Finite element-boundary element methods for electromagnetic scattering.

Abstract

Recent advances in computer speed and storage have led to an increasing interest in developing new methodologies to satisfy a need for accurate and efficient numerical simulation of complex open region electromagnetic scattering problems. In this thesis, several hybrid techniques which employ finite element and boundary element methods are presented. A finite element-boundary element method is presented for computing the scattering by cylindrical objects. The method uses artificial boundaries that can follow the contour of the scatterer so that the discretization region is minimized. More importantly, the method results in a highly sparse or uniformly banded matrix which can be efficiently solved using special algorithms. Results are presented to demonstrate the accuracy of the method as well as its capability and versatility. The method is then extended to treat the scattering by coated wedges and half-planes. In this case, the physical optics approximation is employed to approximate the surface fields away from the edge of the structure. Numerical results are presented to show the surface field and surface impedance behavior near the edge. A finite element-boundary element method is also developed to characterize the scattering and transmission properties of an inhomogeneously filled aperture in a thick conducting plane. Of particular interest in this formulation is the use of a fast Fourier transform to evaluate the boundary integrals and the use of a conjugate gradient method to solve the system of equations. As a result, the method is particularly efficient in dealing with large apertures. The use of isoparametric elements is subsequently presented for modeling arbitrarily shaped and curved geometries. This leads to an improved efficiency and accuracy not shared with traditional elements. Finally, formulations for several hybrid techniques which combine the finite element method with either a surface integral equation or an expansion of vector eigen-functions are presented and discussed for three-dimensional scattering problems.