High order numerical methods to two dimensional delta function integrals in level set methods

doi:10.1016/j.jcp.2009.03.004

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	High order numerical methods to two dimensional delta function integrals in level set methods
	Wen, Xin
	2009-06-20
发表期刊	JOURNAL OF COMPUTATIONAL PHYSICS
ISSN	0021-9991
卷号	228 期号:11 页码:4273-4290
摘要	In this paper we design and analyze a class of high order numerical methods to delta function integrals appearing in level set methods in two dimensional case. The methods comprise approximating the mesh cell restrictions of the delta function integral. In each mesh cell the two dimensional delta function integral can be rewritten as a one dimensional ordinary integral with the smooth integrand being a one dimensional delta function integral, and thus is approximated by applying standard one dimensional high order numerical quadratures and high order numerical methods to one dimensional delta function integrals proposed in [X. Wen, High order numerical methods to a type of delta function integrals, J. Comput. Phys. 226 (2007) 1952-1967]. We establish error estimates for the method which show that the method can achieve any desired accuracy by assigning the corresponding accuracy to the sub-algorithms and has better accuracy under an assumption on the zero level set of the level set function which holds generally. Numerical examples are presented showing that the second to fourth order methods implemented in this paper achieve or exceed the expected accuracy and demonstrating the advantage of using our high order numerical methods. (C) 2009 Elsevier Inc. All rights reserved.
关键词	Delta function integral High order numerical method Error estimate Level set method
DOI	10.1016/j.jcp.2009.03.004
语种	英语
WOS研究方向	Computer Science ; Physics
WOS类目	Computer Science, Interdisciplinary Applications ; Physics, Mathematical
WOS记录号	WOS:000266172400018
出版者	ACADEMIC PRESS INC ELSEVIER SCIENCE
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/7566
专题	中国科学院数学与系统科学研究院
通讯作者	Wen, Xin
作者单位	Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math, LSEC, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Wen, Xin. High order numerical methods to two dimensional delta function integrals in level set methods[J]. JOURNAL OF COMPUTATIONAL PHYSICS,2009,228(11):4273-4290.
APA	Wen, Xin.(2009).High order numerical methods to two dimensional delta function integrals in level set methods.JOURNAL OF COMPUTATIONAL PHYSICS,228(11),4273-4290.
MLA	Wen, Xin."High order numerical methods to two dimensional delta function integrals in level set methods".JOURNAL OF COMPUTATIONAL PHYSICS 228.11(2009):4273-4290.