[petsc-users] Null space and preconditioners

[Matthew Knepley]

On Mon, Mar 21, 2022 at 12:06 PM Mark Adams <mfadams at lbl.gov> wrote:

> The solution for Neumann problems can "float away" if the constant is not
> controlled in some way because floating point errors can introduce it even
> if your RHS is exactly orthogonal to it.
>
> You should use a special coarse grid solver for GAMG but it seems to be
> working for you.
>
> I have lost track of the simply way to have the KSP solver clean the
> constant out, which is what you want.
>
> can someone help Marco?
>

I have not had time to look at the code. However, here are two ways we use
to fix the pure Neumann solution:

1) Attach a null space to the operator using
https://petsc.org/main/docs/manualpages/Mat/MatSetNullSpace.html

2) Use a coarse grid solver that does least-squares

  -mg_coarse_pc_type svd

  Thanks,

     Matt


> Mark
>
>
>
>
>
> On Mon, Mar 21, 2022 at 8:18 AM Marco Cisternino <
> marco.cisternino at optimad.it> wrote:
>
>> Good morning,
>>
>> I’m observing an unexpected (to me) behaviour of my code.
>>
>> I tried to reduce the problem in a toy code here attached.
>> The toy code archive contains a small main, a matrix and a rhs.
>>
>> The toy code solves the linear system and check the norms and the mean of
>> the solution.
>>
>> The problem into the matrix and the rhs is the finite volume
>> discretization of the pressure equation of an incompressible NS solver.
>>
>> It has been cooked as tiny as possible (16 cells!).
>>
>> It is important to say that it is an elliptic problem with homogeneous
>> Neumann boundary conditions only, for this reason the toy code sets a null
>> space containing the constant.
>>
>>
>>
>> The unexpected (to me) behaviour is evident by launching the code using
>> different preconditioners, using -pc-type <pctype>
>> I tested using PCNONE (“none”), PCGAMG (“gamg”) and PCILU (“ilu”). The
>> default solver is KSPFGMRES.
>>
>> Using the three PC, I get 3 different solutions. It seems to me that they
>> differ in the mean value, but GAMG is impressive.
>>
>> PCNONE gives me the zero mean solution I expected. What about the others?
>>
>>
>>
>> Asking for residuals monitor, the ratio ||r||/||b|| shows convergence for
>> PCNONE and PCILU (~10^-16), but it stalls for PCGAMG (~10^-4).
>>
>> I cannot see why. Am I doing anything wrong or incorrectly thinking about
>> the expected behaviour?
>>
>>
>>
>> Generalizing to larger mesh the behaviour is similar.
>>
>>
>>
>> Thank you for any help.
>>
>>
>>
>> Marco Cisternino
>>
>>
>>
>>
>>
>

-- 
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

https://www.cse.buffalo.edu/~knepley/ <http://www.cse.buffalo.edu/~knepley/>
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