Asymptotic models for time-domain scattering by small particles of arbitrary shapes

TL;DR

This paper develops asymptotic models for time-domain wave scattering by small, arbitrarily shaped particles, providing both high-order and simplified approaches with error analysis and numerical validation.

Contribution

It introduces a novel asymptotic boundary integral model for small particle scattering, including simplified and Born approximation methods for computational efficiency.

Findings

High-order asymptotic model validated by numerical experiments

Simplified model reduces computational complexity

Error estimates support model accuracy

Abstract

In this work, we investigate time-dependent wave scattering by multiple small particles of arbitrary shape. To approximate the solution of the associated boundary-value problem, we derive an asymptotic model that is valid in the limit as the particle size tends to zero. Our method relies on a boundary integral formulation, semi-discretized in space using a Galerkin approach with appropriately chosen basis functions, s.t. convergence is achieved as the particle size vanishes rather than by increasing the number of basis functions. Since the computation of the Galerkin matrix involves double integration over particles, the method can become computationally demanding when the number of obstacles is large. To address this, we also derive a simplified model and consider the Born approximation to improve computational efficiency. For the high-order models, we provide an error analysis, supported and validated by numerical experiments.