A numerical method for scattering problems with unbounded interfaces

TL;DR

This paper presents a new numerical approach for solving scattering problems in unbounded domains by decomposing the domain into simpler subdomains with known Green's functions and reformulating the problem as boundary integral equations.

Contribution

The paper introduces the concept of decomposable scattering problems and a practical numerical method based on boundary integral reformulation and complexification techniques.

Findings

Efficient reformulation of scattering problems as boundary integral equations.

Use of domain Green's functions for tractable subdomains.

High-accuracy solutions achievable with the proposed method.

Abstract

We introduce a new class of computationally tractable scattering problems in unbounded domains, which we call decomposable problems. In these decomposable problems, the computational domain can be split into a finite collection of subdomains in which the scatterer has a "simple" structure. A subdomain is simple if the domain Green's function for this subdomain is either available analytically or can be computed numerically with arbitrary accuracy by a tractable method. These domain Green's functions are then used to reformulate the scattering problem as a system of boundary integral equations on the union of the subdomain boundaries. This reformulation gives a practical numerical method, as the resulting integral equations can then be solved, to any desired degree of accuracy, by using coordinate complexification over a finite interval, and standard discretization techniques.