Mon, Jun 22, 2015 at 6:02 PM, Stephan Kramer <s.kramer at imperial.ac.uk>
wrote:

> On Mon, Jun 22, 2015 at 1:13 PM, Stephan Kramer <s.kramer at
>> imperial.ac.uk>
>> wrote:
>>
>>  Dear petsc devs
>>>
>>> I've been trying to move our code from using KSPSetNullSpace to use
>>> MatSetNullSpace instead. Although I appreciate the convenience of the
>>> nullspace being propagated automatically through the solver hierarchy,
>>> I'm
>>> still a little confused on how to deal with the case that mat/=pmat in a
>>> ksp.
>>>
>>> If I read the code correctly I need to call MatSetNullSpace on the pmat
>>> in
>>> order for a ksp to project that nullspace out of the residual during the
>>> krylov iteration. However the nullspaces of mat and pmat are not
>>> necessarily the same. For instance, what should I do if the system that I
>>> want to solve has a nullspace (i.e. the `mat` has a null vector), but the
>>> preconditioner matrix does not.
>>>
>>> As an example of existing setups that we have for which this is the case:
>>> take a standard Stokes velocity, pressure system - where we want to solve
>>> for pressure through a Schur complement. Suppose the boundary conditions
>>> are Dirichlet for velocity on all boundaries, then the pressure equation
>>> has the standard, constant nullspace. A frequently used preconditioner is
>>> the "scaled pressure mass matrix" where G^T K^{-1} G is approximated by a
>>> pressure mass matrix that is scaled by the value of the viscosity. So in
>>> this case the actual system has a nullspace, but the preconditioner
>>> matrix
>>> does not.
>>>
>>> The way we previously used to solve this is by setting the nullspace on
>>> the ksp of the Schur system, where the mat comes from
>>> MatCreateSchurComplement and the pmat is the scaled mass matrix. We then
>>> set the pctype to PCKSP and do not set a nullspace on its associated
>>> ksp. I
>>> don't really see how I can do this using only MatSetNullSpace - unless I
>>> create a copy of the mass matrix and have one copy with and one copy
>>> without a nullspace so that I could use the one with the nullspace for
>>> the
>>> pmat of the Schur ksp (and thus the mat of the pcksp) and the copy
>>> without
>>> the nullspace as the pmat for the pcksp.
>>>
>>> We would very much appreciate some guidance on what the correct way to
>>> deal with this kind of situation is
>>>
>>>
>> I can understand that this is inconsistent (we have not really thought of
>> a
>> good way to make this consistent). However, does
>> this produce the wrong results? If A has a null space, won't you get the
>> same answer by attaching it to P, or am I missing the
>> import of the above example?
>>
>
> Attaching the nullspace to P means it will be applied in the PCKSP solve as
> well - which in this case is just a mass matrix solve which doesn't
> have a nullspace. I was under the impression that removing a nullspace in
> a solve
> where the matrix doesn't having one, would lead to trouble - but I'm happy
> to
> be told wrong.
>

I guess I was saying that this solve is only applied after a system with
that null space,
so I did not think it would change the answer.

  Thanks,

     Matt


> Cheers
> Stephan
>



-- 
What most experimenters take for granted before they begin their
experiments is infinitely more interesting than any results to which their
experiments lead.
-- Norbert Wiener
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