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.