Comparison of numerical algorithms based on elementary and Muller's boundary integral equations in the scattering by dielectric cylinders

TL;DR

This paper compares numerical algorithms based on elementary and Muller's boundary integral equations for scattering by dielectric cylinders, addressing issues near numerical resonances and proposing partial solutions to elementary BIEs' solvability problems.

Contribution

It introduces a comparison framework for BIE-based algorithms and discusses a partial remedy for elementary BIEs' solvability loss.

Findings

Muller's BIEs show better stability near resonances.

Elementary BIEs have solvability issues that can be partially mitigated.

The comparison highlights the advantages and limitations of each approach.

Abstract

We consider boundary integral equations (BIEs) met in the scattering by dielectric cylinders and compare numerical algorithms based on elementary and Muller's BIEs near the "numerical resonances". A procedure of partial removal of well-known defect of elementary BIEs related to the loss of their unique solvability is discussed.