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arXiv · 2403.18970

Two-level overlapping Schwarz preconditioners with universal coarse spaces for $2m$th-order elliptic problems

Jongho Park
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Abstract

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.

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Jongho Park. 2024-03-27. Two-level overlapping Schwarz preconditioners with universal coarse spaces for $2m$th-order elliptic problems. https://doi.org/10.1137/24m1650247

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