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Lawrence Mitchell <[email protected]> writes: >> On 28 Jul 2014, at 23:27, Jed Brown <[email protected]> wrote: >> >> Lawrence Mitchell <[email protected]> writes: >>> Bog-standard P1 on a pretty much regularly meshed square domain (i.e. no >>> reentrant corners or bad elements). >> >> What interpolation is being used? The finite-element embedding should >> work well. > > Coarse to fine is just identity. Fine to coarse a lumped L2 projection. By "identity", do you mean in terms of continuous functions (the finite-element embedding) or something on C-points? Fine-to-coarse is generally taken to be the transpose of the natural prolongation, which is integration. >>>> Is there something special about the decomposition with 2 subdomains? >>> >>> It doesn't look like it, the two subdomains are about the same size. >>> >>>> Are the Chebyshev estimates far from converging? >>> >>> So for the two-level problem, if I compute the extremal eigenvalues of the >>> preconditioned operator being used as a smoother I get (approximately): >>> >>> 1 process: >>> 0.019, 1.0 >>> >>> 2 processes: >>> 0.016, 1.4 >>> >>> 3 processes: >>> 0.016, 1.36 >>> >>> The eigenvalue estimates (from ksp_view) are: >>> >>> 1 process: >>> 0.09, 1.01 >>> >>> 2 processes: >>> 0.09, 1.01 >>> >>> 3 processes: >>> 0.13, 1.47 >>> >>> >>> When I bump to more levels, the estimates are only bad on two processes on >>> the finest grid. >> >> Can you add >> >> -ksp_chebyshev_estimate_eigenvalues_random > > This doesn't help. > >> I wonder if you have a degenerate right hand side that is not exciting >> the largest eigenvalues on two processes. Anyway, try switching from >> GMRES to CG for computing the eigenvalue estimates and also using more >> iterations. > > Switching from GMRES to CG has no real effect. However bumping the number of > iterations used for eigenvalue estimation from 10 to 20 on the finest grid > gives me much better convergence on 2 processes. With fewer iterations the > largest eigenvalue estimate gets stick around 1, once I jump to 20 it goes up > to around 1.33, more in line with the exact 1.39. > > So this looks to be the original culprit. Thanks. It's odd for the estimates to require that many iterations unless the RHS is somehow degenerate. I was hoping that a random right hand side would excite the higher mode sooner.
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