Internally Combined Volume-Surface Integral Equation for a 3-D Electromagnetic Scattering Analysis of High-Contrast Media

An internally combined volume surface integral equation (ICVSIE) for analyzing three-dimensional (3-D) electromagnetic scattering from heterogeneous high-contrast (HC) dielectric objects is proposed. Iteratively solved (generalized) volume integral equations [(g)VIEs] often converge slowly when applied to the analysis of electromagnetic interactions involving dielectric objects with permittivities much higher than those of the surrounding medium [HC breakdown] or discretized using mesh elements much smaller than the wavelength [low-frequency (LF) breakdown]. The proposed ICVSIE hybridizes a VIE and a surface integral equation (SIE) in a manner that eliminates both breakdown phenomena. Just as in previous hybrid VIE-SIE approaches, the ICVSIE invokes Huygens surface equivalence principle to transform the original problem into coupled equivalent exterior and interior scenarios. In the exterior scenario, surface currents radiate in the original surrounding medium; in the interior problem, surface and volume polarization currents radiate in a medium with permittivity closer to that of the object. By judiciously combining integral equations pertinent to both scenarios, the ICVSIE system is assembled. Numerical results show that the proposed ICVSIE is both HC and LF stable when applied to the analysis of 3-D scattering problems.