High-order Numerical Quadratures in a Tetrahedron with an Implicitly Defined Curved Interface

doi:10.1145/3372144

CSpace

	High-order Numerical Quadratures in a Tetrahedron with an Implicitly Defined Curved Interface
	Cui, Tao 1,2; Leng, Wei 1,2; Liu, Huaqing 1,2; Zhang, Linbo 1,2; Zheng, Weiying 1,2
	2020-04-01
发表期刊	ACM TRANSACTIONS ON MATHEMATICAL SOFTWARE
ISSN	0098-3500
卷号	46 期号:1 页码:18
摘要	Given a shape regular tetrahedron and a curved surface that is defined implicitly by a nonlinear level set function and divides the tetrahedron into two sub-domains, a general-purpose, robust, and high-order numerical algorithm is proposed in this article for computing both volume integrals in the sub-domains and surface integrals on their common boundary. The algorithm uses a direct approach that decomposes 3D volume integrals or 2D surface integrals into multiple 1D integrals and computes the 1D integrals with Gaussian quadratures. It only requires finding roots of univariate nonlinear functions in given intervals and evaluating the integrand, the level set function, and the gradient of the level set function at given points. It can achieve arbitrarily high accuracy by increasing the orders of Gaussian quadratures, and it does not need extra a priori knowledge about the integrand and the level set function. The code for the algorithm is freely available in the open-source finite element toolbox Parallel Hierarchical Grid (PHG) and can serve as a basic building block for implementing 3D high-order numerical algorithms involving implicit interfaces or boundaries.
关键词	Quadrature tetrahedral mesh curved surface extended finite element high order
DOI	10.1145/3372144
收录类别	SCI
语种	英语
资助项目	National Key Research and Development Program of China[2016YFB0201304] ; National Magnetic Confinement Fusion Science Program of China[2015GB110003] ; National Natural Science Foundation of China[91430215] ; National Natural Science Foundation of China[91530323] ; National Natural Science Foundation of China[11725106] ; National Natural Science Foundation of China[11831016] ; National Natural Science Foundation of China[11771440] ; State Key Laboratory of Scientific and Engineering Computing (LSEC) ; National Center for Mathematics and Interdisciplinary Sciences of Chinese Academy of Sciences (NCMIS)
WOS研究方向	Computer Science ; Mathematics
WOS类目	Computer Science, Software Engineering ; Mathematics, Applied
WOS记录号	WOS:000582337500003
出版者	ASSOC COMPUTING MACHINERY
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/52410
专题	中国科学院数学与系统科学研究院
通讯作者	Cui, Tao
作者单位	1.Chinese Acad Sci, Acad Math & Syst Sci, 55 East Zhongguancun Rd, Beijing 100190, Peoples R China 2.Univ Chinese Acad Sci, Sch Math Sci, 19A Yuquan Rd, Beijing 100049, Peoples R China
推荐引用方式 GB/T 7714	Cui, Tao,Leng, Wei,Liu, Huaqing,et al. High-order Numerical Quadratures in a Tetrahedron with an Implicitly Defined Curved Interface[J]. ACM TRANSACTIONS ON MATHEMATICAL SOFTWARE,2020,46(1):18.
APA	Cui, Tao,Leng, Wei,Liu, Huaqing,Zhang, Linbo,&Zheng, Weiying.(2020).High-order Numerical Quadratures in a Tetrahedron with an Implicitly Defined Curved Interface.ACM TRANSACTIONS ON MATHEMATICAL SOFTWARE,46(1),18.
MLA	Cui, Tao,et al."High-order Numerical Quadratures in a Tetrahedron with an Implicitly Defined Curved Interface".ACM TRANSACTIONS ON MATHEMATICAL SOFTWARE 46.1(2020):18.