[petsc-users] Null space/Near null space

[Young, Matthew, Adam]

Thanks for the feedback, everyone. My null space is simply the constant vectors and I am setting MatSetNullSpace based on code I had been testing with other PC/KSP options, which grew out of examples. GMRES/BoomerAMG seems to be the best fit for my problem but I stumbled upon that via experimentation (Hurray for KSP/PCSetFromOptions!), rather than via a more informed analysis. I am still in the process of learning about both the GMRES algorithm and multigrid in general, so I asked this question in case it turned out that I could improve my working code.

I'd be interested in that interface to HYPRE_BoomerAMGSetInterpVectors, if it makes it into PETSc.

--Matt

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Matthew Young
Graduate Student
Boston University Dept. of Astronomy
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________________________________________
From: petsc-users-bounces at mcs.anl.gov [petsc-users-bounces at mcs.anl.gov] on behalf of Barry Smith [bsmith at mcs.anl.gov]
Sent: Thursday, July 23, 2015 6:13 AM
To: Lawrence Mitchell
Cc: petsc-users at mcs.anl.gov
Subject: Re: [petsc-users] Null space/Near null space

> On Jul 23, 2015, at 3:42 AM, Lawrence Mitchell <lawrence.mitchell at imperial.ac.uk> wrote:
>
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> On 22/07/15 23:57, Barry Smith wrote:
>>
>> If your matrix has a null space you should always be setting
>> MatSetNullSpace.
>>
>> If you know the near null space then you should also always set it
>> (it cannot do any harm) because some preconditioners can take
>> advantage of it.
>>
>> I do not think PETSc currently has code that transfers near null
>> space information to hypre; I do not know if hypre has any
>> algorithms that can take advantage of it. Only some AMG multigrid
>> methods can utilize near null space information.
>
> FWIW, the HYPRE manual suggests yes:
>
> If the block size is set (PETSc already does this) and nodal systems
> coarsening is requested (PETSc has an option for this) then one can
> provide the near null modes with HYPRE_BoomerAMGSetInterpVectors,
> passing an array of Vecs (PETSc does not do this last step).

   Thanks. So someone should make this small code addition plus a test case that utilizes it to demonstrate that it functions and wrap that up in a pull request.

  Barry

>
> Lawrence
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