On Tue, 26 Feb 2008, Zbigniew Romanowski wrote: > I am particularly interested in positive definite operators > \nabla^2 + U(x) > corresponding to reals eigenvalues. Do the bug appear also for this type > of equation?
Not to my knowledge. I haven't been able to replicate any bug without --enable-complex turned on. But the fact that we've seen any bug at all suggests that some of the eigensolver code isn't as well-tested as it should be. > As far as I know, for efficient adaptive procedure the estimation of the > eigenvalue error is crucial. Could you please provide the documentation > about the eigenvalue error estimators implemented in libMesh for > ordinary and generalized eigenvalue problem? This would be very helpful. There are none that apply to general problems, I'm afraid. One reason is that if you want a rigorous upper bound on your error, you generally need cell residuals, and libMesh only has access to the weak form of the users' PDEs, not the strong form. A second reason is that most of the primary developers have been using adaptivity based on error indicators that are simplified for speed and ease of implementation (e.g. using the jump indicators even on problems for which they are not proportional to a rigorous bound). This is usually sufficient for directing adaptive refinement/coarsening, but it's not enough to prove error bounds on your results. In general (and especially for nonlinear PDEs), proven error bounds depend enough on the particular boundary value problem you're trying to solve that we can't provide a "one size fits all" solution. It looks like you're operating on a simple enough problem (second order, linear, unit coefficient on the linear operator) that you might be able to start with our Kelly jump indicator, add a hand-coded residual corresponding to the U(x) term, and get a real upper bound. But that's just off the top of my head. Even if it works you might get a uselessly loose upper bound. There should be lots of cancellation if it's just the eigenvalue error you're looking for, not the eigenfunction error, and I don't know enough about eigenproblem error analysis to know how that should be handled. --- Roy ------------------------------------------------------------------------- This SF.net email is sponsored by: Microsoft Defy all challenges. Microsoft(R) Visual Studio 2008. http://clk.atdmt.com/MRT/go/vse0120000070mrt/direct/01/ _______________________________________________ Libmesh-users mailing list [email protected] https://lists.sourceforge.net/lists/listinfo/libmesh-users
