<div dir="ltr">On Mon, Oct 28, 2013 at 5:30 AM, Bishesh Khanal <span dir="ltr"><<a href="mailto:bisheshkh@gmail.com" target="_blank">bisheshkh@gmail.com</a>></span> wrote:<br><div class="gmail_extra"><div class="gmail_quote">
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<div class="im">On Fri, Oct 25, 2013 at 10:21 PM, Matthew Knepley <span dir="ltr"><<a href="mailto:knepley@gmail.com" target="_blank">knepley@gmail.com</a>></span> wrote:<br>
</div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left-width:1px;border-left-color:rgb(204,204,204);border-left-style:solid;padding-left:1ex"><div dir="ltr"><div class="im"><div>On Fri, Oct 25, 2013 at 2:55 PM, Bishesh Khanal <span dir="ltr"><<a href="mailto:bisheshkh@gmail.com" target="_blank">bisheshkh@gmail.com</a>></span> wrote:</div>
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On Fri, Oct 25, 2013 at 8:18 PM, Matthew Knepley <span dir="ltr"><<a href="mailto:knepley@gmail.com" target="_blank">knepley@gmail.com</a>></span> wrote:<br>
<blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left-width:1px;border-left-style:solid;border-left-color:rgb(204,204,204);padding-left:1ex"><div dir="ltr"><div><div>On Fri, Oct 25, 2013 at 12:09 PM, Bishesh Khanal <span dir="ltr"><<a href="mailto:bisheshkh@gmail.com" target="_blank">bisheshkh@gmail.com</a>></span> wrote:<br>
</div></div><div class="gmail_extra"><div class="gmail_quote"><div><div>
<blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left-width:1px;border-left-style:solid;border-left-color:rgb(204,204,204);padding-left:1ex"><div dir="ltr"><div><div><div>Dear all,<br></div>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): <br>
<br>
</div>Let's say that I have a 3D binary image (a cube).<br>The binary information of the image partitions the cube into a computational domain and non-computational domain. <br>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<br>
</div><div><br>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).<br><br>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. <br></div><div>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. <br>
Then, once the system is solved, put the values of the solution back to the corresponding positions in the binary image.<br></div><div>Later, I might have to extend this for the staggered grid case too.<br></div><div>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 ?<br>
</div><div><br></div><div>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!) <br>
</div></div></blockquote><div><br></div></div></div><div>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</div><div>alpha code. If you feel comfortable with that level of development, we can help you.</div>
</div></div></div></blockquote><div> </div><div>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.<br>
Just a note: I'm currently using the petsc3.4.3 and have not used the development version before. </div></div></div></div></blockquote><div><br></div></div><div>Okay,</div><div><br></div><div>1) clone the repository using Git and build the 'next' branch.</div>
<div><br></div></div><div class="im"><div>2) then we will need to create a PetscSection that puts unknowns where you want them</div><div><br></div><div>3) Setup the solver as usual</div><div><br></div><div>You can do 1) an 3) before we do 2).</div>
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<div><br></div></div></div></div></div></div></blockquote><div>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). <br>
Please let me know what I should do now.</div></div></div></div></blockquote><div><br></div><div>Okay, now write a loop to setup the PetscSection. I have the DMDA partitioning cells, so you would have</div><div>unknowns in cells. The code should look like this:</div>
<div><br></div><div>PetscSectionCreate(comm, &s);</div><div><div>DMDAGetNumCells(dm, NULL, NULL, NULL, &nC);<br></div></div><div>PetscSectionSetChart(s, 0, nC);</div><div>for (k = zs; k < zs+zm; ++k) {</div><div>
for (j = ys; j < ys+ym; ++j) {</div><div> for (i = xs; i < xs+xm; ++i) {</div><div> PetscInt point;</div><div><br></div><div> DMDAGetCellPoint(dm, i, j, k, &point);</div><div> PetscSectionSetDof(s, point, dof); // You know how many dof are on each vertex</div>
<div> }</div><div> }</div><div>}</div><div>PetscSectionSetUp(s);</div><div>DMSetDefaultSection(dm, s);</div><div>PetscSectionDestroy(&s);</div><div><br></div><div>I will merge the necessary stuff into 'next' to make this work.</div>
<div><br></div><div> Thanks,</div><div><br></div><div> Matt </div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left-width:1px;border-left-color:rgb(204,204,204);border-left-style:solid;padding-left:1ex">
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<div dir="ltr"><div class="gmail_extra"><div class="gmail_quote"><div> If not, just put the identity into</div>
<div>the rows you do not use on the full cube. It will not hurt scalability or convergence.</div></div></div></div></blockquote><div> </div>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:<br>
</div><div class="gmail_quote">1) Having read Jed's answer here : <a href="http://scicomp.stackexchange.com/questions/3426/why-is-pinning-a-point-to-remove-a-null-space-bad/3427#3427" target="_blank">http://scicomp.stackexchange.com/questions/3426/why-is-pinning-a-point-to-remove-a-null-space-bad/3427#3427</a></div>
</div></div></blockquote><div><br></div></div><div>Jed is talking about a constraint on a the pressure at a point. This is just decoupling these unknowns from the rest</div><div>of the problem.</div><div><div>
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<div dir="ltr"><div class="gmail_extra"><div class="gmail_quote">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.<br>
</div></div></div></blockquote><div><br></div></div><div>It can change the exact iteration, but it does not make the matrix conditioning worse.</div><div><br></div><div> Matt</div><div><div> </div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left-width:1px;border-left-color:rgb(204,204,204);border-left-style:solid;padding-left:1ex">
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</div><div class="gmail_quote">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.<br><br></div><div class="gmail_quote">Thanks,<br>
Bishesh<br></div><div class="gmail_quote"><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left-width:1px;border-left-style:solid;border-left-color:rgb(204,204,204);padding-left:1ex"><div dir="ltr">
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<div><br></div><div> Matt</div><div> </div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left-width:1px;border-left-style:solid;border-left-color:rgb(204,204,204);padding-left:1ex">
<div dir="ltr"><div></div>Thanks,<br>Bishesh<span><font color="#888888"><br></font></span></div><span><font color="#888888">
</font></span></blockquote></div><span><font color="#888888"><br><br clear="all"><span><font color="#888888"><div><br></div>-- <br>What most experimenters take for granted before they begin their experiments is infinitely more interesting than any results to which their experiments lead.<br>
-- Norbert Wiener
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</blockquote></div></div><div><br><br clear="all"><div><br></div>-- <br>What most experimenters take for granted before they begin their experiments is infinitely more interesting than any results to which their experiments lead.<br>
-- Norbert Wiener
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</blockquote></div></div><br></div></div>
</blockquote></div><br><br clear="all"><div><br></div>-- <br>What most experimenters take for granted before they begin their experiments is infinitely more interesting than any results to which their experiments lead.<br>
-- Norbert Wiener
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