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