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复合材料特征值的高阶多尺度Rayleigh商校正

张磊1,2, 曹礼群3   

  1. 1. 解放军后勤学院后勤管理系, 北京 100858;
    2. 中国科学院数学与系统科学研究院, 计算数学与科学工程计算研究所, 北京 100190;
    3. LSEC, NCMIS, 计算数学与科学工程计算研究所, 北京 100190
  • 收稿日期:2013-06-04 出版日期:2013-11-15 发布日期:2013-12-03
  • 基金资助:

    国家自然科学基金(60971121,90916027)和国家重点基础研究发展计划(2010CB832702)项目资助。

张磊, 曹礼群. 复合材料特征值的高阶多尺度Rayleigh商校正[J]. 计算数学, 2013, 35(4): 431-448.

Zhang Lei, Cao Liqun. HIGHER-ORDER MULTISCALE RAYLEIGH QUOTIENT CORRECTIONS TO THE EIGENVALUES OF COMPOSITE MATERIALS[J]. Mathematica Numerica Sinica, 2013, 35(4): 431-448.

HIGHER-ORDER MULTISCALE RAYLEIGH QUOTIENT CORRECTIONS TO THE EIGENVALUES OF COMPOSITE MATERIALS

Zhang Lei1,2, Cao Liqun3   

  1. 1. Department of Logistics Management, Logistics Academy, Beijing 100858, China;
    2. Institute of Computational Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China;
    3. LSEC, NCMIS, Institute of Computational Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China
  • Received:2013-06-04 Online:2013-11-15 Published:2013-12-03
本文讨论了周期结构复合材料特征值的多尺度计算,提出了高阶多尺度Rayleigh商校正算法,并给出了收敛性分析. 最后,通过大量数值实验结果表明,新算法是有效且必要的.
In this paper, we discuss the multiscale computation for the eigenvalue problem in composite materials with a periodic microstructure. We present the higher-order multiscale Rayleigh quotient correction method and derive the convergence result. Finally, the numerical experiments show that the method presented in this paper is effective and essential.

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