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

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• 作者：Zhendong Luo ; Fei Teng
• 关键词：reduced ; order finite volume element (FVE) extrapolating format ; proper orthogonal decomposition (POD) ; hyperbolic equation ; error estimate ; numerical simulation
• 刊名：Applied Mathematics and Mechanics
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：38
• 期：2
• 页码：289-310
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Applications of Mathematics; Classical Mechanics; Mathematical Modeling and Industrial Mathematics;
• 出版者：Shanghai University
• ISSN：1573-2754
• 卷排序：38

文摘

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.