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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

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An absolutely stable $hp$-HDG method for the time-harmonic Maxwell equations with high wave number
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by Peipei Lu, Huangxin Chen and Weifeng Qiu PDF
Math. Comp. 86 (2017), 1553-1577 Request permission

Abstract:

We present and analyze a hybridizable discontinuous Galerkin (HDG) method for the time-harmonic Maxwell equations. The divergence-free condition is enforced on the electric field, then a Lagrange multiplier is introduced, and the problem becomes the solution of a mixed curl-curl formulation of the Maxwell’s problem. The method is shown to be an absolutely stable HDG method for the indefinite time-harmonic Maxwell equations with high wave number. By exploiting the duality argument, the dependence of convergence of the HDG method on the wave number $\kappa$, the mesh size $h$ and the polynomial order $p$ is obtained. Numerical results are given to verify the theoretical analysis.
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Additional Information
  • Peipei Lu
  • Affiliation: School of Mathematics Sciences, Soochow University, Suzhou, 215006, People’s Republic of China
  • MR Author ID: 1030345
  • Email: pplu@suda.edu.cn
  • Huangxin Chen
  • Affiliation: School of Mathematical Sciences and Fujian Provincial Key Laboratory on Mathematical Modeling and High Performance Scientific Computing, Xiamen University, Fujian, 361005, People’s Republic of China
  • MR Author ID: 893977
  • Email: chx@xmu.edu.cn
  • Weifeng Qiu
  • Affiliation: Department of Mathematics, City University of Hong Kong, 83 Tat Chee Avenue, Kowloon, Hong Kong, People’s Republic of China
  • MR Author ID: 845089
  • Email: weifeqiu@cityu.edu.hk
  • Received by editor(s): April 2, 2015
  • Received by editor(s) in revised form: October 20, 2015, and January 20, 2016
  • Published electronically: October 27, 2016
  • Additional Notes: The work of the first author was supported by the NSF of China (Grant No.11401417), the Program of Natural Science Research of Jiangsu Higher Education Institutions of China (Grant No. 14KJB110021) and Jiangsu Provincial Key Laboratory for Numerical Simulation of Large Scale Complex Systems (No. 201404).
    The work of the second author was supported by the NSF of China (Grant No. 11201394) and the Fundamental Research Funds for the Central Universities (Grant No. 20720150005).
    The work of the third author was partially supported by a grant from the Research Grants Council of the Hong Kong Special Administrative Region, China (Project No. CityU 11302014).
    The third author is the corresponding author. All authors contributed equally in this paper.
  • © Copyright 2016 American Mathematical Society
  • Journal: Math. Comp. 86 (2017), 1553-1577
  • MSC (2010): Primary 65N12, 65N15, 65N30
  • DOI: https://doi.org/10.1090/mcom/3150
  • MathSciNet review: 3626528