发布求助
文献互助 智能选刊 最新文献

Communications on Analysis and Computation最新文献

筛选
英文 中文
A quasi Monte Carlo-based model reduction method for solving Helmholtz equation in random media 求解随机介质中亥姆霍兹方程的拟蒙特卡罗模型约简方法
Communications on Analysis and Computation Pub Date : 2023-01-01 DOI: 10.3934/cac.2023015
Dingjiong Ma, Zhiwen Zhang
{"title":"A quasi Monte Carlo-based model reduction method for solving Helmholtz equation in random media","authors":"Dingjiong Ma, Zhiwen Zhang","doi":"10.3934/cac.2023015","DOIUrl":"https://doi.org/10.3934/cac.2023015","url":null,"abstract":"Wave propagation in random media has broad applications in materials science and engineering. In this paper, we develop a quasi Monte Carlo (qMC)-based model reduction method for solving random Helmholtz equations. In the physical space, we construct multiscale reduced basis functions by using an optimization method together with the proper orthogonal decomposition method. Then, in the random space we employ the qMC method for discretization. Under mild conditions, we prove that the spatial grid size is only proportional to the wave number, and almost a first-order convergence rate is achieved in the random space with respect to the number of samples. Since the exact solution oscillates in both physical and random spaces, our approach provides an efficient strategy to find its numerical approximation. One significant advantage of our approach over existing methods is its applicability to generic random media which cannot be treated as random perturbations of homogeneous media. These are confirmed by a series of numerical examples.","PeriodicalId":496537,"journal":{"name":"Communications on Analysis and Computation","volume":"33 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135496190","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Efficient numerical method for shape optimization problem constrained by stochastic elliptic interface equation 随机椭圆界面方程约束下形状优化问题的有效数值方法
Communications on Analysis and Computation Pub Date : 2023-01-01 DOI: 10.3934/cac.2023016
Qingguang Guan, Xu Guo, Wenju Zhao
{"title":"Efficient numerical method for shape optimization problem constrained by stochastic elliptic interface equation","authors":"Qingguang Guan, Xu Guo, Wenju Zhao","doi":"10.3934/cac.2023016","DOIUrl":"https://doi.org/10.3934/cac.2023016","url":null,"abstract":"","PeriodicalId":496537,"journal":{"name":"Communications on Analysis and Computation","volume":"16 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134884217","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
0
×
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
现在去查看 取消
×
提示
确定
请完成安全验证×
相关产品
×
本文献相关产品
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：604180095
Book学术官方微信