A modified Galerkin FEM for 1D Helmholtz equations

Hui Zheng; Richard C. Cai; L.S. Pan

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A modified Galerkin FEM for 1D Helmholtz equations

机译：一维Helmholtz方程的改进Galerkin有限元法

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摘要

A method is presented that aims to eliminate the numerical errors inherent in the standard Galerkin finite element method (GFEM) for solving homogeneous Helmholtz equations. An error analysis of the standard GFEM with linear elements is first performed by using the concept of truncation error in finite difference methods, and then the truncation error expression is obtained. A linear GFEM with an artificial stiffness is proposed to solve the Helmholtz equation after investigating the effect of the error on numerical solution. The proposed method is essentially as straightforward as the standard GFEM and thus requires almost no additional computational effort. Numerical results show that present pollution error decreases by 90% compared with that of the standard GFEM.

机译：提出了一种方法，该方法旨在消除标准Galerkin有限元方法（GFEM）求解固有Helmholtz方程时固有的数值误差。首先利用有限差分法中的截断误差的概念对标准线性有限元法进行了误差分析，得到了截断误差的表达式。在研究误差对数值解的影响后，提出了具有人工刚度的线性GFEM求解Helmholtz方程。所提出的方法本质上与标准GFEM一样简单，因此几乎不需要额外的计算工作。数值结果表明，与标准GFEM相比，当前的污染误差降低了90％。

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来源
《Applied Acoustics》 |2013年第1期|211-216|共6页
作者
Hui Zheng; Richard C. Cai; L.S. Pan;
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作者单位

Shanghai Key Laboratory of Digital Autobody Engineering, School of Mechanical Engineering, Shanghai Jiao Tong University, 800 Dongchuan Road, Shanghai 200240, China,Institute of High Performance Computing, 1 Fusionopolis Way, Connexis, #16-16, Singapore 138632, Singapore;

BW Offshore Singapore Pte. Ltd., W Pasir Panjang Road, Mapletree Business City, #17-01, Singapore 117438, Singapore;

Institute of High Performance Computing, 1 Fusionopolis Way, Connexis, #16-16, Singapore 138632, Singapore;

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收录信息美国《科学引文索引》(SCI);美国《工程索引》(EI);
原文格式 PDF
正文语种 eng
中图分类
关键词
finite element method; helmholtz equation; high wave numbers; numerical method; pollution error;

机译：有限元法亥姆霍兹方程高波数数值方法污染误差;

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A modified Galerkin FEM for 1D Helmholtz equations

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