High-order integral equation methods for problems of scattering by bumps and cavities on half-planes

TL;DR

This paper develops high-order integral equation methods to accurately compute electromagnetic scattering by dielectric bumps and cavities on half-planes, demonstrating excellent convergence even at singular points.

Contribution

The paper introduces novel high-order integral equation algorithms applicable to eight classical scattering problems involving dielectric bumps and cavities on half-planes.

Findings

Numerical methods show excellent convergence with refined discretization.

Methods accurately evaluate fields at singular points.

Applicable to a wide range of classical scattering problems.

Abstract

This paper presents high-order integral equation methods for evaluation of electromagnetic wave scattering by dielectric bumps and dielectric cavities on perfectly conducting or dielectric half-planes. In detail, the algorithms introduced in this paper apply to eight classical scattering problems, namely: scattering by a dielectric bump on a perfectly conducting or a dielectric half-plane, and scattering by a filled, overfilled or void dielectric cavity on a perfectly conducting or a dielectric half-plane. In all cases field representations based on single-layer potentials for appropriately chosen Green functions are used. The numerical far fields and near fields exhibit excellent convergence as discretizations are refined--even at and around points where singular fields and infinite currents exist.