A Calderón Multiplicative Preconditioner for Coupled Surface-Volume Electric Field Integral Equations

A well-conditioned coupled set of surface (S) and volume (V) electric field integral equations (S-EFIE and V-EFIE) for analyzing wave interactions with densely discretized composite structures is presented. Whereas the V-EFIE operator is well-posed even when applied to densely discretized volumes, a classically formulated S-EFIE operator is ill-posed when applied to densely discretized surfaces. This renders the discretized coupled S-EFIE and V-EFIE system ill-conditioned, and its iterative solution inefficient or even impossible. The proposed scheme regularizes the coupled set of S-EFIE and V-EFIE using a Calderón multiplicative preconditioner (CMP)-based technique. The resulting scheme enables the efficient analysis of electromagnetic interactions with composite structures containing fine/subwavelength geometric features. Numerical examples demonstrate the efficiency of the proposed scheme.

I. Introduction

Integral equation techniques for modeling electromagnetic interactions with composite structures comprised of perfect electrically conducting (PEC) surfaces and dielectric volumes have many practical applications. These techniques often seek the solution of a coupled set of surface (S) and volume (V) electric field integral equations (EFIEs) that enforce electric field boundary and consistency conditions on PEC surfaces and throughout dielectric volumes, respectively [1]–[3]. To permit the analysis of structures with sub-wavelength geometric features, e.g., microwave circuits and complex antenna feeds, these techniques should apply robustly to PEC surfaces and dielectric volumes approximated by locally or globally-dense spatial meshes.