Simple and efficient computation of electromagnetic fields in arbitrarily shaped inhomogeneous dielectric bodies using transpose-free QMR and FFT

A simple and efficient numerical method is presented for computing electromagnetic fields in three-dimensional (3-D) inhomogeneous-dielectric bodies. The method employs a two-stage discretization to convert an integro-differential equation into an implicit system of linear algebraic equations. This discrete system is then solved using a transpose-free quasi-minimal residual (TFQMR) algorithm, which avoids the calculation of the multiplication between the transpose of the system matrix and a vector. The simple multiplication between the system matrix and a vector required in the TFQMR algorithm is calculated efficiently using only six fast Fourier transforms (FFTs). Numerical results for strongly inhomogeneous and lossy spheres show that the method has a stable convergence behavior and excellent numerical performance.