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

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

Baumann, M.M. (TU Delft Numerical Analysis)
van Gijzen, M.B. (TU Delft Numerical Analysis)

2018

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.

Additive coarse grid correction
Global GMRES
Multi-shift GMRES
Nested multi-shift Krylov methods
Time-harmonic elastic wave equation

http://resolver.tudelft.nl/uuid:1322c96d-23e4-4a8a-ad6b-d21ddeccc226

https://doi.org/10.1016/j.jocs.2018.03.004

2021-11-02

1877-7503

Journal of Computational Science, 26, 285-293

Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.

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© 2018 M.M. Baumann, M.B. van Gijzen