A fast integral equation solution technique for printed circuits in layered media

Abstract

A fast solution for the full electromagnetic simulation of printed circuits in layered media is presented. The method is based on a Galerkin solution of the mixed potential integral equation (MPIE) with high-order vector basis functions and arbitrary discretization. A fast iterative solution is performed via the quadrature sampled precorrected FFT (QSPCFFT) (Gedney, S.D. et al., 2003). The QSPCFFT is in the same class of techniques as the adaptive integral method (AIM) (Bleszynski, E. et al., 1996), the precorrected FFT (Phillips, J.R. and White, J.K., 1997), or the sparse matrix/canonical grid algorithm (Li, S.Q. et al., 2001). Near interactions are computed using the traditional integral equation formulation, and far interactions are computed via the FFT. The proposed technique has distinct advantages over previous methods in that it does not explicitly require the computation of moments or an expansion of the Green's function. It also has the advantage over fast solution methods such as the FMM (fast multipole method) (Ling, F. et al., 1999) in that the size of the near field block is a function of discretization rather than electrical dimensions. It is shown that the QSPCFFT method is highly accurate and efficient. The solution scales with a computational complexity of O(N log N) and memory as O(N).