[petsc-users] Disconnected domains and Poisson equation

[Marco Cisternino]

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.

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<mailto: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

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