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Helmholtz方程外边值问题的基于修正的DtN边界条件的有限元方法

郑权, 高玥, 秦凤   

  1. 北方工业大学理学院, 北京 100144
  • 收稿日期:2015-09-30 出版日期:2016-04-15 发布日期:2016-05-13
  • 基金资助:

    国家自然科学基金项目资助(No.1122014).

郑权, 高玥, 秦凤. Helmholtz方程外边值问题的基于修正的DtN边界条件的有限元方法[J]. 计算数学, 2016, 38(2): 200-211.

Zheng Quan, Gao Yue, Qin Feng. THE FINITE ELEMENT METHOD WITH A MODIFIED DtN BOUNDARY CONDITION FOR EXTERIOR PROBLEMS OF THE HELMHOLTZ EQUATION[J]. Mathematica Numerica Sinica, 2016, 38(2): 200-211.

THE FINITE ELEMENT METHOD WITH A MODIFIED DtN BOUNDARY CONDITION FOR EXTERIOR PROBLEMS OF THE HELMHOLTZ EQUATION

Zheng Quan, Gao Yue, Qin Feng   

  1. College of Sciences, North China University of Technology, Beijing 100144, China
  • Received:2015-09-30 Online:2016-04-15 Published:2016-05-13
本文对于无界区域上的Helmholtz方程研究基于修正的Dirichlet-to-Neumann边界条件(MDtN)的有限元方法,得到了依赖于网格尺寸,MDtN边界条件的位置和MDtN中的级数截断项数的H1-误差估计和L2-误差估计.最后通过数值结果验证了误差分析的正确性以及所提方法的有效性.
In this paper, we investigate a finite element method with a modified Dirichlet-to-Neumann boundary condition (MDtN-FEM) for the Helmholtz equation on unbounded domains in R2. The a priori error estimates depending on the mesh size, the location of MDtN boundary and the truncation of the series in MDtN are established in the H1- and L2-norms. Numerical examples demonstrate the advantage in accuracy and efficiency for the method.

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