A multi-resolution study of the moment method solution to integral equations arising in electromagnetic problems

Abstract

Wavelet multi-resolution analyses have been employed in the numerical solution of many electromagnetic problems recently as they have the potential to sparsify dense complex impedance matrices. In this thesis, the use of wavelets in the method of moments solution to integral equations arising in two typical electromagnetic problems is considered. Firstly, the arbitrarily-shaped patch antenna with resistive wall boundary, formulated as a boundary element method problem is studied. The unknown response is expressed as a twofold summation of shifted and dilated forms of a properly chosen mother wavelet. The efficient computation of the matrix elements involving integrals of the wavelet bases, in a direct wavelet expansion multi-resolution study, is investigated. The impact of matrix sparsification on solution accuracy is investigated with a numerical example. In the second problem, three-dimensional electromagnetic scattering from a large flat conducting plate is studied. A modified wavelet-like transform is presented to sparsify the resulting complex dense impedance matrix resulting from an EFIE formulation with triangular rooftop vector basis functions. The advantages of this modified method are illustrated with a numerical example.