A new class of uniformly stable time-domain Foldy-Lax models for scattering by small particles. Acoustic sound-soft scattering by circles

Maryna Kachanovska (1)

1 POEMS - Propagation des Ondes : Étude Mathématique et Simulation

In this work we study time-domain sound-soft scattering by small particles. Our goal is to derive an asymptotic model for this problem valid when the size of the particles tends to zero. We present a systematic approach to constructing such models, based on a well-chosen Galerkin discretization of a boundary integral equation. The convergence of the method is achieved by decreasing the asymptotic parameter rather than increasing the number of basis functions. For the case of circular obstacles, we prove the second-order convergence of the field error with respect to the particle size. Our findings are illustrated with numerical experiments.

Mots clés: time-domain boundary integral equations; Wave equation; asymptotic model

Domaines: Physique mathématique [math-ph]; Analyse numérique [math.NA]

Maryna Kachanovska. A new class of uniformly stable time-domain Foldy-Lax models for scattering by small particles. Acoustic sound-soft scattering by circles. 2022. ⟨hal-03664569v1⟩