An introduction to operator preconditioning for the fast iterative integral equation solution of time-harmonic scattering problems

Xavier Antoine (1, 2) , Marion Darbas (3)

1 EDP - Equations aux dérivées partielles
2 SPHINX - Systems with physical heterogeneities : inverse problems, numerical simulation, control and stabilization
3 LAMFA - Laboratoire Amiénois de Mathématique Fondamentale et Appliquée

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.

Domaines: Equations aux dérivées partielles [math.AP]; Analyse numérique [math.NA]

Xavier Antoine, Marion Darbas. An introduction to operator preconditioning for the fast iterative integral equation solution of time-harmonic scattering problems. Multiscale Science and Engineering, 2021, 3 (1), pp.1-35. ⟨10.1007/s42493-021-00057-6⟩. ⟨hal-02914922⟩