用于 RBF 插值的安德森加速预处理迭代法

IF 4.2 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY Engineering Analysis with Boundary Elements Pub Date : 2024-09-18 DOI:10.1016/j.enganabound.2024.105970

Chengzhi Liu, Juncheng Li, Lijuan Hu

{"title":"用于 RBF 插值的安德森加速预处理迭代法","authors":"Chengzhi Liu, Juncheng Li, Lijuan Hu","doi":"10.1016/j.enganabound.2024.105970","DOIUrl":null,"url":null,"abstract":"<div><p>Traditional RBF interpolation involves solving a linear system, making it computationally expensive for large datasets. Iterative-based quasi-interpolation combines RBF interpolation with iterative methods to enhance accuracy and convergence. To enhance efficiency and accuracy, we in this paper propose a novel method for RBF quasi-interpolation that combines Anderson acceleration with the asynchronous DCPI, termed Anderson-DCPI. The method alternates between the preconditioning iterative method and Anderson extrapolation, aiming to improve convergence rates. We demonstrate the convergence of Anderson-DCPI for positive definite RBF kernel functions and validate its effectiveness through a series of numerical examples.</p></div>","PeriodicalId":51039,"journal":{"name":"Engineering Analysis with Boundary Elements","volume":"169 ","pages":"Article 105970"},"PeriodicalIF":4.2000,"publicationDate":"2024-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Anderson accelerated preconditioning iterative method for RBF interpolation\",\"authors\":\"Chengzhi Liu, Juncheng Li, Lijuan Hu\",\"doi\":\"10.1016/j.enganabound.2024.105970\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>Traditional RBF interpolation involves solving a linear system, making it computationally expensive for large datasets. Iterative-based quasi-interpolation combines RBF interpolation with iterative methods to enhance accuracy and convergence. To enhance efficiency and accuracy, we in this paper propose a novel method for RBF quasi-interpolation that combines Anderson acceleration with the asynchronous DCPI, termed Anderson-DCPI. The method alternates between the preconditioning iterative method and Anderson extrapolation, aiming to improve convergence rates. We demonstrate the convergence of Anderson-DCPI for positive definite RBF kernel functions and validate its effectiveness through a series of numerical examples.</p></div>\",\"PeriodicalId\":51039,\"journal\":{\"name\":\"Engineering Analysis with Boundary Elements\",\"volume\":\"169 \",\"pages\":\"Article 105970\"},\"PeriodicalIF\":4.2000,\"publicationDate\":\"2024-09-18\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Engineering Analysis with Boundary Elements\",\"FirstCategoryId\":\"5\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0955799724004430\",\"RegionNum\":2,\"RegionCategory\":\"工程技术\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"ENGINEERING, MULTIDISCIPLINARY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Engineering Analysis with Boundary Elements","FirstCategoryId":"5","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0955799724004430","RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"ENGINEERING, MULTIDISCIPLINARY","Score":null,"Total":0}

引用次数: 0

摘要

传统的 RBF 插值法需要求解一个线性系统，因此对于大型数据集来说计算成本很高。基于迭代的准插值将 RBF 插值与迭代方法相结合，以提高精度和收敛性。为了提高效率和准确性，我们在本文中提出了一种新的 RBF 准插值方法，该方法结合了安德森加速和异步 DCPI，称为安德森-DCPI。该方法交替使用预处理迭代法和安德森外推法，旨在提高收敛速度。我们演示了安德森-DCPI 对正定 RBF 核函数的收敛性，并通过一系列数值示例验证了其有效性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文

微信好友朋友圈 QQ好友复制链接

本刊更多论文

Anderson accelerated preconditioning iterative method for RBF interpolation

Traditional RBF interpolation involves solving a linear system, making it computationally expensive for large datasets. Iterative-based quasi-interpolation combines RBF interpolation with iterative methods to enhance accuracy and convergence. To enhance efficiency and accuracy, we in this paper propose a novel method for RBF quasi-interpolation that combines Anderson acceleration with the asynchronous DCPI, termed Anderson-DCPI. The method alternates between the preconditioning iterative method and Anderson extrapolation, aiming to improve convergence rates. We demonstrate the convergence of Anderson-DCPI for positive definite RBF kernel functions and validate its effectiveness through a series of numerical examples.

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

Engineering Analysis with Boundary Elements 工程技术-工程：综合

CiteScore

5.50

自引率

18.20%

发文量

368

审稿时长

56 days

期刊介绍： This journal is specifically dedicated to the dissemination of the latest developments of new engineering analysis techniques using boundary elements and other mesh reduction methods. Boundary element (BEM) and mesh reduction methods (MRM) are very active areas of research with the techniques being applied to solve increasingly complex problems. The journal stresses the importance of these applications as well as their computational aspects, reliability and robustness. The main criteria for publication will be the originality of the work being reported, its potential usefulness and applications of the methods to new fields. In addition to regular issues, the journal publishes a series of special issues dealing with specific areas of current research. The journal has, for many years, provided a channel of communication between academics and industrial researchers working in mesh reduction methods Fields Covered: • Boundary Element Methods (BEM) • Mesh Reduction Methods (MRM) • Meshless Methods • Integral Equations • Applications of BEM/MRM in Engineering • Numerical Methods related to BEM/MRM • Computational Techniques • Combination of Different Methods • Advanced Formulations.