Coarse Spaces Based on Higher-Order Interpolation for Schwarz Preconditioners for Helmholtz Problems

2024/08/07 by Erik Sieburgh, Alexander Heinlein, Sieburgh, Erik +5
Computer Science · Engineering · Mathematics · #FOS: Mathematics #Matrix Theory and Algorithms #Numerical Analysis (math.NA) #Numerical methods in engineering #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.2408.03571

openalex publication_date 2024/08/07 · openalex created_date 2024/11/01 · openalex updated_date 2026/07/28

Abstract

The development of scalable and wavenumber-robust iterative solvers for Helmholtz problems is challenging but also relevant for various application fields. In this work, two-level Schwarz domain decomposition preconditioners are enhanced by coarse space constructed using higher-order Bézier interpolation. The numerical results indicate numerical scalability and robustness with respect the wavenumber, as long as the wavenumber times the element size of the coarse mesh is sufficiently low.

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