TITLE:
Analytical Stability and Spectral Properties of the SVS-Based EFIE Solver for Electromagnetic Scattering Analysis
AUTHORS:
Osman Goni
KEYWORDS:
Electric Field Integral Equations, Single-Source, Surface-Volume-Surface, Volume Equivalence Principle, Method of Moments (MoM)
JOURNAL NAME:
Journal of Electromagnetic Analysis and Applications,
Vol.18 No.8,
August
31,
2026
ABSTRACT: This paper presents a Surface-Volume-Surface (SVS) EFIE formulation that integrates surface and volume integral representations to improve the accuracy and stability of electromagnetic field computation in composite structures. The exact solution of the Surface-Volume-Surface Electric Field Integral Equation (SVS-EFIE) is presented for both electric current (J-type and magnetic current based or M-type) formulations for the problem of radiation and scattering in the vicinity of homogeneous dielectric sphere. The SVS framework enhances field continuity across interfaces and reduces numerical errors associated with conventional EFIE implementations, particularly in near-field and multi-region scenarios. The formulation is implemented using the Method of Moments (MoM) with appropriate basis and testing functions to ensure numerical stability and convergence. It also reveals the spectral properties of its individual operators. The MoM impedance matrix features bounded condition number with increasing order of discretization, similar with analogous exact MoM solution of the surface EFIE on Perfectly Electrically Conducting (PEC) sphere. It also shows that SVS-EFIE-J formulation tends to infinity at low frequency and suffers from low-frequency breakdown issue, likewise regular EFIE. However, with SVS-EFIE-M, the formulation is stable at low frequency. Also, this work suggests that with SVS-EFIE-M, the spectral behavior is almost constant after a certain range of the discretization order.