FMM-LU:三维多尺度边界积分方程的快速直接求解器

IF 16.4 1区 化学 Q1 CHEMISTRY, MULTIDISCIPLINARY
Daria Sushnikova, Leslie Greengard, Michael O’Neil, Manas Rachh
{"title":"FMM-LU:三维多尺度边界积分方程的快速直接求解器","authors":"Daria Sushnikova, Leslie Greengard, Michael O’Neil, Manas Rachh","doi":"10.1137/22m1514040","DOIUrl":null,"url":null,"abstract":"We present a fast direct solver for boundary integral equations on complex surfaces in three dimensions using an extension of the recently introduced recursive strong skeletonization scheme. For problems that are not highly oscillatory, our algorithm computes an ${LU}$-like hierarchical factorization of the dense system matrix, permitting application of the inverse in $\\mathcal O(n)$ time, where $n$ is the number of unknowns on the surface. The factorization itself also scales linearly with the system size, albeit with a somewhat larger constant. The scheme is built on a level-restricted adaptive octree data structure, and therefore it is compatible with highly nonuniform discretizations. Furthermore, the scheme is coupled with high-order accurate locally-corrected Nystr\\\"om quadrature methods to integrate the singular and weakly-singular Green's functions used in the integral representations. Our method has immediate applications to a variety of problems in computational physics. We concentrate here on studying its performance in acoustic scattering (governed by the Helmholtz equation) at low to moderate frequencies, and provide rigorous justification for compression of submatrices via proxy surfaces.","PeriodicalId":1,"journal":{"name":"Accounts of Chemical Research","volume":null,"pages":null},"PeriodicalIF":16.4000,"publicationDate":"2023-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"5","resultStr":"{\"title\":\"FMM-LU: A Fast Direct Solver for Multiscale Boundary Integral Equations in Three Dimensions\",\"authors\":\"Daria Sushnikova, Leslie Greengard, Michael O’Neil, Manas Rachh\",\"doi\":\"10.1137/22m1514040\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We present a fast direct solver for boundary integral equations on complex surfaces in three dimensions using an extension of the recently introduced recursive strong skeletonization scheme. For problems that are not highly oscillatory, our algorithm computes an ${LU}$-like hierarchical factorization of the dense system matrix, permitting application of the inverse in $\\\\mathcal O(n)$ time, where $n$ is the number of unknowns on the surface. The factorization itself also scales linearly with the system size, albeit with a somewhat larger constant. The scheme is built on a level-restricted adaptive octree data structure, and therefore it is compatible with highly nonuniform discretizations. Furthermore, the scheme is coupled with high-order accurate locally-corrected Nystr\\\\\\\"om quadrature methods to integrate the singular and weakly-singular Green's functions used in the integral representations. Our method has immediate applications to a variety of problems in computational physics. We concentrate here on studying its performance in acoustic scattering (governed by the Helmholtz equation) at low to moderate frequencies, and provide rigorous justification for compression of submatrices via proxy surfaces.\",\"PeriodicalId\":1,\"journal\":{\"name\":\"Accounts of Chemical Research\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":16.4000,\"publicationDate\":\"2023-11-03\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"5\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Accounts of Chemical Research\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1137/22m1514040\",\"RegionNum\":1,\"RegionCategory\":\"化学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"CHEMISTRY, MULTIDISCIPLINARY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Accounts of Chemical Research","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1137/22m1514040","RegionNum":1,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"CHEMISTRY, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 5

摘要

本文章由计算机程序翻译,如有差异,请以英文原文为准。
FMM-LU: A Fast Direct Solver for Multiscale Boundary Integral Equations in Three Dimensions
We present a fast direct solver for boundary integral equations on complex surfaces in three dimensions using an extension of the recently introduced recursive strong skeletonization scheme. For problems that are not highly oscillatory, our algorithm computes an ${LU}$-like hierarchical factorization of the dense system matrix, permitting application of the inverse in $\mathcal O(n)$ time, where $n$ is the number of unknowns on the surface. The factorization itself also scales linearly with the system size, albeit with a somewhat larger constant. The scheme is built on a level-restricted adaptive octree data structure, and therefore it is compatible with highly nonuniform discretizations. Furthermore, the scheme is coupled with high-order accurate locally-corrected Nystr\"om quadrature methods to integrate the singular and weakly-singular Green's functions used in the integral representations. Our method has immediate applications to a variety of problems in computational physics. We concentrate here on studying its performance in acoustic scattering (governed by the Helmholtz equation) at low to moderate frequencies, and provide rigorous justification for compression of submatrices via proxy surfaces.
求助全文
通过发布文献求助,成功后即可免费获取论文全文。 去求助
来源期刊
Accounts of Chemical Research
Accounts of Chemical Research 化学-化学综合
CiteScore
31.40
自引率
1.10%
发文量
312
审稿时长
2 months
期刊介绍: Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术官方微信