[petsc-users] [petsc-maint] Poisson with Neumann BC on a stretched grid

Wed Oct 7 08:11:52 CDT 2020

On Wed, Oct 7, 2020 at 8:27 AM Victoria Hamtiaux <
victoria.hamtiaux at uclouvain.be> wrote:

> Thanks for all the answers,
>
>
> How can I do the "semi-coarsening"? I don't really know how those
> preconditionners work so I don't how how to change them or so..
>
>
> You have to write custom code to do semi-coarsening. PETSc does not
provide that and you would not want to do it yourself, most likely.

> I have a question because you both seem to say that my matrix is supposed
> to be symmetric which is not the case. \
>
You said "my matrix is symmetric."

Then you said " I suspect that by stretching the grid, my matrix is not
symmetric anymore and that it might cause a problem."

We are saying that by stretchin the grid the matrix is still symmetric even
if the grid has lost a symmetry. I don't know of a mechanism for stretching
the grid to make the matrix asymmetric. So we are suggesting that you
verify your suspicion that the matrix is symmetric.

And in fact, I don't get how it can be symmetric. Because you will have
> something close to symmetric. For example when you are at the center of
> your domain it will be symmetric, but when your at a point at the
> boundaries I don't get how you can be symmetric, you won't have something
> at the left and the right of your main diagonal... (I don't know if my
> explanations are understandable)
>
You can make a discretization that is not symmetric because of boundary
conditions but I assume that is not the case because you said your matrix
is symmetric.

> Best regards,
>
>
> Victoria
>
>
>
> On 7/10/20 14:20, Mark Adams wrote:
>
> GMG (geometric MG) is stronger as Matt said, but it is affected by
> stretched grids in a similar way. A way to fix this in GMG is
> semi-coarsening, which AMG _can_ do automatically.
>
> On Wed, Oct 7, 2020 at 8:02 AM Matthew Knepley <knepley at gmail.com> wrote:
>
>> On Wed, Oct 7, 2020 at 7:07 AM Victoria Hamtiaux <
>> victoria.hamtiaux at uclouvain.be> wrote:
>>
>>> Hello Matt,
>>>
>>>
>>> I just checked the symmetry of my matrix and it is not symmetric. But it
>>> is not symmetric either when I use a uniform grid.
>>>
>>> The domain is 3D and I'm using finite differences, so I guess it is
>>> normal that at multiple places (when I deal with points near the
>>> boundaries), the matrix is not symmetric.
>>>
>>> So I was wrong, the problem doesn't come from the fact that the matrix
>>> is not symmetric. I don't know where it comes from, but when I switch from
>>> uniform to stretched grid, the solver stops working properly. Could it be
>>> from the preconditionner of the solver that I use?
>>>
>>> Do you have any other idea ?
>>>
>> I would consider using GMG. As Mark says, AMG is very fiddly with
>> stretched grids. For Poisson, GMG works great and you seem to have regular
>> grids.
>>
>>   Thanks,
>>
>>     Matt
>>
>>> Thanks for your help,
>>>
>>>
>>> Victoria
>>>
>>>
>>> On 7/10/20 12:48, Matthew Knepley wrote:
>>>
>>> On Wed, Oct 7, 2020 at 6:40 AM Victoria Hamtiaux <
>>> victoria.hamtiaux at uclouvain.be> wrote:
>>>
>>>> Dear all,
>>>>
>>>>
>>>> After the discretization of a poisson equation with purely Neumann (or
>>>> periodic) boundary conditions, I get a matrix which is singular.
>>>>
>>>>
>>>> The way I am handling this is by using a NullSpace with the following
>>>> code :
>>>>
>>>> MatNullSpace nullspace;
>>>> MatNullSpaceCreate(PETSC_COMM_WORLD, PETSC_TRUE, 0, 0, &nullspace);
>>>> MatSetNullSpace(p_solverp->A, nullspace);
>>>> MatSetTransposeNullSpace(p_solverp->A, nullspace);
>>>> MatNullSpaceDestroy(&nullspace);
>>>>
>>>>
>>>> Note that I am using the hypre preconditionner BOOMERANG and the
>>>> default
>>>> solver GMRES.
>>>>
>>>>
>>>>      KSPCreate(PETSC_COMM_WORLD,&p_solverp->ksp);
>>>>      KSPSetOperators(p_solverp->ksp, p_solverp->A, p_solverp->A);
>>>>      PC prec;
>>>>      KSPGetPC(p_solverp->ksp, &prec);
>>>>      PCSetType(prec,PCHYPRE);//PCHYPRE seems the best
>>>>      PCHYPRESetType(prec,"boomeramg"); //boomeramg is the best
>>>>      KSPSetInitialGuessNonzero(p_solverp->ksp,PETSC_TRUE);
>>>>      KSPSetFromOptions(p_solverp->ksp);
>>>>      KSPSetTolerances(p_solverp->ksp, 1.e-10, 1e-10, PETSC_DEFAULT,
>>>> PETSC_DEFAULT);
>>>>      KSPSetReusePreconditioner(p_solverp->ksp,PETSC_TRUE);
>>>>      KSPSetUseFischerGuess(p_solverp->ksp,1,5);
>>>>      KSPGMRESSetPreAllocateVectors(p_solverp->ksp);
>>>>      KSPSetUp(p_solverp->ksp);
>>>>
>>>>
>>>>
>>>> And this works fine when my grid is uniform, so that my matrix is
>>>> symmetric.
>>>>
>>>>
>>>> But when I stretch the grid near the boundary (my grid is then
>>>> non-uniform), it doesn't work properly anymore. I suspect that by
>>>> stretching the grid, my matrix is not symmetric anymore and that it
>>>> might cause a problem.
>>>>
>>>
>>> Symmetry is a property of the operator, so you should be symmetric on
>>> your
>>> stretched grid. If not, I think you have the discretization wrong. You
>>> can check
>>> symmetry using
>>>
>>>
>>> https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Mat/MatIsSymmetric.html
>>> <https://eur03.safelinks.protection.outlook.com/?url=https%3A%2F%2Fwww.mcs.anl.gov%2Fpetsc%2Fpetsc-current%2Fdocs%2Fmanualpages%2FMat%2FMatIsSymmetric.html&data=02%7C01%7Cvictoria.hamtiaux%40uclouvain.be%7C494a0f05bd214b5974f008d86abb6e02%7C7ab090d4fa2e4ecfbc7c4127b4d582ec%7C0%7C0%7C637376700525925749&sdata=nWt0sejio7o1PzMoc7tPu7JOvcNqofRuMQ91ynW54r4%3D&reserved=0>
>>>
>>> Also, if you suspect your discretization, you should probably do an MMS
>>> test to
>>> verify that you discretization converges at the correct rate.
>>>
>>>   Thanks,
>>>
>>>      Matt
>>>
>>>
>>>> I tried fixing the solution at an arbitrary point, but sometimes doing
>>>> this, I get errors near that fixed point. I 've seen on the petsc-users
>>>> forum that you usually don't recommend to fix a point, but I don't
>>>> really know how to proceed differently.
>>>>
>>>>
>>>> What would you recommend to solve this problem?
>>>>
>>>>
>>>> Thanks for your help,
>>>>
>>>>
>>>> Best regards,
>>>>
>>>>
>>>> Victoria
>>>>
>>>>
>>>>
>>>
>>> --
>>> 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/
>>> <https://eur03.safelinks.protection.outlook.com/?url=http:%2F%2Fwww.cse.buffalo.edu%2F~knepley%2F&data=02%7C01%7Cvictoria.hamtiaux%40uclouvain.be%7C494a0f05bd214b5974f008d86abb6e02%7C7ab090d4fa2e4ecfbc7c4127b4d582ec%7C0%7C0%7C637376700525925749&sdata=LHARUv3BxSwWnxN2LUJnX3vr2ZJ9f50EMQzw44Hy%2FqY%3D&reserved=0>
>>>
>>>
>>
>> --
>> 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/
>> <https://eur03.safelinks.protection.outlook.com/?url=http:%2F%2Fwww.cse.buffalo.edu%2F~knepley%2F&data=02%7C01%7Cvictoria.hamtiaux%40uclouvain.be%7C494a0f05bd214b5974f008d86abb6e02%7C7ab090d4fa2e4ecfbc7c4127b4d582ec%7C0%7C0%7C637376700525935751&sdata=kOKe%2FLj7pvAdzldpTNlRfC7BS6Vv4S5mU6Cb8pPpmrE%3D&reserved=0>
>>
>
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