Local Solvers for High-Order Patch Smoothers via p-Multigrid

Fuente: arXiv
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Main Author: Wichrowski, Michał
Format: Preprint
Published: 2025
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author Wichrowski, Michał
author_facet Wichrowski, Michał
contents I propose a vertex patch smoother where local problems are solved inexactly by a nested, matrix-free p-multigrid, creating a multigrid-within-multigrid framework. A single iteration of the local solver can be evaluated with $\mathcal{O}(p^{d+1})$ operations, and the approach is applicable to non-separable problems on unstructured meshes. Numerical experiments demonstrate limited sensitivity to geometric distortion and high-contrast coefficients. When used in a global geometric multigrid solver, the method achieves robustness with respect to both polynomial degree $p$ and mesh refinement, even on heavily distorted meshes.
format Preprint
id arxiv_https___arxiv_org_abs_2510_17785
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Local Solvers for High-Order Patch Smoothers via p-Multigrid
Wichrowski, Michał
Numerical Analysis
65N30, 65N55, 65F08, 65Y20
I propose a vertex patch smoother where local problems are solved inexactly by a nested, matrix-free p-multigrid, creating a multigrid-within-multigrid framework. A single iteration of the local solver can be evaluated with $\mathcal{O}(p^{d+1})$ operations, and the approach is applicable to non-separable problems on unstructured meshes. Numerical experiments demonstrate limited sensitivity to geometric distortion and high-contrast coefficients. When used in a global geometric multigrid solver, the method achieves robustness with respect to both polynomial degree $p$ and mesh refinement, even on heavily distorted meshes.
title Local Solvers for High-Order Patch Smoothers via p-Multigrid
topic Numerical Analysis
65N30, 65N55, 65F08, 65Y20
url https://arxiv.org/abs/2510.17785