Matt Landreman <[email protected]> writes: > On Jed's comment, the application I have in mind is indeed a > convection-dominated equation (a steady linear 3D convection-diffusion > equation with smoothly varying anisotropic coefficients and recirculating > convection). Gamg and hypre-boomerAMG have been working on it ok if I > discretize with low-order upwind differences in Pmat and use Amat=Pmat, but > I'd like higher order accuracy. Using gmres with a higher-order > discretization in Amat and low-order Pmat works ok, but the number of KSP > iterations required gets large as the diffusion gets small compared to > convection, even with -pc_type lu. So I'm working to see if geometric mg > with defect correction at each level can do better.
You asked about algebraic multigrid. A first order discretization has a ton of numerical diffusion so no matter how hard you try, you can't actually produce a large cell Peclet number. I.e., AMG working on the low-order operator has nothing to do with high Peclet number. With geometric multigrid, you typically rediscretize the coarse operators and defect correction makes sense.
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