Two-Grid Based Adaptive Proper Orthogonal Decomposition Method for Time Dependent Partial Differential Equations

被引：3
作者：
Dai, Xiaoying [1 ,2 ]
Kuang, Xiong [1 ,2 ]
Xin, Jack [3 ]
Zhou, Aihui [1 ,2 ]
机构：
[1] Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math & Sci Engn Comp, LSEC, Beijing 100190, Peoples R China
[2] Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China
[3] Univ Calif Irvine, Dept Math, Irvine, CA 92697 USA
来源：
JOURNAL OF SCIENTIFIC COMPUTING | 2020年 / 84卷 / 03期
基金：
中国国家自然科学基金;
关键词：
Proper orthogonal decomposition; Galerkin projection; Error indicator; Adaptive; Two grid; KPP FRONT SPEEDS; MODEL-REDUCTION; ELEMENT; POD; OPTIMIZATION; SIMULATION; DYNAMICS; SCHEME; FLOW;
D O I：
10.1007/s10915-020-01288-9
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this article, we propose a two-grid based adaptive proper orthogonal decomposition (POD) method to solve the time dependent partial differential equations. Based on the error obtained in the coarse grid, we propose an error indicator for the numerical solution obtained in the fine grid. Our new method is cheap and easy to be implement. We apply our new method to the solution of time-dependent advection-diffusion equations with the Kolmogorov flow and the ABC flow. The numerical results show that our method is more efficient than the existing POD methods.
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页数：27
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