On Fri, Nov 11, 2011 at 10:08, Mark F. Adams <mark.adams at columbia.edu>wrote:
> First, "my" matrices (actually XGC1 matrices from one of my projects and I > don't even know exactly what they do) put 1.0 on the diagonal for BCs and > god knows how the thing is scaled (1e13 apparently). But this does not > matter because the RHS and initial guess are 0.0 so the BCs have been > completely removed from the algebra, even if they are still in the data > structures. > So what happens when you use the same method with inhomogeneous Dirichlet conditions? This is especially bad if the interior is scaled by, say, 1e-13 instead of 1e+13, because the boundary conditions dominate the initial residual. > > As I recall the preconditioned residual was confusing because since these > are Laplacian matrices with a scale of 1e13, as you found, the residual > dropped like 10 orders of magnitude in the first iteration, which was > pretty confusing. > The preconditioned residual fixes the scaling. If you evaluate the initial unpreconditioned residual, then you see the confusing scaling. But preconditioning, even with just Jacobi, fixes the scaling. > > So I don't see these XGC1 problems as being arguments for preconditioned > residual, in fact they argue against it, right? > The preconditioned residual fixes the scaling, assuming it is no worse than Jacobi. -------------- next part -------------- An HTML attachment was scrubbed... URL: <http://lists.mcs.anl.gov/pipermail/petsc-dev/attachments/20111111/9b4a317a/attachment.html>
