Volume Integral Equation-Based Diakoptic Method for Electromagnetic Modeling

A novel diakoptic method based on volume integral equation (VIE) modeling of subsystems is proposed for 3-D electromagnetic analysis. The theoretical foundation of the method is the surface and volume equivalence principles, as it combines the VIE and surface integral equation (SIE) formulations, in conjunction with the method of moments (MoM). The method breaks the original structure into a number of nonoverlapping closed-region subsystems that contain inhomogeneous dielectric materials and an open-region subsystem. Each subsystem is analyzed completely independently applying the double higher order large-domain Galerkin generalized MoM-VIE-SIE (VSIE) or MoM-SIE solvers. The final solution is obtained from diakoptic matrices expressing linear relations between the electric and magnetic equivalent surface current coefficients on diakoptic surfaces. The proposed VSIE-diakoptic method is validated, evaluated, and discussed in several characteristic examples. The examples demonstrate that the diakoptic method substantially increases the efficiency of the conventional MoM-VIE approach. When compared with the pure MoM-VIE double higher order technique, the diakoptic approach enables very considerable accelerations and memory savings, while fully preserving the accuracy of the analysis.