[petsc-users] Nullspaces
Matthew Knepley
knepley at gmail.com
Wed Jan 19 06:19:06 CST 2022
On Wed, Jan 19, 2022 at 4:52 AM Marco Cisternino <
marco.cisternino at optimad.it> wrote:
> Thank you Matthew.
>
> But I cannot get the point. I got the point about the test but to try to
> explain my doubt I’m going to prepare another toy code.
>
>
>
> By words…
>
> I usually have a finite volume discretization of the Laplace operator with
> homogeneous Neumann BC on an octree mesh and it reads
>
> Aij * xj = bi,
>
> being the discretization of
>
> Int|Vi(nabla^2 pi dV) = Int|Vi(nabla dot ui)
>
> (I omit constants), where Int|Vi(…dV) is a volume integral on the I cell,
> pi is cell pressure, ui is the cell velocity.
>
> The computational domain contains 2 separated sub-domains.
>
> Let’s consider 4 cells into the whole domain and 2 cells for each
> sub-domain.
>
> I would expect a null space made of 2 vectors and from your patch they
> should look like [1/sqrt(2) 1/sqrt(2) 0 0] and [0 0 1/sqrt(2) 1/sqrt(2)],
> i.e. norm2 = 1 for both.
>
> With MatNullSpaceCreate(getCommunicator(), PETSC_TRUE, 0, nullptr,
> &nullspace) I’m saying that [1/sqrt(4) 1/sqrt(4) 1/sqrt(4) 1/sqrt(4)] is
> the null space, which is not but it is in the null space.
>
> But this is not the case I sent you, not exactly.
>
>
>
> The case I sent is 1/Vi * Aij * xj = 1/Vi bi, where Vi is the volume of
> the cell i.
>
> Let’s admit that yj is in the null space of of Aij, it should be in the
> null space of 1/Vi * Aij, therefore Aij*yj = 0 and 1/Vi * Aij*yj = 0 too.
>
> But in the framework of the test, this is true with infinite precision.
>
> What happens if norm2(Aij*yj) = 10^-15 and Vi = 10^-5? Norm2(1/Vi * Aij *
> yj) = 10^-10!!! Is yi still in the null space numerically?
>
> Let’s say yi is the constant vector over the whole domain, i.e. [1/sqrt(4)
> 1/sqrt(4) 1/sqrt(4) 1/sqrt(4)]. Should this be in the null space of 1/Vi *
> Aij, shouldn’t it?
>
> An analogous argument should be for the compatibility condition that
> concerns bi.
>
>
>
> My current problem is that properly creating the null space for Aij, i.e.
> [1/sqrt(2) 1/sqrt(2) 0 0] and [0 0 1/sqrt(2) 1/sqrt(2)], allows me to solve
> and find xi, but multiplying by 1/Vi, I cannot get any solution using both
> FGMRES+ILU and FGMRE+GAMG.
>
>
>
> The tiny problem will load Aij, Vi and bi and show the problem by testing
> the proper null space and trying to solve. I will include the patch to my
> PETSc version. I hope to come back to you very soon.
>
This sounds like a dimensionalization problem to me. It is best to choose
length (and other) units that make the matrix entries about 1. It seems
like you are far from this, and it is causing a loss of accuracy (your null
vector has a residual of about 1e-7).
Thanks,
Matt
> Thank you very much for your support!
>
>
>
>
>
> Marco Cisternino
>
>
>
> *From:* Matthew Knepley <knepley at gmail.com>
> *Sent:* martedì 18 gennaio 2022 21:25
> *To:* Marco Cisternino <marco.cisternino at optimad.it>
> *Cc:* petsc-users <petsc-users at mcs.anl.gov>
> *Subject:* Re: [petsc-users] Nullspaces
>
>
>
> I made a fix for this:
>
>
>
> https://gitlab.com/petsc/petsc/-/merge_requests/4729
>
>
>
> Thanks,
>
>
>
> Matt
>
>
>
> On Tue, Jan 18, 2022 at 3:20 PM Matthew Knepley <knepley at gmail.com> wrote:
>
> On Thu, 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:
>
> 1. MatNullSpaceCreate(getCommunicator(), PETSC_TRUE, 0, nullptr,
> &nullspace);
> 2. 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.
>
>
>
> Marco, please forgive me for taking so long to get to your issue. It has
> been crazy.
>
>
>
> You are correct, we had a bug. it is in MatNullSpaceTest. The
> normalization for the constant vector was wrong:
>
>
>
> diff --git a/src/mat/interface/matnull.c b/src/mat/interface/matnull.c
> index f8ab2925988..0c4c3855be0 100644
> --- a/src/mat/interface/matnull.c
> +++ b/src/mat/interface/matnull.c
> @@ -429,7 +429,7 @@ PetscErrorCode MatNullSpaceTest(MatNullSpace sp,Mat
> mat,PetscBool *isNull)
> if (sp->has_cnst) {
> ierr = VecDuplicate(l,&r);CHKERRQ(ierr);
> ierr = VecGetSize(l,&N);CHKERRQ(ierr);
> - sum = 1.0/N;
>
> + sum = 1.0/PetscSqrtReal(N);
> ierr = VecSet(l,sum);CHKERRQ(ierr);
> ierr = MatMult(mat,l,r);CHKERRQ(ierr);
> ierr = VecNorm(r,NORM_2,&nrm);CHKERRQ(ierr);
>
>
>
> With this fix, your two cases give the same answer, namely that the
> constant vector is not a null vector of your
>
> operator, but it is close, as your can see using -mat_null_space_test_view.
>
>
>
> Thanks,
>
>
>
> Matt
>
>
>
> Thanks for any help.
>
>
>
> Marco Cisternino
>
>
>
>
>
> Marco Cisternino, PhD
> marco.cisternino at optimad.it
>
> ______________________
>
> Optimad Engineering Srl
>
> Via Bligny 5, Torino, Italia.
> +3901119719782
> www.optimad.it
>
>
>
> *From:* Marco Cisternino <marco.cisternino at optimad.it>
> *Sent:* martedì 7 dicembre 2021 19:36
> *To:* Matthew Knepley <knepley at gmail.com>
> *Cc:* petsc-users <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>
> *Sent:* Tuesday, December 7, 2021 7:25:43 PM
> *To:* Marco Cisternino <marco.cisternino at optimad.it>
> *Cc:* petsc-users <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> 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
> marco.cisternino at optimad.it
>
> ______________________
>
> Optimad Engineering Srl
>
> Via Bligny 5, Torino, Italia.
> +3901119719782
> www.optimad.it
>
>
>
>
>
>
> --
>
> 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/>
>
>
>
>
> --
>
> 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/>
>
>
>
>
> --
>
> 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/>
>
--
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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