ON THE CONVERGENCE TO LOCAL LIMIT OF NONLOCAL MODELS WITH APPROXIMATED INTERACTION NEIGHBORHOODS

doi:10.1137/21M1448227

	ON THE CONVERGENCE TO LOCAL LIMIT OF NONLOCAL MODELS WITH APPROXIMATED INTERACTION NEIGHBORHOODS
	Du, Qiang 2; Xie, Hehu 3,4; Yin, Xiaobo 1,5
刊名	SIAM JOURNAL ON NUMERICAL ANALYSIS
	2022
卷号	60 期号:4 页码:2046-2068
关键词	nonlocal model peridynamics polygonal approximation horizon parameter asymptotically compatible convergence
ISSN号	0036-1429
DOI	10.1137/21M1448227
英文摘要	Many nonlocal models have adopted Euclidean balls as the nonlocal interaction neighborhoods. When solving them numerically, it is sometimes convenient to adopt polygonal ap-proximations of such balls. A crucial question is to what extent such approximations affect the nonlocal operators and the corresponding solutions. While recent works have analyzed this issue for a fixed horizon parameter, the question remains open in the case of a small or vanishing horizon parameter, which happens often in many practical applications and has a significant impact on the reliability and robustness of nonlocal modeling and simulations. In this work, we are interested in addressing this issue and establishing the convergence of the nonlocal solutions associated with polygonally approximated interaction neighborhoods to the local limit of the original nonlocal so-lutions. Our finding reveals that the new nonlocal solution does not converge to the correct local limit when the number of sides of polygons is uniformly bounded. On the other hand, if the number of sides tends to infinity, the desired convergence can be established. These results may be used to guide future computational studies of nonlocal models.
资助项目	National Science Foundation[DMS-2012562] ; National Science Foundation[DMS-1937254] ; Beijing Natural Science Foundation[Z200003] ; National Natural Science Foundations of China[11771434] ; National Center for Mathematics and Interdisciplinary Science, CAS ; National Natural Science Foundation of China[11671165] ; Hubei Provincial Science and Technology Innovation Base (Platform) special project[2020DFH002]
WOS研究方向	Mathematics
语种	英语
出版者	SIAM PUBLICATIONS
WOS记录号	WOS:000862256800003
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/60974]
专题	中国科学院数学与系统科学研究院
通讯作者	Du, Qiang
作者单位	1.Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China 2.Columbia Univ, Dept Appl Phys & Appl Math, New York, NY 10027 USA 3.Chinese Acad Sci, Acad Math & Syst Sci, LSEC, ICMSEC, Beijing 100190, Peoples R China 4.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China 5.Cent China Normal Univ, Hubei Key Lab Math Sci, Wuhan 430079, Peoples R China
推荐引用方式 GB/T 7714	Du, Qiang,Xie, Hehu,Yin, Xiaobo. ON THE CONVERGENCE TO LOCAL LIMIT OF NONLOCAL MODELS WITH APPROXIMATED INTERACTION NEIGHBORHOODS[J]. SIAM JOURNAL ON NUMERICAL ANALYSIS,2022,60(4):2046-2068.
APA	Du, Qiang,Xie, Hehu,&Yin, Xiaobo.(2022).ON THE CONVERGENCE TO LOCAL LIMIT OF NONLOCAL MODELS WITH APPROXIMATED INTERACTION NEIGHBORHOODS.SIAM JOURNAL ON NUMERICAL ANALYSIS,60(4),2046-2068.
MLA	Du, Qiang,et al."ON THE CONVERGENCE TO LOCAL LIMIT OF NONLOCAL MODELS WITH APPROXIMATED INTERACTION NEIGHBORHOODS".SIAM JOURNAL ON NUMERICAL ANALYSIS 60.4(2022):2046-2068.