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

doi:10.1137/21M1448227

CSpace

	ON THE CONVERGENCE TO LOCAL LIMIT OF NONLOCAL MODELS WITH APPROXIMATED INTERACTION NEIGHBORHOODS
	Du, Qiang 1; Xie, Hehu 2,3; Yin, Xiaobo 4,5
	2022
发表期刊	SIAM JOURNAL ON NUMERICAL ANALYSIS
ISSN	0036-1429
卷号	60 期号:4 页码:2046-2068
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.
关键词	nonlocal model peridynamics polygonal approximation horizon parameter asymptotically compatible convergence
DOI	10.1137/21M1448227
收录类别	SCI
语种	英语
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
WOS类目	Mathematics, Applied
WOS记录号	WOS:000862256800003
出版者	SIAM PUBLICATIONS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/60975
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.Columbia Univ, Dept Appl Phys & Appl Math, New York, NY 10027 USA 2.Chinese Acad Sci, Acad Math & Syst Sci, LSEC, ICMSEC, Beijing 100190, Peoples R China 3.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China 4.Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, 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.