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

[Bishesh Khanal]

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.

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
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.
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
>
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