A REDUCED FE FORMULATION BASED ON POD METHOD FOR HYPERBOLIC EQUATIONS

doi:10.1016/S0252-9602(12)60155-6

数学物理学报(英文版) ›› 2012, Vol. 32 ›› Issue (5): 1997-2009.doi: 10.1016/S0252-9602(12)60155-6

A REDUCED FE FORMULATION BASED ON POD METHOD FOR HYPERBOLIC EQUATIONS

罗振东^1*|欧秋兰¹|吴加荣¹|谢正辉²

1.School of Mathematics and Physics, North China Electric Power University, Beijing 102206, China； 2.LASG, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029, China

收稿日期:2011-03-18 修回日期:2011-10-18 出版日期:2012-09-20 发布日期:2012-09-20
通讯作者: 罗振东,zhdluo@163.com E-mail:zhdluo@163.com; sj200510700001@yahoo.cn; saijiarong@163.com; zxie@lasg.iap.ac.cn
基金资助:
Research of this work was supported by the National Science Foundation of China (11061009, 40821092), the National Basic Research Program (2010CB428403, 2009CB421407, 2010CB951001), and Natural Science Foundation of Hebei Province (A2010001663).

A REDUCED FE FORMULATION BASED ON POD METHOD FOR HYPERBOLIC EQUATIONS

LUO Zhen-Dong^1*, OU Qiu-Lan¹, WU Jia-Rong¹, XIE Zheng-Hui²

1.School of Mathematics and Physics, North China Electric Power University, Beijing 102206, China； 2.LASG, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029, China

Received:2011-03-18 Revised:2011-10-18 Online:2012-09-20 Published:2012-09-20
Contact: LUO Zhen-Dong,zhdluo@163.com E-mail:zhdluo@163.com; sj200510700001@yahoo.cn; saijiarong@163.com; zxie@lasg.iap.ac.cn
Supported by:
Research of this work was supported by the National Science Foundation of China (11061009, 40821092), the National Basic Research Program (2010CB428403, 2009CB421407, 2010CB951001), and Natural Science Foundation of Hebei Province (A2010001663).

摘要/Abstract

摘要：

A proper orthogonal decomposition (POD) method was successfully used in the reduced-order modeling of complex systems. In this paper, we extend the applications of POD method, namely, apply POD method to a classical finite element (FE) formulation for second-order hyperbolic equations with real practical applied background, establish a reduced FE formulation with lower dimensions and high enough accuracy, and provide the error estimates between the reduced FE solutions and the classical FE solutions and the implementation of algorithm for solving reduced FE formulation so as to provide scientific theoretic basis for service applications. Some numerical examples illustrate the fact that the results of numerical computation are consistent with theoretical conclusions. Moreover,
it is shown that the reduced FE formulation based on POD method is feasible and efficient for solving FE formulation for second-order hyperbolic equations.

关键词: proper orthogonal decomposition, finite element formulation, error estimate, hyperbolic equations

Abstract:

Key words: proper orthogonal decomposition, finite element formulation, error estimate, hyperbolic equations

中图分类号:

65N30

罗振东, 欧秋兰, 吴加荣, 谢正辉. A REDUCED FE FORMULATION BASED ON POD METHOD FOR HYPERBOLIC EQUATIONS[J]. 数学物理学报(英文版), 2012, 32(5): 1997-2009.

LUO Zhen-Dong, OU Qiu-Lan, WU Jia-Rong, XIE Zheng-Hui. A REDUCED FE FORMULATION BASED ON POD METHOD FOR HYPERBOLIC EQUATIONS[J]. Acta mathematica scientia,Series B, 2012, 32(5): 1997-2009.

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A REDUCED FE FORMULATION BASED ON POD METHOD FOR HYPERBOLIC EQUATIONS

A REDUCED FE FORMULATION BASED ON POD METHOD FOR HYPERBOLIC EQUATIONS

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