[petsc-users] Disconnected domains and Poisson equation

[Matthew Knepley]

On Wed, Sep 29, 2021 at 11:53 AM Marco Cisternino <
marco.cisternino at optimad.it> wrote:

> Thank you Barry for the quick reply.
>
> About the null space: I already tried what you suggest, building 2 Vec
> (constants) with 0 and 1 chosen by sub-domain, normalizing them and setting
> the null space like this
>
>
> MatNullSpaceCreate(PETSC_COMM_WORLD,PETSC_FALSE,nconstants,constants,&nullspace);
>
> The solution is slightly different in values but it is still different in
> the two sub-domains.
>
> About the solver: I tried BCGS, GMRES and FGMRES. The linear system is a
> pressure system in a navier-stokes solver and only solving with FGMRES
> makes the CFD stable, with BCGS and GMRES the CFD solution diverges.
> Moreover, in the same case but with a single domain, CFD solution is stable
> using all the solvers, but FGMRES converges in much less iterations than
> the others.
>

I think this means something is wrong with the implementation. FGMRES is
the same as GMRES _if_ the preconditioner is a linear operator. The fact
that they are different means
that your preconditioner is nonlinear. Is this what you expect?

  Thanks,

      Matt


> Marco Cisternino
>
>
>
> *From:* Barry Smith <bsmith at petsc.dev>
> *Sent:* mercoledì 29 settembre 2021 15:59
> *To:* Marco Cisternino <marco.cisternino at optimad.it>
> *Cc:* petsc-users at mcs.anl.gov
> *Subject:* Re: [petsc-users] Disconnected domains and Poisson equation
>
>
>
>
>
>   The problem actually has a two dimensional null space; constant on each
> domain but possibly different constants. I think you need to build the
> MatNullSpace by explicitly constructing two vectors, one with 0 on one
> domain and constant value on the other and one with 0 on the other domain
> and constant on the first.
>
>
>
>    Separate note: why use FGMRES instead of just GMRES? If the problem is
> linear and the preconditioner is linear (no GMRES inside the smoother) then
> you can just use GMRES and it will save a little space/work and be
> conceptually clearer.
>
>
>
>   Barry
>
>
>
> On Sep 29, 2021, at 8:46 AM, Marco Cisternino <marco.cisternino at optimad.it>
> wrote:
>
>
>
> Good morning,
>
> I want to solve the Poisson equation on a 3D domain with 2 non-connected
> sub-domains.
>
> I am using FGMRES+GAMG and I have no problem if the two sub-domains see a
> Dirichlet boundary condition each.
>
> On the same domain I would like to solve the Poisson equation imposing
> periodic boundary condition in one direction and homogenous Neumann
> boundary conditions in the other two directions. The two sub-domains are
> symmetric with respect to the separation between them and the operator
> discretization and the right hand side are symmetric as well. It would be
> nice to have the same solution in both the sub-domains.
>
> Setting the null space to the constant, the solver converges to a solution
> having the same gradients in both sub-domains but different values.
>
> Am I doing some wrong with the null space? I’m not setting a block matrix
> (one block for each sub-domain), should I?
>
> I tested the null space against the matrix using MatNullSpaceTest and the
> answer is true. Can I do something more to have a symmetric solution as
> outcome of the solver?
>
> Thank you in advance for any comments and hints.
>
>
>
> Best regards,
>
>
>
> 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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