Robust Field-Only Surface Integral Equations: Scattering from a Perfect Electric Conductor

TL;DR

This paper introduces a new boundary integral method for electromagnetics that directly computes electric fields around perfect conductors without surface currents, enabling higher precision with fewer elements.

Contribution

A novel field-only boundary integral formulation for PEC scattering that avoids surface currents and divergent kernels, improving accuracy and computational efficiency.

Findings

Enables high-order surface discretization with fewer degrees of freedom.

Provides physical insights into the role of surface curvature in scattering.

Demonstrates robustness and accuracy through numerical examples.

Abstract

A robust field-only boundary integral formulation of electromagnetics is derived without the use of surface currents that appear in the Stratton-Chu formulation. For scattering by a perfect electrical conductor (PEC), the components of the electric field are obtained directly from surface integral equation solutions of three scalar Helmholtz equations for the field components. The divergence-free condition is enforced via a boundary condition on the normal component of the field and its normal derivative. Field values and their normal derivatives at the surface of the PEC are obtained directly from surface integral equations that do not contain divergent kernels. Consequently, high-order elements with fewer degrees of freedom can be used to represent surface features to a higher precision than the traditional planar elements. This theoretical framework is illustrated with numerical examples that provide further physical insight into the role of the surface curvature in scattering problems.