Alp Kalpalp <[email protected]> writes: > Thanks for the answers, > > Please forgive me, I forgot to say that my stiffness matrix is not changing > during time steps. I could not remember directly but just after a google > search..I just hit this > > http://web.stanford.edu/group/frg/publications/recent/FETI-stoch.pdf > > please look around eq37 > > My problem is not related to this random paper I found. But, I think I can > find several others that shows the enhancing power of orthogonalization > with successive directions when the system's behaviour is not changing > rapidly. In my current sample case a gradually increasing force is applied > to a linear system.
Is the force moving or just increasing? The idea with this class of methods is that you add a Galerkin coarse correction where the basis functions approximate some low-frequency eigenvectors of the system. The projection is relatively expensive in parallel, but could save iterations. It's not "scalable" for many outlier eigenvalues because the projection space would get too big as the problem size is increased, but when combined with a decent-but-not-too-good preconditioner, could improve performance. You can implement this in the general case using PCCOMPOSITE+PCGALERKIN or with PCMG. You can also use KSPDGMRES or KSPAGMRES (man page missing in the release -- I reactivated, but look at the code until it regenerates), which attempt to automatically build a space. http://www.mcs.anl.gov/petsc/petsc-dev/docs/manualpages/KSP/KSPDGMRES.html You could implement a deflated CG in a similar way if you want to automatically extract the deflation vectors from the CG iteration.
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