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An Introduction to Operator Preconditioning for the Fast Iterative Integral Equation Solution of Time-Harmonic Scattering Problems

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Abstract

The aim of this paper is to provide an introduction to the improved iterative Krylov solution of boundary integral equations for time-harmonic scattering problems arising in acoustics, electromagnetism and elasticity. From the point of view of computational methods, considering large frequencies is a challenging issue in engineering since it leads to solving highly indefinite large scale complex linear systems which generally implies a convergence breakdown of iterative methods. More specifically, we explain the problematic and some partial solutions through analytical preconditioning for high-frequency acoustic scattering problems and the introduction of new combined field integral equations. We complete the paper with some recent extensions to the case of electromagnetic and elastic waves equations.

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Authors and Affiliations

  1. Université de Lorraine, CNRS, Inria, IECL, 54000, Nancy, France

    Xavier Antoine

  2. LAGA UMR CNRS 7539, Université Sorbonne Paris Nord, 99 avenue Jean-Baptiste Clément, 93430, Villetaneuse, France

    Marion Darbas

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  1. Xavier Antoine
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  2. Marion Darbas
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Correspondence to Xavier Antoine.

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Antoine, X., Darbas, M. An Introduction to Operator Preconditioning for the Fast Iterative Integral Equation Solution of Time-Harmonic Scattering Problems. Multiscale Sci. Eng. 3, 1–35 (2021). https://doi.org/10.1007/s42493-021-00057-6

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  • DOI: https://doi.org/10.1007/s42493-021-00057-6

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