On a Helmholtz transmission problem in planar domains with corners

TL;DR

This paper introduces a numerical scheme combining integral equations and discretization techniques to accurately solve a Helmholtz transmission problem involving dielectric cylinders with corners, relevant to surface plasmon wave studies.

Contribution

It proposes a novel approach for solving Helmholtz transmission problems in domains with corners, achieving high accuracy in electromagnetic field computations.

Findings

High-accuracy solutions for total magnetic and electric fields

Effective handling of sharp edges in dielectric cylinders

Numerical examples demonstrate scheme's robustness

Abstract

A particular mix of integral equations and discretization techniques is suggested for the solution of a planar Helmholtz transmission problem with relevance to the study of surface plasmon waves. The transmission problem describes the scattering of a time harmonic transverse magnetic wave from an infinite dielectric cylinder with complex permittivity and sharp edges. Numerical examples illustrate that the resulting scheme is capable of obtaining total magnetic and electric fields to very high accuracy in the entire computational domain.