A fast algorithm for the electromagnetic scattering from a large rectangular cavity in three dimensions

TL;DR

This paper introduces a fast computational algorithm for simulating three-dimensional electromagnetic scattering from large rectangular cavities, utilizing Fourier transforms and efficient linear system solutions.

Contribution

It presents a novel, efficient algorithm combining Fourier methods and Gaussian elimination to solve scattering problems in large cavities with improved speed and accuracy.

Findings

The algorithm significantly reduces computation time for large cavities.

It accurately evaluates Fourier transforms of singular integrals.

Numerical results demonstrate superior performance over existing methods.

Abstract

The paper is concerned with the three-dimensional electromagnetic scattering from a large open rectangular cavity that is embedded in a perfectly electrically conducting infinite ground plane. By introducing a transparent boundary condition, the scattering problem is formulated into a boundary value problem in the bounded cavity. Based on the Fourier expansions of the electric field, the Maxwell equation is reduced to one-dimensional ordinary differential equations for the Fourier coefficients. A fast algorithm, employing the fast Fourier transform and the Gaussian elimination, is developed to solve the resulting linear system for the cavity which is filled with either a homogeneous or a layered medium. In addition, a novel scheme is designed to evaluate rapidly and accurately the Fourier transform of singular integrals. Numerical experiments are presented for large cavities to demonstrate the superior performance of the proposed method.