Generalized Volume-Surface Integral Equation for Modeling Inhomogeneities Within High Contrast Composite Structures

Abstract

Numerical solutions of volume integral equations with high contrast inhomogeneous materials require extremely fine discretization rates making their utility very limited. Given the application of such materials for antennas and metamaterials, it is extremely important to explore computationally efficient modeling methods. In this paper, we propose a novel volume integral equation technique where the domain is divided into different material regions each represented by a corresponding uniform background medium coupled with a variation, together representing the overall inhomogeneity. This perturbational approach enables us to use different Green's functions for each material region. Hence, the resulting volume-surface integral equation alleviates the necessity for higher discretizations within the higher contrast regions. With the incorporation of a junction resolution algorithm for the surface integral equations defined on domain boundaries, we show that the proposed volume-surface integral equation formulation can be generalized to model arbitrary composite structures incorporating conducting bodies as well as highly inhomogeneous material regions.