Non-singular field-only surface integral equations for electromagnetic scattering

TL;DR

This paper introduces a boundary integral method for electromagnetic scattering that directly computes electric and magnetic fields without surface currents, using non-singular kernels for high-precision results on complex geometries.

Contribution

It develops a non-singular, surface-only integral formulation for electromagnetics that avoids surface currents and improves numerical accuracy and stability.

Findings

High-precision field computation at surfaces

Effective handling of closely spaced geometries

Compatibility with quadratic surface elements

Abstract

A boundary integral formulation of electromagnetics that involves only the components of $\boldsymbol{E}$ and $\boldsymbol{H}$ is derived without the use of surface currents that appear in the classical PMCHWT formulation. The kernels of the boundary integral equations for $\boldsymbol{E}$ and $\boldsymbol{H}$ are non-singular so that all field quantities at the surface can be determined to high precision and also geometries with closely spaced surfaces present no numerical difficulties. Quadratic elements can readily be used to represent the surfaces so that the surface integrals can be calculated to higher numerical precision than using planar elements for the same numbers of degrees of freedom.