[petsc-users] using petsc tools to solve isolated irregular domains with finite difference

[Matthew Knepley]

On Mon, Oct 28, 2013 at 5:30 AM, Bishesh Khanal <bisheshkh at gmail.com> wrote:

>
>
>
> On Fri, Oct 25, 2013 at 10:21 PM, Matthew Knepley <knepley at gmail.com>wrote:
>
>> On Fri, Oct 25, 2013 at 2:55 PM, Bishesh Khanal <bisheshkh at gmail.com>wrote:
>>
>>> On Fri, Oct 25, 2013 at 8:18 PM, Matthew Knepley <knepley at gmail.com>wrote:
>>>
>>>> On Fri, Oct 25, 2013 at 12:09 PM, Bishesh Khanal <bisheshkh at gmail.com>wrote:
>>>>
>>>>> Dear all,
>>>>> I would like to know if some of the petsc objects that I have not used
>>>>> so far (IS, DMPlex, PetscSection) could be useful in the following case (of
>>>>> irregular domains):
>>>>>
>>>>> Let's say that I have a 3D binary image (a cube).
>>>>> The binary information of the image partitions the cube into a
>>>>> computational domain and non-computational domain.
>>>>> I must solve a pde (say a Poisson equation) only on the computational
>>>>> domains (e.g: two isolated spheres within the cube). I'm using finite
>>>>> difference and say a dirichlet boundary condition
>>>>>
>>>>> I know that I can create a dmda that will let me access the
>>>>> information from this 3D binary image, get all the coefficients, rhs values
>>>>> etc using the natural indexing (i,j,k).
>>>>>
>>>>> Now, I would like to create a matrix corresponding to the laplace
>>>>> operator (e.g. with standard 7 pt. stencil), and the corresponding RHS that
>>>>> takes care of the dirchlet values too.
>>>>> But in this matrix it should have the rows corresponding to the nodes
>>>>> only on the computational domain. It would be nice if I can easily (using
>>>>> (i,j,k) indexing) put on the rhs dirichlet values corresponding to the
>>>>> boundary points.
>>>>> Then, once the system is solved, put the values of the solution back
>>>>> to the corresponding positions in the binary image.
>>>>> Later, I might have to extend this for the staggered grid case too.
>>>>> So is petscsection or dmplex suitable for this so that I can set up
>>>>> the matrix with something like DMCreateMatrix ? Or what would you suggest
>>>>> as a suitable approach to this problem ?
>>>>>
>>>>> I have looked at the manual and that led me to search for a simpler
>>>>> examples in petsc src directories. But most of the ones I encountered are
>>>>> with FEM (and I'm not familiar at all with FEM, so these examples serve
>>>>> more as a distraction with FEM jargon!)
>>>>>
>>>>
>>>> It sounds like the right solution for this is to use PetscSection on
>>>> top of DMDA. I am working on this, but it is really
>>>> alpha code. If you feel comfortable with that level of development, we
>>>> can help you.
>>>>
>>>
>>> Thanks, with the (short) experience of using Petsc so far and being
>>> familiar with the awesomeness (quick and helpful replies) of this mailing
>>> list, I would like to give it a try. Please give me some pointers to get
>>> going for the example case I mentioned above. A simple example of using
>>> PetscSection along with DMDA for finite volume (No FEM) would be great I
>>> think.
>>> Just a note: I'm currently using the petsc3.4.3 and have not used the
>>> development version before.
>>>
>>
>> Okay,
>>
>> 1)  clone the repository using Git and build the 'next' branch.
>>
>> 2) then we will need to create a PetscSection that puts unknowns where
>> you want them
>>
>> 3) Setup the solver as usual
>>
>> You can do 1) an 3) before we do 2).
>>
>> I've done 1) and 3). I have one .cxx file that solves the system using
> DMDA (putting identity into the rows corresponding to the cells that are
> not used).
> Please let me know what I should do now.
>

Okay, now write a loop to setup the PetscSection. I have the DMDA
partitioning cells, so you would have
unknowns in cells. The code should look like this:

PetscSectionCreate(comm, &s);
DMDAGetNumCells(dm, NULL, NULL, NULL, &nC);
PetscSectionSetChart(s, 0, nC);
for (k = zs; k < zs+zm; ++k) {
  for (j = ys; j < ys+ym; ++j) {
    for (i = xs; i < xs+xm; ++i) {
      PetscInt point;

      DMDAGetCellPoint(dm, i, j, k, &point);
      PetscSectionSetDof(s, point, dof); // You know how many dof are on
each vertex
    }
  }
}
PetscSectionSetUp(s);
DMSetDefaultSection(dm, s);
PetscSectionDestroy(&s);

I will merge the necessary stuff into 'next' to make this work.

  Thanks,

     Matt

>
>>  If not, just put the identity into
>>>> the rows you do not use on the full cube. It will not hurt scalability
>>>> or convergence.
>>>>
>>>
>>> In the case of Poisson with Dirichlet condition this might be the case.
>>> But is it always true that having identity rows in the system matrix will
>>> not hurt convergence ? I thought otherwise for the following reasons:
>>> 1)  Having read Jed's answer here :
>>> http://scicomp.stackexchange.com/questions/3426/why-is-pinning-a-point-to-remove-a-null-space-bad/3427#3427
>>>
>>
>> Jed is talking about a constraint on a the pressure at a point. This is
>> just decoupling these unknowns from the rest
>> of the problem.
>>
>>
>>> 2) Some observation I am getting (but I am still doing more experiments
>>> to confirm) while solving my staggered-grid 3D stokes flow with schur
>>> complement and using -pc_type gamg for A00 matrix. Putting the identity
>>> rows for dirichlet boundaries and for ghost cells seemed to have effects on
>>> its convergence. I'm hoping once I know how to use PetscSection, I can get
>>> rid of using ghost cells method for the staggered grid and get rid of the
>>> identity rows too.
>>>
>>
>> It can change the exact iteration, but it does not make the matrix
>> conditioning worse.
>>
>>    Matt
>>
>>
>>>  Anyway please provide me with some pointers so that I can start trying
>>> with petscsection on top of a dmda, in the beginning for non-staggered case.
>>>
>>> Thanks,
>>> Bishesh
>>>
>>>>
>>>>   Matt
>>>>
>>>>
>>>>> Thanks,
>>>>> Bishesh
>>>>>
>>>>
>>>>
>>>>
>>>> --
>>>> 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
>>>>
>>>
>>>
>>
>>
>> --
>> 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
>>
>
>


-- 
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
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