In FETI, system is replaced with a coarse problem of dual variables (drastically smaller coarse problem size) and by using a projector more well-conditioned system is obtained. Condition number is limited to 1+log(H/h)^2. As the literature suggests, I need to apply projector on PCG. I tested KSPDGMRES and it seems CG is more successful. So it seems my only way is to implement my own variant of KSPCG. May I just copy the files and definitions related to KSPCG and rename all as KSPPCPG. And then I can make the orthogonolization implementation similar to KSPDGMRES..
Jed, please warn me if this is a really hard task? I dont want to put myself into a long journey of implementation :) best regards, On Sun, Dec 28, 2014 at 8:48 PM, Jed Brown <[email protected]> wrote: > Umut Tabak <[email protected]> writes: > > Preconditioner side: my experience was that one should be really lucky > > to get a good preconditioner which is really really rare, as mentioned, > > especially for ill-conditioned problems, almost impossible. If my > > condition number estimate is above, say, 1e4 1e5, I do not expect much > > from iterative methods, > > Ill-conditioning is a red herring. For example, FMG can solve > well-behaved problems with 1e12 condition number in one cycle (about 5 > "work units"). OTOH, very well-conditioned problems with eigenvalues > encircling the origin converge extremely slowly (these are > nonsymmetric). Anyway, some SPD industrial problems see poor > performance with AMG, BDDC, and similar otherwise-scalable methods due > to discretization or physical features that elude the heuristics used to > produce good coarse spaces. Sometimes these problems can be formulated > in more solver-friendly ways. Other times, custom methods would be > needed. Or the methods could converge well, but only with high grid > complexity (coarse spaces that do not decay in size fast enough). >
