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I'm searching for robust smoothers for geometric multigrids.

By robust I mean:

  • Effective for high order approximations (say spectral element, spectral Discontinuous Galerkin),
  • Parallel (suitable for co-processors),
  • Effective for heterogeneity and anisotropy problems.

From what I can gather, Schwarz type smoothers may be promising (Fischer et al); and block/line/ plane, and ILU smoothers are also recommended (Trottenberg et al).

Are there any other state-of-the-art smoothers I should consider?

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  • $\begingroup$ Are these for elliptic problems? $\endgroup$ – Jesse Chan Apr 27 '16 at 19:22
  • $\begingroup$ Ideally, elliptic, parabolic, or hyperbolic. I'm not necessarily looking for a "one size fits all"; i.e. if there is a smoother that is intended only for elliptic problems, this is alright. $\endgroup$ – user331493 Apr 27 '16 at 19:37
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Polynomial smoothers as described in M. Adams, M. Brezina, J. Hu, and R. Tuminaro, "Parallel multigrid smoothing: polynomial versus Gauss-Seidel", J. Comp. Physics, vol. 188, pp. 593-610 (2003).

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    $\begingroup$ It would be helpful if a summary of their results were included in your answer. $\endgroup$ – Paul Jan 22 '18 at 5:18

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