Discretization in Multilayered Media with High Contrasts: Is It All About the Boundaries?

TL;DR

This paper investigates the numerical challenges of wave propagation in multilayered media with high contrasts, proposing an adaptive boundary integral method that focuses on the background medium for efficient and accurate discretization.

Contribution

It introduces an adaptive boundary integral approach that emphasizes the background medium's wavenumber, improving efficiency and accuracy in multilayered media with high contrasts.

Findings

Standard meshing strategies are inefficient for multilayered media.

The background medium's wavenumber dominates the discretization decision.

The proposed adaptive method achieves uniform accuracy and scalability.

Abstract

Wave propagation in multilayered media with high material contrasts poses significant numerical challenges, as large variations in wavenumbers lead to strong reflections and complex transmission of the incoming wave field. To address these difficulties, we employ a boundary integral formulation thereby avoiding volumetric discretization. In this framework, the accuracy of the numerical solution depends strongly on how the material interfaces are discretized. In this work, we demonstrate that standard meshing strategies based on resolving the maximum wavenumber across the domain become computationally inefficient in multilayered configurations, where high wavenumbers are confined to localized subdomains. Through a systematic study of multilayer transmission problems, we show that no simple discretization rule based on the maximum wavenumber or material contrasts emerges. Instead, the wavenumber of the background (exterior) medium plays a dominant role in determining the optimal boundary resolution. Building on these insights, we propose an adaptive approach that achieves uniform accuracy and efficient computation across multiple layers. Numerical experiments for a range of multilayer configurations demonstrate the scalability and robustness of the proposed approach.