Shiva Rudraraju <[email protected]> writes: >>I did unstructured hexes. You still haven't said what you'll use for >>relaxation. > High-order discretizations tend to have poor h-ellipticity, so they either > need heavy smoothers or a correction based on a discretization with better > h-ellipticity. > Quite frankly, I was not aware of the poor h-ellipticity of higher order > elements and I was assuming I would use the regular GS/GMRES/etc for > relaxation. I looked up h-ellipticity of higher order elements and now this > adds to my worries :(. I may be asking for too much here.... but what do > you mean by heavy smoothers? or correction based on a discretization?.
You can use one discretization for evaluating residuals, but then use an embedded low-order discretization to apply the correction. See "defect correction" in Achi's multigrid guide or in Trottenberg. The paper I mentioned earlier was doing something simpler and less intrusive: assemble the embedded low-order operator and feed it to algebraic multigrid, but evaluate residuals matrix-free using the high-order discretization. But if you have a reasonable geometric hierarchy, the defect correction schemes are better.
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