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高波数波动问题的多水平方法

卢培培1, 许学军2,3   

  1. 1. 苏州大学数学科学学院, 苏州 215006;
    2. LSEC, 中国科学院数学与系统科学研究院, 北京 100190;
    3. 同济大学数学科学学院, 上海, 200092
  • 收稿日期:2017-08-09 出版日期:2018-06-15 发布日期:2018-05-15
  • 基金资助:

    国家自然科学基金(11401417,11671302)资助项目.

卢培培, 许学军. 高波数波动问题的多水平方法[J]. 计算数学, 2018, 40(2): 119-134.

Lu Peipei, Xu Xuejun. MULTILEVEL METHODS FOR THE WAVE PROBLEMS WITH HIGH WAVE NUMBER[J]. Mathematica Numerica Sinica, 2018, 40(2): 119-134.

MULTILEVEL METHODS FOR THE WAVE PROBLEMS WITH HIGH WAVE NUMBER

Lu Peipei1, Xu Xuejun2,3   

  1. 1. School of Mathematics Sciences, Soochow University, Suzhou 215006, China;
    2. LSEC, Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing 100190, China;
    3. School of Mathematical Sciences, Tongji University, Shanghai 200092, China
  • Received:2017-08-09 Online:2018-06-15 Published:2018-05-15
本文主要讨论求解高波数Helmholtz方程的多水平方法,主要回顾了一些具有代表性的多重网格方法.如Erlangga等人的shifted Laplacian预处理的多重网格法;Elman等提出的修正的多重网格方法;以及我们的基于连续内罚有限元(CIP-FEM)离散代数系统的多水平算法.最后还介绍了求解高波数时谐Maxwell方程的CIP-FEM离散代数系统的多水平算法.
In this paper, we mainly review some multilevel preconditioners for the Helmholtz equation with high wave number, which include the shifted Laplacian preconditioner proposed by Erlangga etc.; A modified multigrid method proposed by Elman etc.; and our multilevel methods based on the continuous interior penalty method(CIP-FEM). Finally, we also introduce an efficient multilevel method for the time-harmonic Maxwell equation with high wave number.

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