Higher-order mixed spectral element method for Maxwell eigenvalue problem

2013 ◽  
Author(s):  
Na Liu ◽  
Yifa Tang ◽  
Xiaozhang Zhu ◽  
Luis Tobon ◽  
Qinghuo Liu
Keyword(s):  
Eigenvalue Problem ◽  
Spectral Element Method ◽  
Spectral Element ◽  
Higher Order ◽  
Element Method

Mixed Spectral Element Method for 2D Maxwell's Eigenvalue Problem

2015 ◽  
Vol 17 (2) ◽  
pp. 458-486 ◽  
Author(s):  
Na Liu ◽  
Luis Tobón ◽  
Yifa Tang ◽  
Qing Huo Liu
Keyword(s):  
Finite Element ◽  
Eigenvalue Problem ◽  
Spectral Element Method ◽  
Spectral Element ◽  
Higher Order ◽  
The Finite Element Method ◽  
Rigorous Analysis ◽  
Edge Element ◽  
Weak Divergence ◽  
Element Method

AbstractIt is well known that conventional edge elements in solving vector Maxwell'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'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.

Mixed Spectral-Element Method for 3-D Maxwell's Eigenvalue Problem

2015 ◽  
Vol 63 (2) ◽  
pp. 317-325 ◽  
Author(s):  
Na Liu ◽  
Luis Eduardo Tobon ◽  
Yanmin Zhao ◽  
Yifa Tang ◽  
Qing Huo Liu
Keyword(s):  
Eigenvalue Problem ◽  
Spectral Element Method ◽  
Spectral Element ◽  
Element Method

The Spectral Element Method for the Steklov Eigenvalue Problem

2013 ◽  
Vol 853 ◽  
pp. 631-635 ◽  
Author(s):  
Yan Jun Li ◽  
Yi Du Yang ◽  
Hai Bi
Keyword(s):  
Eigenvalue Problem ◽  
Spectral Element Method ◽  
A Priori ◽  
Spectral Element ◽  
Element Approximation ◽  
Steklov Eigenvalue ◽  
Steklov Eigenvalue Problem ◽  
Priori Error Estimates ◽  
Shaped Domain ◽  
Element Method

This paper discusses the spectral element approximation with LGL node basis for the Steklov eigenvalue problem, and analyzes the a priori error estimates. Finally, numerical experi-ments on the square and the L-shaped domain are carried out to get very accurate approximations by the spectral element method.

Wave transmission characteristics for higher-order sandwich panel with flexible core using time-domain spectral element method

2016 ◽  
Vol 19 (3) ◽  
pp. 364-393 ◽  
Author(s):  
B Raja Sekhar ◽  
S Gopalakrishnan ◽  
MVVS Murthy
Keyword(s):  
Wave Propagation ◽  
Time Domain ◽  
Spectral Element Method ◽  
Sandwich Panel ◽  
Spectral Element ◽  
Free Vibrations ◽  
Higher Order ◽  
Frequency Wave ◽  
Beam Design ◽  
Element Method

A new time-domain spectral element with nine degrees of freedom per node is formulated based on higher-order sandwich panel theory, incorporating the flexible behaviour of the core with composite face sheets. Static, free vibrations and wave propagation analysis are carried out using the formulated element. Results obtained using this element are compared with those available in the literature and with commercial finite element codes. The fast convergence of the spectral element method is demonstrated by solving the high-frequency wave propagation problem. A method of computing the wave characteristics, namely wavenumbers and group velocities, in a higher-order sandwich panel is developed using the formulated element. The effect of core damping is studied in detail with different core types, which can be used effectively in sandwich beam design.

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