Numerical computation of electromagnetic scattering from large cavities

Abstract

Numerical computation of electromagnetic scattering from large cavities has attracted much attention recently because of the significant industrial and military applications, particularly in radar cross section (RCS) prediction. Mathematical analysis of cavity models has been well conducted by several approaches. In this thesis, we develop efficiently numerical methods for solving the electromagnetic scattering from large two dimensional (2-D) cavities, which is governed by the Helmholtz equation on an unbounded domain subject to the Sommerfeld radiation condition at infinity and standard boundary conditions on the ground plane and the walls of the cavity. For non-overfilled cavity models, the classical transparent boundary condition is proposed on the aperture of the cavity to reduce the unbounded domain problem to the bounded one. A hyper-singular integral operator and a weakly singular integral operator are involved in the transverse magnetic (TM) and the transverse electric (TE) polarizations, respectively. Toeplitz-type approximations are used for the numerical computations. For the linear systems derived from the finite difference discretization of the cavity model, we design several preconditioning techniques: layered medium preconditioning, sine and cosine transform based preconditioning. The base of these preconditioning techniques is the fast Fourier transform. Numerical results of open cavity and partly covered cavity models demonstrate the efficiency of these preconditioning techniques. We also prove the existence and uniqueness of the finite difference solution of the partly covered cavity model with layered media. For overfilled cavity models, especially for elongated cavity and multiple cavity models, a transparent boundary condition is proposed on a semi-ellipse using Mathieu functions. The 2-D scattering problem is approximated in terms of the elliptic coordinate system with Mathieu functions in the exterior domain, and a finite element method in the interior domain. In addition, for a rectangular cavity with a homogeneous medium, another transparent boundary condition is introduced on the aperture of the cavity, which produces a smaller computational domain. The existence and uniqueness of the solutions of the variational formulations for the TM and the TE polarizations are established. Numerical experiments show the efficiency and accuracy of the new boundary conditions.

Date of Award	2 Oct 2009
Original language	English
Awarding Institution	City University of Hong Kong
Supervisor	Weiwei SUN (Supervisor)