Inexact Subdomain Solves Using Deflated GMRES for Helmholtz Problems

Conference paper (2022)

Authors

N. Bootland University of Strathclyde
V.N.S.R. Dwarka Numerical Analysis - EEMCS
P. Jolivet ENSIACET
Victorita Dolean University of Strathclyde, Université Côte d'Azur
Cornelis Vuik Delft Institute of Applied Mathematics
Research Group
Numerical Analysis (EEMCS) (TU Delft)
Copyright: © 2022 N. Bootland, V.N.S.R. Dwarka, P. Jolivet, V. Dolean, Cornelis Vuik
DOI: https://doi.org/10.1007/978-3-030-95025-5_11
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Published Date

2022

Language

English

Faculty

Electrical Engineering, Mathematics and Computer Science

Department

Delft Institute of Applied Mathematics

Research Group

Numerical Analysis

Abstract

In recent years, domain decomposition based preconditioners have become popular tools to solve the Helmholtz equation. Notorious for causing a variety of convergence issues, the Helmholtz equation remains a challenging PDE to solve numerically. Even for simple model problems, the resulting linear system after discretisation becomes indefinite and tailored iterative solvers are required to obtain the numerical solution efficiently. At the same time, the mesh must be kept fine enough in order to prevent numerical dispersion ‘polluting’ the solution [4]. This leads to very large linear systems, further amplifying the need to develop economical solver methodologies.