Reduced-order proper orthogonal decomposition extrapolating finite volume element format for two-dimensional hyperbolic equations

doi:10.1007/s10483-017-2162-9

Applied Mathematics and Mechanics (English Edition) ›› 2017, Vol. 38 ›› Issue (2): 289-310.doi: https://doi.org/10.1007/s10483-017-2162-9

• 论文 • 上一篇

Reduced-order proper orthogonal decomposition extrapolating finite volume element format for two-dimensional hyperbolic equations

Zhendong LUO¹, Fei TENG²

1. School of Mathematics and Physics, North China Electric Power University, Beijing 102206, China;
2. School of Control and Computer Engineering, North China Electric Power University, Beijing 102206, China

收稿日期:2016-05-30 修回日期:2016-08-06 出版日期:2017-02-01 发布日期:2017-02-01
通讯作者: Zhendong LUO,E-mail:zhdluo@ncepu.edu.cn E-mail:zhdluo@ncepu.edu.cn
基金资助:
Project supported by the National Natural Science Foundation of China (Nos.11271127 and 11671106)

Reduced-order proper orthogonal decomposition extrapolating finite volume element format for two-dimensional hyperbolic equations

Zhendong LUO¹, Fei TENG²

1. School of Mathematics and Physics, North China Electric Power University, Beijing 102206, China;
2. School of Control and Computer Engineering, North China Electric Power University, Beijing 102206, China

Received:2016-05-30 Revised:2016-08-06 Online:2017-02-01 Published:2017-02-01
Contact: Zhendong LUO E-mail:zhdluo@ncepu.edu.cn
Supported by:
Project supported by the National Natural Science Foundation of China (Nos.11271127 and 11671106)

摘要/Abstract

摘要：

This paper is concerned with establishing a reduced-order extrapolating finite volume element(FVE) format based on proper orthogonal decomposition(POD) for two-dimensional(2D) hyperbolic equations. For this purpose, a semi discrete variational format relative time and a fully discrete FVE format for the 2D hyperbolic equations are built, and a set of snapshots from the very few FVE solutions are extracted on the first very short time interval. Then, the POD basis from the snapshots is formulated, and the reduced-order POD extrapolating FVE format containing very few degrees of freedom but holding sufficiently high accuracy is built. Next, the error estimates of the reduced-order solutions and the algorithm procedure for solving the reduced-order format are furnished. Finally, a numerical example is shown to confirm the correctness of theoretical conclusions. This means that the format is efficient and feasible to solve the 2D hyperbolic equations.

关键词: proper orthogonal decomposition(POD), error estimate, numerical simulation, hyperbolic equation, reduced-order finite volume element(FVE) extrapolating format

Abstract:

Key words: error estimate, numerical simulation, reduced-order finite volume element(FVE) extrapolating format, hyperbolic equation, proper orthogonal decomposition(POD)

中图分类号:

O241.82

Zhendong LUO, Fei TENG. Reduced-order proper orthogonal decomposition extrapolating finite volume element format for two-dimensional hyperbolic equations[J]. Applied Mathematics and Mechanics (English Edition), 2017, 38(2): 289-310.

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Reduced-order proper orthogonal decomposition extrapolating finite volume element format for two-dimensional hyperbolic equations

Reduced-order proper orthogonal decomposition extrapolating finite volume element format for two-dimensional hyperbolic equations

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