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Hamiltonian Analysis and Dual Vector Spectral Elements for 2D Maxwell Eigenproblems

Part of: Equations of mathematical physics and other areas of application Numerical problems in dynamical systems Partial differential equations, boundary value problems

Published online by Cambridge University Press:  07 February 2017

Hongwei Yang ,
Bao Zhu  and
Jiefu Chen
Hongwei Yang*
Affiliation:
College of Applied Sciences, Beijing University of Technology, Beijing 100124, P.R. China
Bao Zhu*
Affiliation:
School of Materials Science and Engineering, Dalian University of Technology, Dalian, Liaoning 116023, P.R. China
Jiefu Chen*
Affiliation:
Department of Electrical and Computer Engineering, University of Houston, Houston, TX 77004, USA
*
*Corresponding author.Email addresses:yanghongwei@bjut.edu.cn (H. Yang), bzhu@dlut.edu.cn (B. Zhu), jchen84@uh.edu (J. Chen)
*Corresponding author.Email addresses:yanghongwei@bjut.edu.cn (H. Yang), bzhu@dlut.edu.cn (B. Zhu), jchen84@uh.edu (J. Chen)
*Corresponding author.Email addresses:yanghongwei@bjut.edu.cn (H. Yang), bzhu@dlut.edu.cn (B. Zhu), jchen84@uh.edu (J. Chen)

Abstract

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The 2D Maxwell eigenproblems are studied from a new point of view. An electromagnetic problem is cast from the Lagrangian system with single variable into the Hamiltonian system with dual variables. The electric and magnetic components transverse to the wave propagation direction are treated as dual variables to each other. Higher order curl-conforming and divergence-conforming vector basis functions are used to construct dual vector spectral elements. Numerical examples demonstrate some unique advantages of the proposed method.

Keywords

Maxwell eigenproblemHamiltonian systemsymplectic eigenvalue analysisdual variablesspectral element method

MSC classification

Secondary: 35Q61: Maxwell equations 65P10: Hamiltonian systems including symplectic integrators 65N30: Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods 65N25: Eigenvalue problems

Information

Type
Research Article
Information
Communications in Computational Physics , Volume 21 , Issue 2 , February 2017 , pp. 515 - 525
Copyright
Copyright © Global-Science Press 2017 

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