Integral Equations and Iterative Schemes for Acoustic Scattering Problems

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

1 SPHINX - Systems with physical heterogeneities : inverse problems, numerical simulation, control and stabilization
2 IECL - Institut Élie Cartan de Lorraine
3 LAMFA - Laboratoire Amiénois de Mathématique Fondamentale et Appliquée - UMR CNRS 7352

The aim of this chapter is to provide an introduction to the iterative Krylov solution of integral equations for time-harmonic acoustic scattering. From the point of view of computational methods, considering large frequencies in acoustics is challenging since it leads to solving highly indefinite large scale complex linear systems which generally implies a convergence breakdown of iterative methods. Most specifically, we develop the problematic and explain some partial solutions through analytical preconditioning for high frequency scattering and the introduction of new combined field integral equations.

Mots clés: preconditioners; GMRES; Krylov solver; acoustic scattering; high-frequency; integral equation; well-conditioned integral equation

Domaines: Analyse numérique [math.NA]

Xavier Antoine, Marion Darbas. Integral Equations and Iterative Schemes for Acoustic Scattering Problems. F. Magoulès. Numerical Methods for Acoustics Problems, Saxe-Coburg Editors, 2016, 978-1-874672-46-3. ⟨hal-00591456⟩