<html><head><meta http-equiv="Content-Type" content="text/html charset=utf-8"></head><body style="word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space;" class=""><div class="">I have now experimented with different AMG solvers (gamg, ML, hypre ) through petsc, and have a mixed bag of results. I have used -pc_gamg_threshold 0.1 for all cases.</div><div class=""><br class=""></div><div class="">The problem is that of plate-bending that is clamped on all ends, and has a uniformly distributed load. </div><div class=""><br class=""></div><div class="">The problem has 6 dofs per node: {u, v, w, tx, ty, tz}. u, v are the in-plane deformations related to membrane action. w, tx, ty get the stiffness from the Mandlin first-order shear deformation theory. tz doesn’t really do anything in the problem, and the stiffness matrix has small diagonal values to avoid singularity problems. </div><div class=""><br class=""></div><div class=""><br class=""></div><div class="">I have tested AMG solvers for number of unknowns from a few hundred to about 1.5e6. </div><div class=""><br class=""></div><div class="">First off, I am absolutely thrilled to be able to solve that large a system of equations coming from a bending operator on my laptop! So a big thanks to the petsc team for giving us the tools! </div><div class=""><br class=""></div><div class="">I have not done a very thorough convergence study, but following are some general observations: </div><div class=""><br class=""></div><div class="">— Without providing the near null space, all three solvers work.</div><div class=""><br class=""></div><div class="">— The convergence of the solvers is significantly better when the near null space is provided. There are 6 near-null space modes provided: 3 rigid-body translations and 3-rigid body rotations. </div><div class=""><br class=""></div><div class="">— With the near null space provided, both hypre and ML work without problems, but GAMG quits the error of zero-pivot in LU decomposition. I am guessing this happens for the coarsest level. I was able to get around this with -mg_levels_pc_type jacobi . (I saw some earlier discussion on the mailing list about this, and got the sense that this may be a non-deterministic issue (?) ).</div><div class=""><br class=""></div><div class="">— With -pc_gamg_threshold 0.1 and -pc_mg_type full, I get the fastest convergence from ML. </div><div class=""><br class=""></div><div class=""><div class="">— GAMG seems to take about twice the amount of memory than ML. </div><div class=""><br class=""></div></div><div class=""><br class=""></div><div class="">I am now keen to play around with various parameters to see how to influence the convergence. </div><div class=""><br class=""></div><div class="">Any comments would be greatly appreciated. </div><div class=""><br class=""></div><div class="">Regards,</div><div class="">Manav</div><div class=""><br class=""></div><div class=""><br class=""></div><br class=""><div><blockquote type="cite" class=""><div class="">On Feb 25, 2016, at 6:21 AM, Mark Adams <<a href="mailto:mfadams@lbl.gov" class="">mfadams@lbl.gov</a>> wrote:</div><br class="Apple-interchange-newline"><div class=""><div dir="ltr" class="">I added ", which is often the null space of the operator without boundary conditions" to the web page doc for MatSetNearNullSpace.</div><div class="gmail_extra"><br class=""><div class="gmail_quote">On Wed, Feb 24, 2016 at 10:57 AM, Matthew Knepley <span dir="ltr" class=""><<a href="mailto:knepley@gmail.com" target="_blank" class="">knepley@gmail.com</a>></span> wrote:<br class=""><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div dir="ltr" class=""><div class="gmail_extra"><div class="gmail_quote"><span class="">On Wed, Feb 24, 2016 at 9:45 AM, Manav Bhatia <span dir="ltr" class=""><<a href="mailto:bhatiamanav@gmail.com" target="_blank" class="">bhatiamanav@gmail.com</a>></span> wrote:<br class=""><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">Hi,<br class="">
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I typically apply Dirichlet BCs by modifying the Jacobin and rhs: zero constrained rows of matrix with 1.0 at diagonal, and zero corresponding rows of rhs.<br class="">
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While using GAMG, is it still recommended to provide the near-null space (given that the zero-eigenvalues have been removed by specification of DIrichlet BCs)?<br class=""></blockquote><div class=""><br class=""></div></span><div class="">Yes.</div><span class=""><div class=""> </div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
If that information is still needed, should the vectors be modified in any manner to be consistent with the Dirichlet BCs?<br class=""></blockquote><div class=""><br class=""></div></span><div class="">No. You can see that if you take a small piece of the domain, apart from the boundary, it will have this as a null space.</div><div class=""><br class=""></div><div class=""> Matt</div><div class=""> </div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
Thanks,<br class="">
Manav<br class="">
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</font></span></blockquote></div><span class="HOEnZb"><font color="#888888" class=""><br class=""><br clear="all" class=""><div class=""><br class=""></div>-- <br class=""><div class="">What most experimenters take for granted before they begin their experiments is infinitely more interesting than any results to which their experiments lead.<br class="">-- Norbert Wiener</div>
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