A generalized precorrected-FFT method for electromagnetic analysis

Abstract

Boundary Element Methods (BEM) can be ideal approaches for simulating the behavior of physical systems in which the volumes have homogeneous properties. These, especially the so-called "fast" or "accelerated" BEM approaches often have significant computational advantages over other well-known methods which solve partial differential equations on a volume domain. However, the implementation of techniques used to accelerate BEM approaches often comes at a loss of some generality, reducing their applicability to many problems and preventing engineers and researchers from easily building on a common, popular base of code. In this thesis we create a BEM solver which uses the Pre-Corrected FFT technique for accelerating computation, and uses a novel approach which allows users to provide arbitrary basis functions. We demonstrate its utility for both electrostatic and full-wave electromagnetic problems in volumes with homogeneous isotropic permittivity, bounded by arbitrarily complex surface geometries. The code is shown to have performance characteristics similar to the best known approaches for these problems. It also provides an increased level of generality, and is designed in such a way that should allow it to easily be extended by other researchers.