HIGH ORDER NUMERICAL METHODS TO THREE DIMENSIONAL DELTA FUNCTION INTEGRALS IN LEVEL SET METHODS

doi:10.1137/090758295

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	HIGH ORDER NUMERICAL METHODS TO THREE DIMENSIONAL DELTA FUNCTION INTEGRALS IN LEVEL SET METHODS
	Wen, Xin
	2010
发表期刊	SIAM JOURNAL ON SCIENTIFIC COMPUTING
ISSN	1064-8275
卷号	32 期号:3 页码:1288-1309
摘要	In this paper we propose a class of high order numerical methods to delta function integrals appearing in level set methods in the three dimensional case by extending the idea for designing high order methods to two dimensional delta function integrals in [ X. Wen, J. Comput. Phys., 228 (2009), pp. 4273-4290]. The methods comprise approximating the mesh cell restrictions of the delta function integral. In each mesh cell the three dimensional delta function integral can be rewritten as a two dimensional ordinary integral with the smooth integrand being a one dimensional delta function integral. A key idea in designing high order methods in this paper is that the high order accuracy of the methods is not ensured in each mesh cell, and the methods are designed in a consistent way to foster error cancelations in mesh cells where high order accuracy is not ensured in the individual cell. This issue is essentially related to the construction of integral area for the two dimensional ordinary integral in each mesh cell, which is achieved by considering the intersection points between the zero level set and the edges or sides of the mesh cell. The mesh cell restrictions of the three dimensional delta function integral are then approximated by applying standard two dimensional high order numerical quadratures and high order numerical methods to one dimensional delta function integrals. Numerical examples are presented showing that our methods in this paper achieve or exceed the expected second to fourth order accuracy and demonstrating the stability of shifting mesh for our methods and the advantage of using our high order numerical methods.
关键词	delta function integral high order numerical method level set method
DOI	10.1137/090758295
语种	英语
资助项目	Chinese Academy of Sciences[K3502012S8] ; NSFC[10601062] ; National Basic Research Program[2010CB731505]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000278576300009
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/10032
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, LSEC, Inst Computat Math, Acad Math & Syst Sci, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Wen, Xin. HIGH ORDER NUMERICAL METHODS TO THREE DIMENSIONAL DELTA FUNCTION INTEGRALS IN LEVEL SET METHODS[J]. SIAM JOURNAL ON SCIENTIFIC COMPUTING,2010,32(3):1288-1309.
APA	Wen, Xin.(2010).HIGH ORDER NUMERICAL METHODS TO THREE DIMENSIONAL DELTA FUNCTION INTEGRALS IN LEVEL SET METHODS.SIAM JOURNAL ON SCIENTIFIC COMPUTING,32(3),1288-1309.
MLA	Wen, Xin."HIGH ORDER NUMERICAL METHODS TO THREE DIMENSIONAL DELTA FUNCTION INTEGRALS IN LEVEL SET METHODS".SIAM JOURNAL ON SCIENTIFIC COMPUTING 32.3(2010):1288-1309.