# [petsc-users] Nullspaces

Barry Smith bsmith at petsc.dev
Fri Dec 24 16:56:40 CST 2021

```   I tried your code but it appears the ./gyroid_solution.txt contains a vector of all zeros. Is this intended?

Actually VecDuplicateVecs() does not copy the values in the vector so your nsp[0] will contain the zero vector anyways.

Would you be able to send the data that indicates what rows of the vector are associated with each subdomain? For example a vector with all 1s on the first domain and all 2s on the second domain?  I think with this one should be able to construct the 2 dimensional null space.

Barry

> On Dec 16, 2021, at 11:09 AM, Marco Cisternino <marco.cisternino at optimad.it> wrote:
>
> Hello Matthew,
> as promised I prepared a minimal (112960 rows. I’m not able to produce anything smaller than this and triggering the issue) example of the behavior I was talking about some days ago.
> What I did is to produce matrix, right hand side and initial solution of the linear system.
>
> As I told you before, this linear system is the discretization of the pressure equation of a predictor-corrector method for NS equations in the framework of finite volume method.
> This case has homogeneous Neumann boundary conditions. Computational domain has two independent and separated sub-domains.
> I discretize the weak formulation and I divide every row of the linear system by the volume of the relative cell.
> The underlying mesh is not uniform, therefore cells have different volumes.
> The issue I’m going to explain does not show up if the mesh is uniform, same volume for all the cells.
>
> I usually build the null space sub-domain by sub-domain with
> MatNullSpaceCreate(getCommunicator(), PETSC_FALSE, nConstants, constants, &nullspace);
> Where nConstants = 2 and constants contains two normalized arrays with constant values on degrees of freedom relative to the associated sub-domain and zeros elsewhere.
>
> However, as a test I tried the constant over the whole domain using 2 alternatives that should produce the same null space:
> MatNullSpaceCreate(getCommunicator(), PETSC_TRUE, 0, nullptr, &nullspace);
> Vec* nsp;
> VecDuplicateVecs(solution, 1, &nsp);
> VecSet(nsp[0],1.0);
> VecNormalize(nsp[0], nullptr);
> MatNullSpaceCreate(getCommunicator(), PETSC_FALSE, 1, nsp, &nullspace);
>
> Once I created the null space I test it using:
> MatNullSpaceTest(nullspace, m_A, &isNullSpaceValid);
>
> The case 1 pass the test while case 2 don’t.
>
> I have a small code for matrix loading, null spaces creation and testing.
> Unfortunately I cannot implement a small code able to produce that linear system.
>
> As attachment you can find an archive containing the matrix, the initial solution (used to manually build the null space) and the rhs (not used in the test code) in binary format.
> You can also find the testing code in the same archive.
> I used petsc 3.12(gcc+openMPI) and petsc 3.15.2(intelOneAPI) same results.
> If the attachment is not delivered, I can share a link to it.
>
> Thanks for any help.
>
> Marco Cisternino
>
>
> Marco Cisternino, PhD
> ______________________
> Via Bligny 5, Torino, Italia.
> +3901119719782
>
> Sent: martedì 7 dicembre 2021 19:36
> To: Matthew Knepley <knepley at gmail.com <mailto:knepley at gmail.com>>
> Cc: petsc-users <petsc-users at mcs.anl.gov <mailto:petsc-users at mcs.anl.gov>>
> Subject: Re: [petsc-users] Nullspaces
>
> I will, as soon as possible...
>
> Scarica Outlook per Android <https://aka.ms/AAb9ysg>
> From: Matthew Knepley <knepley at gmail.com <mailto:knepley at gmail.com>>
> Sent: Tuesday, December 7, 2021 7:25:43 PM
> Cc: petsc-users <petsc-users at mcs.anl.gov <mailto:petsc-users at mcs.anl.gov>>
> Subject: Re: [petsc-users] Nullspaces
>
> On Tue, Dec 7, 2021 at 11:19 AM Marco Cisternino <marco.cisternino at optimad.it <mailto:marco.cisternino at optimad.it>> wrote:
> Good morning,
>
> I’m still struggling with the Poisson equation with Neumann BCs.
>
> I discretize the equation by finite volume method and I divide every line of the linear system by the volume of the cell. I could avoid this division, but I’m trying to understand.
>
> My mesh is not uniform, i.e. cells have different volumes (it is an octree mesh).
>
> Moreover, in my computational domain there are 2 separated sub-domains.
>
> I build the null space and then I use MatNullSpaceTest to check it.
>
>
>
> If I do this:
>
> MatNullSpaceCreate(getCommunicator(), PETSC_TRUE, 0, nullptr, &nullspace);
>
> It works
>
>
> This produces the normalized constant vector.
>
> If I do this:
>
> Vec nsp;
>
> VecDuplicate(m_rhs, &nsp);
>
> VecSet(nsp,1.0);
>
> VecNormalize(nsp, nullptr);
>
> MatNullSpaceCreate(getCommunicator(), PETSC_FALSE, 1, &nsp, &nullspace);
>
> It does not work
>
>
> This is also the normalized constant vector.
>
> So you are saying that these two vectors give different results with MatNullSpaceTest()?
> Something must be wrong in the code. Can you send a minimal example of this? I will go
> through and debug it.
>
>   Thanks,
>
>      Matt
>
> Probably, I have wrong expectations, but should not it be the same?
>
>
>
> Thanks
>
>
>
> Marco Cisternino, PhD
> ______________________
>
>
> Via Bligny 5, Torino, Italia.
> +3901119719782
>
>
>
>
> --
> 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/><nullspaceTest.tar.gz>

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