Convergence and complexity study of GMRES variants for solving multi-frequency elastic wave propagation problems

Journal article (2018)

Authors

M.M. Baumann Numerical Analysis - EEMCS
M.B. van Gijzen Numerical Analysis - EEMCS
Research Group
Numerical Analysis (EEMCS) (TU Delft)
Copyright: © 2018 M.M. Baumann, M.B. van Gijzen
DOI
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https://doi.org/10.1016/j.jocs.2018.03.004
Time-harmonic elastic wave equation Additive coarse grid correction Global GMRES Multi-shift GMRES Nested multi-shift Krylov methods
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Published Date

2018

Language

English

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Faculty

Electrical Engineering, Mathematics and Computer Science

Department

Delft Institute of Applied Mathematics

Research Group

Numerical Analysis

Abstract

In this paper we present a comparison study of three different frameworks of iterative Krylov methods that we have recently developed for the simultaneous numerical solution of frequency-domain wave propagation problems when multiple wave frequencies are present. The three approaches have in common that they require the application of a single shift-and-invert preconditioner at a suitable seed frequency. In particular for three-dimensional problems, we present the efficient application of the elastic shift-and-invert preconditioner by means of an additive coarse grid correction. The focus of the present work lies, however, on the performance of the respective iterative method. We conclude with numerical examples that provide guidance concerning the suitability of the three methods.