High order numerical methods to two dimensional delta function integrals in level set methods
文献类型：期刊论文
| 作者 | Wen, Xin |
| 刊名 | JOURNAL OF COMPUTATIONAL PHYSICS
 |
| 出版日期 | 2009-06-20 |
| 卷号 | 228期号:11页码:4273-4290 |
| 关键词 | Delta function integral High order numerical method Error estimate Level set method |
| ISSN号 | 0021-9991 |
| DOI | 10.1016/j.jcp.2009.03.004 |
| 英文摘要 | 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. |
| 语种 | 英语 |
| WOS记录号 | WOS:000266172400018 |
| 出版者 | ACADEMIC PRESS INC ELSEVIER SCIENCE |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/7565]  |
| 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. |
入库方式： OAI收割
来源：数学与系统科学研究院
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