This Is AuburnElectronic Theses and Dissertations

Paired Pulse Basis Functions and Triangular Patch Modeling for the Method of Moments Calculation of Electromagnetic Scattering from Three-Dimensional, Arbitrarily-Shaped Bodies




Mackenzie, Anne

Type of Degree



Electrical and Computer Engineering


Due to an increasing emphasis on fabrication with composite materials, it is important to be able to model accurately the electromagnetic properties of composite structures. In this work, we demonstrate a new pair of orthogonal pulse vector basis functions for the calculation of electromagnetic scattering from arbitrarily-shaped material bodies. These subdomain basis functions are intended for use with triangular surface patch modeling applied to a method of moments (MoM) solution. For modeling the behavior of dielectric materials, several authors have used the same set of basis functions to represent equivalent electric and magnetic surface currents. This practice can result in zero-valued or very small diagonal terms in the moment matrix and an unstable numerical solution. To provide a more stable solution, we have developed orthogonally placed, pulse basis vectors: one for the electric surface current and one for the magnetic surface current. The basis function for the electric surface current is placed perpendicular to each patch edge, while the basis function for the magnetic surface current is placed parallel to each patch edge. This combination, together with appropriate testing functions, ensures strongly diagonal moment matrices. The basis functions are suitable for implementing solutions using the electric field integral equation (EFIE) or the magnetic field integral equation (HFIE.) To obtain unique solutions at all frequencies, including characteristic frequencies for closed bodies, the EFIE and HFIE may be expanded with paired pulse vector basis functions and then arithmetically combined by any of the combined-field methods such as combined field integral equation (CFIE), Poggio-Miller-Chang-Harrington-Wu-Tsai (PMCHWT), or M¨uller formulations. In this work, we describe the numerical implementations of EFIE and HFIE solutions and show example results for three-dimensional, canonical figures. Those scattering results obtained by using pulse vector basis functions are compared to results obtained from an exact method or a more accurate numerical method specialized for a particular type of geometry, such as a body of revolution. In successive chapters, the numerical procedures and solutions are shown for perfect conductors (PEC’s), dielectric bodies, and PEC/dielectric composites. The composite scatterers may contain multiple dielectric and PEC parts, either touching or non-touching.