Decoupled Potential Integral Equations for Electromagnetic Scattering from Dielectric Objects

TL;DR

This paper introduces a well-conditioned decoupled potential integral equation (DPIE) for electromagnetic scattering from dielectric objects, improving numerical stability and avoiding common computational issues.

Contribution

It presents a novel DPIE formulation for dielectric scattering, extending previous work and ensuring better conditioning and analytical properties.

Findings

DPIE is a second kind integral equation.

DPIE does not suffer from low frequency breakdown.

Results show improved conditioning and spectrum analysis.

Abstract

Recent work on developing novel integral equation formulations has involved using potentials as opposed to fields. This is a consequence of the additional flexibility offered by using potentials to develop well conditioned systems. Most of the work in this arena has wrestled with developing this formulation for perfectly conducting objects (Vico et al., 2014 and Liu et al., 2015), with recent effort made to addressing similar problems for dielectrics (Li et al., 2017). In this paper, we present well-conditioned decoupled potential integral equation (DPIE) formulated for electromagnetic scattering from homogeneous dielectric objects, a fully developed version of that presented in the conference communication (Li et al., 2017). The formulation is based on boundary conditions derived for decoupled boundary conditions on the scalar and vector potentials. The resulting DPIE is the second kind integral equation, and does not suffer from either low frequency or dense mesh breakdown. Analytical properties of the DPIE are studied. Results on the sphere analysis are provided to demonstrate the conditioning and spectrum of the resulting linear system.