Multilevel fast multipole method solution of volume integral equations using parametric geometry modeling

Field computations for problems involving inhomogeneous materials have mostly been confined to either analytical approximations for canonical problem geometries or differential equation solvers, such as the finite element (FE) method. Integral equation formulations for inhomogeneous materials have not been exploited due to their high computational cost. However, recent developments in fast algorithms, such as the multilevel fast multipole method (MLFMM) have enabled direct method of moments (MoM) solutions of volumetric integral equation formulations. This paper outlines the MLFMM solution of a volume integral equation for scattering by arbitrarily shaped inhomogeneous dielectric structures. The approach uses three-dimensional conformal parametric subdomains to ensure fidelity of the geometrical representation. This low complexity computer code can be used in various areas of applied computational electromagnetics, ranging from microwave circuit simulations to remote sensing applications.