[petsc-users] using petsc tools to solve isolated irregular domains with finite difference
Matthew Knepley
knepley at gmail.com
Tue Oct 29 11:37:55 CDT 2013
On Tue, Oct 29, 2013 at 5:31 AM, Bishesh Khanal <bisheshkh at gmail.com> wrote:
> On Mon, Oct 28, 2013 at 9:00 PM, Matthew Knepley <knepley at gmail.com>wrote:
>
>> On Mon, Oct 28, 2013 at 2:51 PM, Bishesh Khanal <bisheshkh at gmail.com>wrote:
>>
>>> On Mon, Oct 28, 2013 at 6:19 PM, Matthew Knepley <knepley at gmail.com>wrote:
>>>
>>>> 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.
>>>>
>>>
>>> Pulled it thanks, but compiler was complaining that it didn't find
>>> DMDAGetCellPoint.
>>> Doing grep -R 'DMDAGetCellPoint' include/
>>> returned nothing although the implementation is there in dalocal.c
>>> So I added the declaration to petscdmda.h file just above the
>>> declaration of DMDAGetNumCells.
>>>
>>
>> I will add the declaration.
>>
>>
>>> I have also added you as a collaborator in the github project
>>> repository so that you can edit and add comments to the file I linked
>>> above. My computeMatrix still uses the DMDA instead of the PetscSection, so
>>> is it where the changes need to be made ?
>>>
>>
>> Instead of MatSetValuesStencil(), you would go back to using
>> MatSetValues(), and calculate the indices using PetscSection.
>> You get the section
>>
>> DMGetDefaultGlobalSection(dm, &gs)
>>
>> and then
>>
>> DMDAGetCellPoint(dm, i, j, k, &p);
>> PetscSectionGetOffset(gs, p, &ind);
>> row = ind < 0 ? -(ind+1) : ind;
>>
>>
>
> I'm sorry but did not understood. For e.g., in 2D, for each point p, I
> have 2 dof. Does PetsSectionGetOffset give me the two offsets for the dof
> sth like ind[0] = 0 and ind[1] = 1 ?
> How would you change the following code that sets 2D laplacian stencil
> for 2 dof to use petscsection and Matsetvalues instead ?
>
Forget about multiple degrees of freedom until your scalar problem works.
> ierr = KSPGetDM(ksp,&da);CHKERRQ(ierr);
> ierr = DMDAGetLocalInfo(da,&info);CHKERRQ(ierr);
> ierr = DMGetDefaultGlobalSection(dm,&gs);CHKERRQ(ierr); /*Here I get
> the PetscSection*/
> for(PetscInt dof = 0; dof < 2; ++dof) {
> row.c = dof;
> for(PetscInt k = 0; k < 5; ++k) {
> col[k].c = dof;
> }
>
I can't imagine that this is what you want. You have two non-interacting
problems.
> for(PetscInt j = info.ys; j<info.ys+info.ym; ++j) {
> for(PetscInt i = info.xs; i<info.xs+info.xm; ++i) {
> num = 0;
> /*ierr =
> DMDAGetCellPoint(da,i,j,0,&point);CHKERRQ(ierr);*/ /*Get the PetscPoint*/
> /*But I did now understand how I would emulate the row.c
> and col.c info with PetscSection*/
> row.i = i; row.j = j;
>
Here you would call
ierr = DMDAGetCellPoint(da, i, j, 0, &cell);CHKERRQ(ierr);
ierr = PetscSectionGetOffset(da, cell, &row);CHKERRQ(ierr);
ierr = PetscSectionGetDof(da, cell, &dof);CHKERRQ(ierr);
This means that this cell has global rows = [row, row+dof).
> col[num].i = i; col[num].j = j;
> if (isPosInDomain(ctx,i,j)) { /*put the operator for
> only the values for only the points lying in the domain*/
> v[num++] = -4;
> if(isPosInDomain(ctx,i+1,j)) {
> col[num].i = i+1; col[num].j = j;
> v[num++] = 1;
> }
> if(isPosInDomain(ctx,i-1,j)) {
> col[num].i = i-1; col[num].j = j;
> v[num++] = 1;
> }
> if(isPosInDomain(ctx,i,j+1)) {
> col[num].i = i; col[num].j = j+1;
> v[num++] = 1;
> }
> if(isPosInDomain(ctx,i,j-1)) {
> col[num].i = i; col[num].j = j-1;
> v[num++] = 1;
> }
> } else {
> v[num++] = dScale; /*set Dirichlet identity rows for
> points in the rectangle but outside the computational domain*/
> }
>
You do the same thing for the columns, and then call
ierr = MatSetValues(A, dof, rows, num*dof, cols, v,
INSERT_VALUES);CHKERRQ(ierr);
> ierr =
> MatSetValuesStencil(A,1,&row,num,col,v,INSERT_VALUES);CHKERRQ(ierr);
> }
> }
> }
>
>
>> Thanks,
>>
>> Matt
>>
>>
>>>
>>>> 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
>>>>
>>>
>>>
>>
>>
>> --
>> 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
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://lists.mcs.anl.gov/pipermail/petsc-users/attachments/20131029/817326df/attachment-0001.html>
More information about the petsc-users
mailing list