Modified Rayleigh Conjecture method for multidimensional obstacle scattering problems

TL;DR

This paper introduces a Modified Rayleigh Conjecture (MRC) method for solving multidimensional obstacle scattering problems, demonstrating its effectiveness and ease of implementation for complex 2D and 3D geometries.

Contribution

The paper develops and validates numerical algorithms based on the MRC for 2D and 3D obstacle scattering, including complex shapes like cubes and ellipsoids.

Findings

MRC provides accurate solutions for various obstacle shapes.

The method is easy to implement for complex geometries.

MRC is a viable alternative to existing scattering methods.

Abstract

The Rayleigh conjecture on the representation of the scattered field in the exterior of an obstacle $D$ is widely used in applications. However this conjecture is false for some obstacles. AGR introduced the Modified Rayleigh Conjecture (MRC), and in this paper we present successful numerical algorithms based on the MRC for various 2D and 3D obstacle scattering problems. The 3D obstacles include a cube and an ellipsoid. The MRC method is easy to implement for both simple and complex geometries. It is shown to be a viable alternative for other obstacle scattering methods.