Low-Frequency Stable Internally Combined Volume-Surface Integral Equation for High-Contrast Scatterers

Volume integral equations (VIEs) are commonly used to analyze scattering from inhomogeneous dielectric objects. Unfortunately, when VIEs are applied to high-contrast scatterers, their discretization results in ill-conditioned systems of equations. Oftentimes volume-surface integral equations (VSIEs) are used to eliminate this effect. However, when the scatterer's mesh has elements that are much smaller than the wavelength, VSIEs become ill-conditioned, too. This letter introduces a new set of internally combined VSIEs (ICVSIEs) that exhibit neither of these ill-conditioning phenomena. Just like in previous VSIE methods, surface currents are used to artificially increase the effective permittivity of the background medium in which volume polarization currents radiate. To remove ill-conditioning due to electrical size, coupling between the surface and volume is accounted for by judiciously adding contributions due to “exterior” and “interior” surface currents. Numerical data obtained by analyzing time-harmonic TE scattering from various 2-D layered cylinders suggests that discretization of the new ICVSIE yields matrices that are unaffected by the scatterer's maximum permittivity and electrical size.