@Article{CiCP-17-2,
author = {Na, Liu and Tobón, Luis and Yifa, Tang and Qing, Liu, Huo},
title = {Mixed Spectral Element Method for 2D Maxwell's Eigenvalue Problem},
journal = {Communications in Computational Physics},
year = {2015},
volume = {17},
number = {2},
pages = {458--486},
abstract = {<p style="text-align: justify;">It is well known that conventional edge elements in solving vector Maxwell&#39;s
eigenvalue equations by the finite element method will lead to the presence of spurious
zero eigenvalues. This problem has been addressed for the first order edge element
by Kikuchi by the mixed element method. Inspired by this approach, this paper
describes a higher order mixed spectral element method (mixed SEM) for the computation
of two-dimensional vector eigenvalue problem of Maxwell&#39;s equations. It
utilizes Gauss-Lobatto-Legendre (GLL) polynomials as the basis functions in the finite-element
framework with a weak divergence condition. It is shown that this method
can suppress all spurious zero and nonzero modes and has spectral accuracy. A rigorous
analysis of the convergence of the mixed SEM is presented, based on the higher
order edge element interpolation error estimates, which fully confirms the robustness
of our method. Numerical results are given for homogeneous, inhomogeneous, L-shape,
coaxial and dual-inner-conductor cavities to verify the merits of the proposed
method.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.230113.140814a},
url = {https://global-sci.com/article/80386/mixed-spectral-element-method-for-2d-maxwells-eigenvalue-problem}
}