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

[Matthew Knepley]

On Mon, Oct 28, 2013 at 9:06 AM, Bishesh Khanal <bisheshkh at gmail.com> wrote:

>
> On Mon, Oct 28, 2013 at 1:40 PM, Matthew Knepley <knepley at gmail.com>wrote:
>
>> 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.
>>
>
> I have put an example without the PetscSection here:
> https://github.com/bishesh/petscPoissonIrregular/blob/master/poissonIrregular.cxx
> From the code you have written above, how do we let PetscSection select
> only those cells that lie in the computational domain ?  Is it that for
> every "point" inside the above loop, we check whether it lies in the domain
> or not, e.g using the function isPosInDomain(...) in the .cxx file I linked
> to?
>

1) Give me permission to comment on the source (I am 'knepley')

2) You mask out the (i,j,k) that you do not want in that loop

   Matt


>
>>   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
>>
>
>


-- 
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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