A highly efficient and accurate numerical method for the electromagnetic scattering problem with rectangular cavities

TL;DR

This paper introduces a highly efficient numerical method for electromagnetic scattering problems involving multi-layered cavities, utilizing Fourier series expansion and transparent boundary conditions to reduce computational complexity and improve accuracy.

Contribution

The paper develops a novel numerical approach combining Fourier series and transparent boundary conditions, enabling efficient and accurate solutions for complex cavity scattering problems.

Findings

Method achieves high accuracy in numerical experiments

Reduces computational complexity by focusing on aperture Fourier coefficients

Handles weakly singular integrals effectively

Abstract

This paper presents a robust numerical solution to the electromagnetic scattering problem involving multiple multi-layered cavities in both transverse magnetic and electric polarizations. A transparent boundary condition is introduced at the open aperture of the cavity to transform the problem from an unbounded domain into that of bounded cavities. By employing Fourier series expansion of the solution, we reduce the original boundary value problem to a two-point boundary value problem, represented as an ordinary differential equation for the Fourier coefficients. The analytical derivation of the connection formula for the solution enables us to construct a small-scale system that includes solely the Fourier coefficients on the aperture, streamlining the solving process. Furthermore, we propose accurate numerical quadrature formulas designed to efficiently handle the weakly singular integrals that arise in the transparent boundary conditions. To demonstrate the effectiveness and versatility of our proposed method, a series of numerical experiments are conducted.