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

Abstract

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. Index Terms-Preconditioner, regularized volume integral equations (VIE), strongly-inhomogenous scatterers.

Mutual Impedance Computation of a Waveguide Slot-fed Arbitrary Patch Using Combined Conventional Moment Method and Equivalent Electric and Magnetic Dipole Method

“…In previous research [16], a comparison was performed between the results obtained by surface and volume integral equations in analyzing dielectric resonators. Combined surface-volume integral equations are employed to take advantage of inhomogeneous dielectrics analysis via volume integrals and reduce the computations of surface integrals [17][18][19][20]. In this paper, we have also formulated the combined surfacevolume integral equations.…”

Diseño de lentes metálicas usando la teoría de modos característicos.

“…Como siguiente paso, es conveniente formular el problema en términos de un equivalente, para que pueda ser más fácil de resolver el problema en la región de interés [132]. Se puede usar el principio de equivalencia de superficie (SEP) [133] o de volumen (VEP) [134].…”