Pierre Jolivet <[email protected]> writes: > Hello, > Given this block matrix: > A = [A11,A12,A13,A14; > A21,A22,A23,A24; > A31,A32,A33,A34; > A41,A42,A43,A44]; > It is trivial to precondition Ax = b with M^-1 = diag(A11^-1, A22^-1, > A33^-1, A44^-1); > My application requires a slightly fancier preconditionner which should > be M^-1 = diag(inv([A11,A12;A21,A22]),inv([A33,A34;A43,A44])); > I'm not sure what is the right tool for this. > I've stopped at a 4x4 block matrix, but at scale I have a matrix with > few thousands x few thousands blocks (still with the nested 2 x 2 block > structure).
Are all of these blocks distributed on your communicator or do they have some locality? PCFieldSplit is intended for problems where the blocks are all distributed and solving them sequentially is acceptable. The other limiting case for an additive preconditioner like you have above is block Jacobi (perhaps with multi-process subdomains or multiple subdomains per process; such decompositions are supported).
signature.asc
Description: PGP signature
