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

TL;DR

This paper introduces enhanced two-level Schwarz preconditioners for Helmholtz problems using coarse spaces built with higher-order Bézier interpolation, demonstrating improved scalability and robustness with respect to wavenumber.

Contribution

It presents a novel coarse space construction method based on higher-order Bézier interpolation for Schwarz preconditioners, improving scalability and robustness for Helmholtz problems.

Findings

Numerical results show scalability with increasing wavenumber.

Preconditioners are robust when wavenumber times coarse mesh element size is low.

Enhanced preconditioners outperform traditional methods in tested scenarios.

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 B\'ezier 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.