二维和三维椭圆型偏微分方程的局部傅里叶配置方法:理论和MATLAB代码

IF 3.4 Q1 ENGINEERING, MECHANICAL 国际机械系统动力学学报(英文) Pub Date : 2022-12-13 DOI:10.1002/msd2.12061
Yan Gu, Zhuojia Fu, Mikhail V. Golub
{"title":"二维和三维椭圆型偏微分方程的局部傅里叶配置方法:理论和MATLAB代码","authors":"Yan Gu,&nbsp;Zhuojia Fu,&nbsp;Mikhail V. Golub","doi":"10.1002/msd2.12061","DOIUrl":null,"url":null,"abstract":"<p>A localized Fourier collocation method is proposed for solving certain types of elliptic boundary value problems. The method first discretizes the entire domain into a set of overlapping small subdomains, and then in each of the subdomains, the unknown functions and their derivatives are approximated using the pseudo-spectral Fourier collocation method. The key idea of the present method is to combine the merits of the quick convergence of the pseudo-spectral method and the high sparsity of the localized discretization technique to yield a new framework that may be suitable for large-scale simulations. The present method can be viewed as a competitive alternative for solving numerically large-scale boundary value problems with complex-shape geometries. Preliminary numerical experiments involving Poisson, Helmholtz, and modified-Helmholtz equations in both two and three dimensions are presented to demonstrate the accuracy and efficiency of the proposed method.</p>","PeriodicalId":60486,"journal":{"name":"国际机械系统动力学学报(英文)","volume":"2 4","pages":"339-351"},"PeriodicalIF":3.4000,"publicationDate":"2022-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/msd2.12061","citationCount":"3","resultStr":"{\"title\":\"A localized Fourier collocation method for 2D and 3D elliptic partial differential equations: Theory and MATLAB code\",\"authors\":\"Yan Gu,&nbsp;Zhuojia Fu,&nbsp;Mikhail V. Golub\",\"doi\":\"10.1002/msd2.12061\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>A localized Fourier collocation method is proposed for solving certain types of elliptic boundary value problems. The method first discretizes the entire domain into a set of overlapping small subdomains, and then in each of the subdomains, the unknown functions and their derivatives are approximated using the pseudo-spectral Fourier collocation method. The key idea of the present method is to combine the merits of the quick convergence of the pseudo-spectral method and the high sparsity of the localized discretization technique to yield a new framework that may be suitable for large-scale simulations. The present method can be viewed as a competitive alternative for solving numerically large-scale boundary value problems with complex-shape geometries. Preliminary numerical experiments involving Poisson, Helmholtz, and modified-Helmholtz equations in both two and three dimensions are presented to demonstrate the accuracy and efficiency of the proposed method.</p>\",\"PeriodicalId\":60486,\"journal\":{\"name\":\"国际机械系统动力学学报(英文)\",\"volume\":\"2 4\",\"pages\":\"339-351\"},\"PeriodicalIF\":3.4000,\"publicationDate\":\"2022-12-13\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://onlinelibrary.wiley.com/doi/epdf/10.1002/msd2.12061\",\"citationCount\":\"3\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"国际机械系统动力学学报(英文)\",\"FirstCategoryId\":\"1087\",\"ListUrlMain\":\"https://onlinelibrary.wiley.com/doi/10.1002/msd2.12061\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"ENGINEERING, MECHANICAL\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"国际机械系统动力学学报(英文)","FirstCategoryId":"1087","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1002/msd2.12061","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"ENGINEERING, MECHANICAL","Score":null,"Total":0}
引用次数: 3

摘要

针对椭圆型边值问题,提出了一种局部傅里叶配点法。该方法首先将整个域离散为一组重叠的小子域,然后在每个子域中,使用伪谱傅里叶配置法对未知函数及其导数进行近似。该方法的核心思想是将伪谱法的快速收敛性和局部离散化技术的高稀疏性相结合,形成一种适用于大规模模拟的新框架。该方法是求解具有复杂几何形状的数值大尺度边值问题的一种有竞争力的替代方法。通过二维和三维泊松方程、亥姆霍兹方程和修正亥姆霍兹方程的初步数值实验,验证了该方法的准确性和有效性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。

摘要图片

查看原文
分享 分享
微信好友 朋友圈 QQ好友 复制链接
本刊更多论文
A localized Fourier collocation method for 2D and 3D elliptic partial differential equations: Theory and MATLAB code

A localized Fourier collocation method is proposed for solving certain types of elliptic boundary value problems. The method first discretizes the entire domain into a set of overlapping small subdomains, and then in each of the subdomains, the unknown functions and their derivatives are approximated using the pseudo-spectral Fourier collocation method. The key idea of the present method is to combine the merits of the quick convergence of the pseudo-spectral method and the high sparsity of the localized discretization technique to yield a new framework that may be suitable for large-scale simulations. The present method can be viewed as a competitive alternative for solving numerically large-scale boundary value problems with complex-shape geometries. Preliminary numerical experiments involving Poisson, Helmholtz, and modified-Helmholtz equations in both two and three dimensions are presented to demonstrate the accuracy and efficiency of the proposed method.

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
CiteScore
3.50
自引率
0.00%
发文量
0
期刊最新文献
Issue Information Cover Image, Volume 4, Number 3, September 2024 Design of bionic water jet thruster with double-chamber driven by electromagnetic force A data-assisted physics-informed neural network (DA-PINN) for fretting fatigue lifetime prediction Comparison of the performance and dynamics of the asymmetric single-sided and symmetric double-sided vibro-impact nonlinear energy sinks with optimized designs
×
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
0
微信
客服QQ
Book学术公众号 扫码关注我们
反馈
×
意见反馈
请填写您的意见或建议
请填写您的手机或邮箱
已复制链接
已复制链接
快去分享给好友吧!
我知道了
×
扫码分享
扫码分享
Book学术官方微信
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术
文献互助 智能选刊 最新文献 互助须知 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 Book学术 All rights reserved.
ghs 京公网安备 11010802042870号 京ICP备2023020795号-1