Low-frequency stable internally combined volume-surface integral equation for 3D high-contrast scatterers

Volume-surface integral equations (VSIEs) are often used to analyze electromagnetic scattering by piecewise homogeneous dielectric objects (Usner et al., IEEE Trans. Antennas Propagat., vol. 54, pp. 68–75, 2006). Unfortunately, when these objects include high-contrast (HC) regions, viz. regions with permittivities that are much higher than those of their surrounding media, discretization of many VSIEs results in ill-conditioned systems of equations. In addition, VSIEs invariably suffer from low-frequency (LF) breakdown: when the mesh that discretizes the scatterer contains elements with dimensions that are much smaller than the wavelength, their discretization results in ill-conditioned systems of equations. Both HC and LF breakdown phenomena severely limit the usefulness of VSIEs in the analysis of bio-electromagnetic and geophysical applications. Previously, we developed a novel internally combined volume-surface integral equation (ICVSIE) and showed that it is immune from HC and LF breakdown when used to analyze TE scattering from various 2D inhomogeneous cylinders (Gomez et al., USNC/URSI Nat. Radio Sci. Meeting, 2013).