A New Class of Uniformly Stable Time-Domain Foldy–Lax Models for Scattering by Small Particles. Acoustic Sound-Soft Scattering by Circles

Multiscale Modeling &Simulation, Volume 22, Issue 1, Page 1-38, March 2024.
Abstract. In this work we study time-domain sound-soft scattering by small circles. Our goal is to derive an asymptotic model for this problem that is 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. We prove the second-order convergence of the field error with respect to the particle size. Our findings are illustrated with numerical experiments.