Analysis and application of an overlapped FEM-BEM for wave propagation in unbounded and heterogeneous media

TL;DR

This paper presents a rigorous numerical analysis and practical implementation of an overlapped FEM-BEM coupling method for wave propagation in unbounded, heterogeneous media, enabling accurate far-field computations without shape restrictions.

Contribution

The authors develop and analyze a novel overlapped FEM-BEM framework for Helmholtz problems in complex media, including detailed numerical validation and applications to scattering configurations.

Findings

The FEM-BEM coupling accurately computes far-fields in heterogeneous media.

Numerical experiments demonstrate efficiency and robustness of the method.

Application to non-convex Janus particle configurations shows versatility.

Abstract

An overlapped continuous model framework, for the Helmholtz wave propagation problem in unbounded regions comprising bounded heterogeneous media, was recently introduced and analyzed by the authors ({\tt J. Comput. Phys., {\bf 403}, 109052, 2020}). The continuous Helmholtz system incorporates a radiation condition (RC) and our equivalent hybrid framework facilitates application of widely used finite element methods (FEM) and boundary element methods (BEM), and the resulting discrete systems retain the RC exactly. The FEM and BEM discretizations, respectively, applied to the designed interior heterogeneous and exterior homogeneous media Helmholtz systems include the FEM and BEM solutions matching in artificial interface domains, and allow for computations of the exact ansatz based far-fields. In this article we present rigorous numerical analysis of a discrete two-dimensional FEM-BEM overlapped coupling implementation of the algorithm. We also demonstrate the efficiency of our discrete FEM-BEM framework and analysis using numerical experiments, including applications to non-convex heterogeneous multiple particle Janus configurations. Simulations of the far-field induced differential scattering cross sections (DSCS) of heterogeneous configurations and orientation-averaged (OA) counterparts are important for several applications, including inverse wave problems. Our robust FEM-BEM framework facilities computations of such quantities of interest, without boundedness or homogeneity or shape restrictions on the wave propagation model.