A variant of the plane wave least squares method for the time-harmonic Maxwell's equations
This is an incremental improvement for researchers working on numerical methods for Maxwell's equations, providing a variant with better error estimates.
The authors propose a variant of the plane wave least squares method for time-harmonic Maxwell's equations that achieves a desired L2 error estimate, with numerical results showing slightly smaller L2 errors than standard methods, and extends to layered media models.
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.