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

Matthew Knepley knepley at gmail.com
Mon Oct 28 12:19:34 CDT 2013 

On Mon, Oct 28, 2013 at 10:13 AM, Bishesh Khanal <bisheshkh at gmail.com>wrote:

>
>
>
> On Mon, Oct 28, 2013 at 3:49 PM, Matthew Knepley <knepley at gmail.com>wrote:
>
>> 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
>>
>
> Done.
> I mask it out using isPosInDomain() function::
>        if(isPosInDomain(&testPoisson,i,j,k)) {
>             ierr = DMDAGetCellPoint(dm, i, j, k, &point);CHKERRQ(ierr);
>             ierr = PetscSectionSetDof(s, point, testPoisson.mDof); // You
> know how many dof are on each vertex
>           }
>
> And please let me know when I can rebuild the 'next' branch of petsc so
> that DMDAGetCellPoint can be used. Currently compiler complains as it
> cannot find it.
>

Pushed.

   Matt


>
>>    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
>>
>
>


-- 
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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