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

doi:10.12286/jssx.2016.2.200

计算数学 ›› 2016, Vol. 38 ›› Issue (2): 200-211.DOI: 10.12286/jssx.2016.2.200

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

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).

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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

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.

关键词： 无界区域, Helmholtz方程, 修正的Dirichlet-to-Neumann边界条件, 有限元方法, 误差估计

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.

Key words: unbounded domain, Helmholtz equation, finite element method, modified Dirichlet-to-Neumann boundary condition, error estimate

MR(2010)主题分类:

65N30

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摘要

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

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

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