Augmented Electric-Field Integral Equation for Inhomogeneous Media

The augmented electric-field integral equation is extended for the analysis of inhomogeneous media at low frequencies. The internal surface integral equation for inhomogeneous region is derived from the vector potential ( ${{\mathbf A}}$ ) and the scalar potential ( ${{\mathbf \Phi }}$ ) equations, which are free of low-frequency breakdown. In the new equations, Green's functions of ${{\mathbf A}}$ and ${{\mathbf \Phi }}$ for inhomogeneous media are incorporated. Due to the absence of the analytic solutions, Green's functions for ${{\mathbf A}}$ and ${{\mathbf \Phi }}$ are solved numerically with the finite-element method and represented in matrix forms. Numerical examples are presented to demonstrate the validity of the proposed scheme in the study of inhomogeneous objects at low frequencies.