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.

本文关注的是大矩形矩形空腔中的三维电磁散射，该矩形空腔嵌入完美导电的无限接地平面中。通过引入透明边界条件，将散射问题公式化为有界腔中的边界值问题。基于电场的傅立叶展开，将麦克斯韦方程简化为傅立叶系数的一维常微分方程。开发了一种采用快速傅里叶变换和高斯消去的快速算法，以解决由此产生的线性系统，该线性系统填充有均质或分层介质。另外，设计了一种新颖的方案来快速而准确地评估奇异积分的傅立叶变换。