A variant of the plane wave least squares method for the time-harmonic Maxwell's equations

TL;DR

This paper introduces a modified plane wave least squares method for 3D time-harmonic Maxwell's equations, providing better error estimates and improved accuracy over standard methods, especially in layered media.

Contribution

A novel variant of the PWLS method that achieves reliable L2 error estimates and demonstrates improved numerical accuracy in complex layered media models.

Findings

The new method has smaller L2 errors than standard approaches.

It provides valid L2 error estimates for more general layered media models.

Numerical results confirm the effectiveness of the proposed variant.

Abstract

In this paper we are concerned with the plane wave method for the discretization of time-harmonic Maxwell's equations in three dimensions. As pointed out in [6], it is difficult to derive a satisfactory L2 error estimate of the standard plane wave approximation of the time-harmonic Maxwell's equations. We propose a variant of the plane wave least squares (PWLS) method and show that the new plane wave approximations possess the desired L2 error estimate. Moreover, the numerical results indicate that the new approximations have sightly smaller L2 errors than the standard plane wave approximations. More importantly, the results are derived for more general models in layered media.