| 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 |
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| 引用本文： | 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. |
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| 作者姓名： | 郑权 高玥 秦凤 |
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| 作者单位： | 北方工业大学理学院, 北京 100144 |
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| 基金项目： | 国家自然科学基金项目资助(No.1122014) |
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| 摘 要： | 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H~1-误差估计和L~2-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.
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| 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 |
| 收稿时间： | 2015-09-30; |
THE FINITE ELEMENT METHOD WITH A MODIFIED DtN BOUNDARY CONDITION FOR EXTERIOR PROBLEMS OF THE HELMHOLTZ EQUATION |
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| 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. |
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| Authors: | Zheng Quan Gao Yue Qin Feng |
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| Institution: | College of Sciences, North China University of Technology, Beijing 100144, China |
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| Abstract: | 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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| Keywords: | unbounded domain Helmholtz equation finite element method modified Dirichlet-to-Neumann boundary condition error estimate |
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