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小周期结构Helmholtz方程的多尺度计算 被引量：1

Heterogeneous Multi-scale Method for Helmholtz Equation with Period Micro-structure
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摘要 本文研究小周期结构Helmholtz方程的多尺度计算。我们用各向异性多尺度方法(HMM)求解小周期结构Helmholtz问题。借助于渐近分析技术,在对HMM方法深入分析的基础上,我们给出了精确与HMM方法近似解之间的误差估计,并讨论和分析了利用微结构信息校正HMM逼近解的技巧。最后,我们用数值例了验证了理论结果的正确性。 in this paper, the heterogeneous multi-scale method (HMM) is used to solve the Heklmholtz equation with periodic micrcstructure. Based on the comprehensive analysis of HMM, the error estimates between the HMM approximation and the exact: solution are provided. Strategies for retrieving the microstructural information from the HMM solutions are discussed and analyzed. Some numerical examples demonstrating our theoretical results are also provided in the paper.
作者 陈培敏 严宁宁
机构地区 中科院数学与系统科学院系统所
出处 《工程数学学报》 CSCD 北大核心 2004年第F12期145-149,共5页 Chinese Journal of Engineering Mathematics
基金 国家重大基础研究发展规划项目(No.G2000067102)国家自然科学基金项目(No.60474027)中科 院数学与系统科学研究创新基金
关键词 HELMHOLTZ方程 周期结构 逼近解 精确解 近似解 误差估计 渐近分析 HMM 多尺度方法 例子 Helmholtz equation periodic microstructure heterogeneous multi-scale method asymptotic expansion homogenization
分类号 O241 [理学—计算数学] TN912 [电子电信—通信与信息系统]
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参考文献7

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同被引文献12

  • 1王自强,宋士仓,曹俊英.小周期复合材料热传导问题的双尺度渐近展开及收敛性分析[J].高校应用数学学报（A辑）,2008,23(2):145-152. 被引量：7
  • 2宋士仓,崔俊芝,刘红生.复合材料稳态热传导问题多尺度计算的一个数学模型[J].应用数学,2005,18(4):560-566. 被引量：15
  • 3Doina C,Patrizia D.An Introduction to Homogennization[M].New York:Oxford University Press,1999.
  • 4Cao L Q,Cui J Z.Asymptotic expasions and numerical algorithms of eigenvalues and eigenfunctions of the Dirichlet problem for second order elliptic equation in perforated[J].Numerical Mathematics,2004,96:525-581.
  • 5Chen J R,Cui J Z.A multicale finite element method for elliptic problems with oscillatory coefficients[J].Mathematics of Comptation,2004,50:1-13.
  • 6He W M,Cui J Z.A local error estimate of the method of multi-scale asymptotic expansions for elliptic problems with rapidly coefficients[J].Journal of Mathematical Analysis and Applications,2007,329:547-556.
  • 7Chen Z M,Hou T Y.A mixed multiscale finite element method for elliptic problems with oscillating coefficients[J].Mathematics of compution,2002,72(242):541-576.
  • 8Ming P B,Zhang P W.Analysis of the heterogenous multiscale method for parabolic homogenization problems[J].Math Comput,2006,76(257):153-177.
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  • 10Ciarlet P G.The Finite Element Method for Elliptic Problems[M].New York:North-Holland,1978.

引证文献1

工程数学学报
2004年 第F12期

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