Dear Timo and Martin, Thank you very much for the help and advice. I'll definitely take the time to read the references of Martin and look into what you are suggesting. Clearly, I need to exploit the structure of the matrix significantly more to be able to extract more performance out of the solver. Thank you very much your time:). Now it's back to reading! The complexity of these equations never ceases to amaze me. Take care Bruno
On Monday, December 7, 2020 at 9:27:09 a.m. UTC-5 Timo Heister wrote: > > If I understand correctly, you mean formulating the problem using a > BlockMatrix and a BlockVector, then preconditioning each matrix of the > block independently? > > Correct. You perform a block LU decomposition by hand and use that as > your preconditioner. Then approximate the blocks as best as you can. > The advantage is that you can exploit PDE specifics: > - lumping of mass matrices > - AMG/GMG for laplace-like operators > - ILU/Jacobi for mass matrix-like operators > - spectrally-equivalent matrices to approximate Schur complements > - and more > > We have many tutorial steps that teach this (but not precisely for > your problem). > > > I guess this would be best achieved using the linear operators within > deal.II right? > > Not necessarily. See step-55 and step-57 for example. The linear > operator framework helps, especially to define implicit operators > (step-20), but is not required. > > > What would be the added benefit of that? I would presume that since each > block have more "coherent units", this would at least to a better > conditioning of the final system, but is there anything else there? > > I doubt you can get optimal preconditioners (in the sense of cost > independent of h and other problem parameters) without exploiting > PDE-specifics. > > > -- > Timo Heister > http://www.math.clemson.edu/~heister/ > -- The deal.II project is located at http://www.dealii.org/ For mailing list/forum options, see https://groups.google.com/d/forum/dealii?hl=en --- You received this message because you are subscribed to the Google Groups "deal.II User Group" group. To unsubscribe from this group and stop receiving emails from it, send an email to dealii+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/dealii/f7fac411-ee55-4988-b42d-e4bf81c793b1n%40googlegroups.com.
