[petsc-users] Multigrid with defect correction

[Jed Brown]

Matt Landreman <matt.landreman at gmail.com> 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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