On Wed, Dec 21, 2011 at 6:40 PM, Mohamad M. Nasr-Azadani <mmnasr at gmail.com>wrote:
> Thank you Jed for the detailed explanation. To tell you the truth, that > was a bit overwhelming/scary for an engineer like me-that I have to be > supercareful when using those solvers and preconditioners- :D > For my case though, I decided to fix the pressure at one node in the > domain so I won't end up with a null-space case of the Pressure equation. > I assume that way, I would not have to worry about the nullspace problems > and the convergence issues you pointed out, right? > Nope. You have removed the null space from the operator on the full domain, but not the subdomains that Jed was talking about. I think this method only complicates things since now one subdomain looks weird, and the behavior of the coarse operator in unpredictable since i don't know where this point is. Matt > Best, > Mohamad > > > > On Mon, Dec 19, 2011 at 9:09 PM, Jed Brown <jedbrown at mcs.anl.gov> wrote: > >> On Mon, Dec 19, 2011 at 20:57, Barry Smith <bsmith at mcs.anl.gov> wrote: >> >>> So please tell use how we SHOULD use AMG with those "indefinite problem >>> produced by most discretizations of incompressible flow" dear teacher :-) >> >> >> If only there was a nice complete answer... >> >> We can do block preconditioners advocated by Elman and others. These are >> the most flexible and the simplest for code reuse. For low Reynolds number, >> they can also have optimal complexity, although the constants are usually >> not the best. Most variants are well-supported by PCFieldSplit (e.g. with >> PCLSC), but some need the user to provide auxiliary operators (e.g. the >> "pressure convection-diffusion" variant). We could improve support for >> these cases, but it's a delicate balance and I don't know any way to avoid >> asking the user to understand a reasonable amount about the method and >> usually to provide auxiliary information. >> >> We can do coupled multigrid with fieldsplit or "distributed relaxation" >> as a smoother. These can often be made more robust, but they tend to be >> more intrusive to implement. These are not usually purely algebraic due to >> inf-sup issues when coarsening the dual variables (pressure), though Mark >> Adams' work on this for contact mechanics could be used to coarsen pressure >> algebraically. I would like to experiment with this in PCGAMG. >> >> We can do coupled multigrid with compatible Vanka-type smoothers. Whether >> these are algorithmically effective and/or efficient is quite dependent on >> the discretization. These methods are also usually geometric, though it's >> possible to algebraically define a Vanka-smoother (though not necessarily >> efficient). This is straightforward for MAC finite differences on >> structured grids. For continuous finite elements, the "rotated Q1" >> Rannacher-Turek elements are most attractive for these smoothers, but >> Rannacher-Turek elements do not satisfy a discrete Korn's inequality, so >> they are unusable for many problems. Some variants of DG for incompressible >> flow seem to be the most interesting for this approach in general domains. >> > > -- 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/20111221/c0cc6f04/attachment.htm>
