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

doi:10.1007/s10915-020-01288-9

	Two-Grid Based Adaptive Proper Orthogonal Decomposition Method for Time Dependent Partial Differential Equations
	Dai, Xiaoying1,2 ; Kuang, Xiong 1,2; Xin, Jack 3; Zhou, Aihui1,2
	2020-08-29
发表期刊	JOURNAL OF SCIENTIFIC COMPUTING
ISSN	0885-7474
卷号	84 期号:3 页码:27
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.
关键词	Proper orthogonal decomposition Galerkin projection Error indicator Adaptive Two grid
DOI	10.1007/s10915-020-01288-9
收录类别	SCI
语种	英语
资助项目	National Key Research and Development Program of China[2019YFA0709601] ; National Natural Science Foundation of China[91730302] ; National Natural Science Foundation of China[11671389] ; Chinese Academy of Sciences[QYZDJ-SSW-SYS010] ; NSF[IIS-1632935] ; NSF[DMS-1854434]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000563635700001
出版者	SPRINGER/PLENUM PUBLISHERS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/52037
专题	计算数学与科学工程计算研究所
通讯作者	Dai, Xiaoying
作者单位	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
推荐引用方式 GB/T 7714	Dai, Xiaoying,Kuang, Xiong,Xin, Jack,et al. Two-Grid Based Adaptive Proper Orthogonal Decomposition Method for Time Dependent Partial Differential Equations[J]. JOURNAL OF SCIENTIFIC COMPUTING,2020,84(3):27.
APA	Dai, Xiaoying,Kuang, Xiong,Xin, Jack,&Zhou, Aihui.(2020).Two-Grid Based Adaptive Proper Orthogonal Decomposition Method for Time Dependent Partial Differential Equations.JOURNAL OF SCIENTIFIC COMPUTING,84(3),27.
MLA	Dai, Xiaoying,et al."Two-Grid Based Adaptive Proper Orthogonal Decomposition Method for Time Dependent Partial Differential Equations".JOURNAL OF SCIENTIFIC COMPUTING 84.3(2020):27.