Two-level overlapping Schwarz preconditioners with universal coarse spaces for $2m$th-order elliptic problems
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866908636808216576 |
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| author | Park, Jongho |
| author_facet | Park, Jongho |
| contents | We propose a novel universal construction of two-level overlapping Schwarz preconditioners for $2m$th-order elliptic boundary value problems, where $m$ is a positive integer. The word "universal" here signifies that the coarse space construction can be applied to any finite element discretization for any $m$ that satisfies some common assumptions. We present numerical results for conforming, nonconforming, and discontinuous Galerkin-type finite element discretizations for high-order problems to demonstrate the scalability of the proposed two-level overlapping Schwarz preconditioners. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_18970 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Two-level overlapping Schwarz preconditioners with universal coarse spaces for $2m$th-order elliptic problems Park, Jongho Numerical Analysis 65N55, 65F08, 65N30 We propose a novel universal construction of two-level overlapping Schwarz preconditioners for $2m$th-order elliptic boundary value problems, where $m$ is a positive integer. The word "universal" here signifies that the coarse space construction can be applied to any finite element discretization for any $m$ that satisfies some common assumptions. We present numerical results for conforming, nonconforming, and discontinuous Galerkin-type finite element discretizations for high-order problems to demonstrate the scalability of the proposed two-level overlapping Schwarz preconditioners. |
| title | Two-level overlapping Schwarz preconditioners with universal coarse spaces for $2m$th-order elliptic problems |
| topic | Numerical Analysis 65N55, 65F08, 65N30 |
| url | https://arxiv.org/abs/2403.18970 |