Local Solvers for High-Order Patch Smoothers via p-Multigrid
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866914104489279488 |
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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 |