On Fourier analysis of polynomial multigrid for arbitrary multi-stage cycles

Will Trojak; Freddie D. Witherden

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arXiv · 2008.05463

On Fourier analysis of polynomial multigrid for arbitrary multi-stage cycles

Will Trojak·Freddie D. Witherden

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Abstract

The Fourier analysis of the \emph{p}-multigrid acceleration technique is considered for a dual-time scheme applied to the advection-diffusion equation with various cycle configurations. It is found that improved convergence can be achieved through \emph{V}-cycle asymmetry where additional prolongation smoothing is applied. Experiments conducted on the artificial compressibility formulation of the Navier--Stokes equations found that these analytic findings could be observed numerically in the pressure residual, whereas velocity terms---which are more hyperbolic in character---benefited primarily from increased pseudo-time steps.

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Will Trojak, Freddie D. Witherden. 2020-08-12. On Fourier analysis of polynomial multigrid for arbitrary multi-stage cycles. https://arxiv.org/abs/2008.05463

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