Volume 53, Number 1, January–February 2019
|Page(s)||85 - 103|
|Published online||02 April 2019|
A variant of the plane wave least squares method for the time-harmonic Maxwell’s equations
LSEC, ICMSEC, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, 100190 Beijing, China
2 School of Mathematical Sciences, University of Chinese Academy of Sciences, 100049 Beijing, China
Accepted: 29 June 2018
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 Hiptmair et al. (Math. Comput. 82 (2013) 247–268), 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 yield 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 inhomogeneous media.
Mathematics Subject Classification: 65N30 / 65N55
Key words: Maxwell’s equations / plane wave method / variational problem / L2 error estimate
© The authors. Published by EDP Sciences, SMAI 2019
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.