Analysis and applications of multi-dimensional cauchy integral equation based on clifford number to scattering and radiation of electromagnetic fields

Abstract

Integral equation methods in computational electromagnetics have been particularly attractive for researchers who need to analyse the performance of antennas in unbounded regions. These methods are formulated either from the electric field integral equation (EFIE) or from the magnetic field integral equation (MFIE). However spurious solutions can appear at some frequencies, even when the differentiation of the singular function in the kernel under the integral is approximated carefully. The problem is often avoided by using some combination of EFIE and MFIE, that is to say a combined field integral equation of CFIE. It is the purpose of this thesis to provide a particular combination of EFIE and MFIE which solves the same problem but in a different way. A new method is presented for calculating the solution of Maxwell’s equations based on the Cauchy integral and formulated in the guise of Clifford algebra. Electric and magnetic fields are embedded together as a single entity in a single Clifford number. The formulation has a geometric interpretation leading to an iterative method of solution which is easily proven as convergent and valid for both perfectly reflective and perfectly transmissive objects. The method avoids any explicit representation of current density vector on the surface of perfect electric conductors. The numerical results prove that the method can be employed to describe the behavior of scattered and radiated fields in unbounded regions of three dimensional space