A POD REDUCED-ORDER SPDMFE EXTRAPOLATING ALGORITHM FOR HYPERBOLIC EQUATIONS

doi:10.1016/S0252-9602(14)60056-4

数学物理学报(英文版) ›› 2014, Vol. 34 ›› Issue (3): 872-890.doi: 10.1016/S0252-9602(14)60056-4

A POD REDUCED-ORDER SPDMFE EXTRAPOLATING ALGORITHM FOR HYPERBOLIC EQUATIONS

罗振东, 李宏

School of Mathematics and Physics, North China Electric Power University, Beijing 102206, China； School of Mathematical Sciences, Inner Mongolia University, Huhhot 010021, China

收稿日期:2013-04-30 修回日期:2013-10-12 出版日期:2014-05-20 发布日期:2014-05-20
基金资助:
Research of this work was mainly supported by the National Science Foundation of China (11271127, 11361035), Science Research of Guizhou Education Department (QJHKYZ[2013]207), and Natural Science Foundation of Inner Mongolia (2012MS0106).

A POD REDUCED-ORDER SPDMFE EXTRAPOLATING ALGORITHM FOR HYPERBOLIC EQUATIONS

LUO Zhen-Dong, LI Hong

School of Mathematics and Physics, North China Electric Power University, Beijing 102206, China； School of Mathematical Sciences, Inner Mongolia University, Huhhot 010021, China

Received:2013-04-30 Revised:2013-10-12 Online:2014-05-20 Published:2014-05-20
Supported by:
Research of this work was mainly supported by the National Science Foundation of China (11271127, 11361035), Science Research of Guizhou Education Department (QJHKYZ[2013]207), and Natural Science Foundation of Inner Mongolia (2012MS0106).

摘要/Abstract

摘要：

In this article, a proper orthogonal decomposition (POD) method is used to study a classical splitting positive definite mixed finite element (SPDMFE) formulation for second-order hyperbolic equations. A POD reduced-order SPDMFE extrapolating algorithm with lower dimensions and sufficiently high accuracy is established for second-order hyperbolic equations. The error estimates between the classical SPDMFE solutions and the reduced-order SPDMFE solutions obtained from the POD reduced-order SPDMFE extrapolating algorithm are provided. The implementation for solving the POD reduced-order SPDMFE extrapolating algorithm is given. Some numerical experiments are presented illustrating that the results of numerical computation are consistent with theoretical conclusions, thus validating that the POD reduced-order SPDMFE extrapolating algorithm is feasible and efficient for solving second-order hyperbolic equations.

关键词: Proper orthogonal decomposition, splitting positive definite mixed finite ele-ment formulation, hyperbolic equations, error estimate

Abstract:

Key words: Proper orthogonal decomposition, splitting positive definite mixed finite ele-ment formulation, hyperbolic equations, error estimate

中图分类号:

65N30

罗振东, 李宏. A POD REDUCED-ORDER SPDMFE EXTRAPOLATING ALGORITHM FOR HYPERBOLIC EQUATIONS[J]. 数学物理学报(英文版), 2014, 34(3): 872-890.

LUO Zhen-Dong, LI Hong. A POD REDUCED-ORDER SPDMFE EXTRAPOLATING ALGORITHM FOR HYPERBOLIC EQUATIONS[J]. Acta mathematica scientia,Series B, 2014, 34(3): 872-890.

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A POD REDUCED-ORDER SPDMFE EXTRAPOLATING ALGORITHM FOR HYPERBOLIC EQUATIONS

A POD REDUCED-ORDER SPDMFE EXTRAPOLATING ALGORITHM FOR HYPERBOLIC EQUATIONS

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