Dear Jed, During my recent visit to ETH, I talked at length about multi-grid with Dave May who warned me about the issues of large coefficient-contrasts. Most of my problems of interest for tectonophysics and earthquake simulations are cases of relatively smooth variations in elastic moduli. So I am not too worried about this aspect of the problem. I appreciate your advice about trying simpler solutions first. I have tested at length direct solvers of 2-D and 3-D problems of elastic deformation and I am quite happy with the results. My primary concern now is computation speed, especially for 3-D problems, where i have of the order 512^3 degrees of freedom. I was planning to test Jacobi and SOR smoothers. Is there another smoother you recommend for this kind of problem?
Thanks, Sylvain 2011/5/11 Jed Brown <jed at 59a2.org>: > On Wed, May 11, 2011 at 04:20, Sylvain Barbot <sylbar.vainbot at gmail.com> > wrote: >> >> I am still trying to design a >> multigrid preconditionner for the Navier's equation of elasticity. > > I have heard, through an external source, that you have large jumps in both > Young's modulus and Poisson ratio that are not grid aligned, including > perhaps thin structures that span a large part of the domain. Such problems > are pretty hard, so I suggest you focus on robustness and do not worry about > low-memory implementation at this point. That is, you should assemble the > matrices in a usual PETSc format instead of using MatShell to do everything > matrix-free. This gives you access to much stronger smoothers. > After you find a scheme that is robust enough for your purposes, _then_ you > can make it low-memory by replacing some assembled matrices by MatShell. To > realize most of the possible memory savings, it should be sufficient to do > this on the finest level only.
