KMS Of Academy of mathematics and systems sciences, CAS
| High-order Numerical Quadratures in a Tetrahedron with an Implicitly Defined Curved Interface | |
| Cui, Tao1,2; Leng, Wei1,2; Liu, Huaqing1,2; Zhang, Linbo1,2; Zheng, Weiying1,2 | |
| 2020-04-01 | |
| Source Publication | ACM TRANSACTIONS ON MATHEMATICAL SOFTWARE
 |
| ISSN | 0098-3500 |
| Volume | 46Issue:1Pages:18 |
| Abstract | 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. |
| Keyword | Quadrature tetrahedral mesh curved surface extended finite element high order |
| DOI | 10.1145/3372144 |
| Indexed By | SCI |
| Language | 英语 |
| Funding Project | 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 Research Area | Computer Science ; Mathematics |
| WOS Subject | Computer Science, Software Engineering ; Mathematics, Applied |
| WOS ID | WOS:000582337500003 |
| Publisher | ASSOC COMPUTING MACHINERY |
| Citation statistics | |
| Document Type | 期刊论文 |
| Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/52410 |
| Collection | 中国科学院数学与系统科学研究院 |
| Corresponding Author | Cui, Tao |
| Affiliation | 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 |
| Recommended Citation 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. |
| Files in This Item: | There are no files associated with this item. | |||||
Items in the repository are protected by copyright, with all rights reserved, unless otherwise indicated.
Edit Comment