Generalized volume-surface integral equation for modeling inhomogeneities within high contrast composite structures

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.     

Conformal Galerkin testing for VIE using parametric geometry

A moment method solution of a volume integral equation (VIE) using parametric geometry is presented. Typical Galerkin testing is shown not to be appropriate for curvilinear geometries, and a new testing scheme is proposed. By exploiting the orthogonality relationships between covariant and contravariant unitary vectors, testing functions in contravariant projection form and field expansion basis in covariant projection form were chosen.     

Doubly periodic volume?surface integral equation formulation for modelling metamaterials

A generalised volume-surface integral equation is extended by way of the periodic Green's function to model arbitrarily complex designs of metamaterials consisting of high-contrast inhomogeneous anisotropic material regions as well as metallic inclusions. The unique aspect of the formulation is the integration of boundary and volume integral equations to increase modelling efficiency and capability. Specifically, the boundary integral approach with equivalent surface currents is adopted over regions consisting of piecewise homogeneous materials as well as metallic perfect electric/magnetic conductor inclusions, whereas the volume integral equation is employed only in inhomogeneous and/or anisotropic material regions. Because the periodic Green's function only needs to be evaluated for the equivalent surface currents enclosing an inhomogeneous and/or anisotropic region, matrix fill time is much less as compared to using a volume formulation. Furthermore, the incorporation of curvilinear finite elements allows for greater geometrical modelling flexibility for arbitrarily shaped high-contrast regions found in typical designs of engineered metamaterials