与双谐方程相关的反边界值问题的消隐正则化方法

IF 2.1 2区数学 Q1 MATHEMATICS, APPLIED

Journal of Computational and Applied Mathematics Pub Date : 2024-09-18 DOI:10.1016/j.cam.2024.116285

{"title":"与双谐方程相关的反边界值问题的消隐正则化方法","authors":"","doi":"10.1016/j.cam.2024.116285","DOIUrl":null,"url":null,"abstract":"<div><div>In this paper, we propose a numerical algorithm that combines the fading regularization method with the method of fundamental solutions (MFS) to solve a Cauchy problem associated with the biharmonic equation. We introduce a new stopping criterion for the iterative process and compare its performance with previous criteria. Numerical simulations using MFS validate the accuracy of this stopping criterion for both compatible and noisy data and demonstrate the convergence, stability, and efficiency of the proposed algorithm, as well as its ability to deblur noisy data.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":2.1000,"publicationDate":"2024-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Fading regularization method for an inverse boundary value problem associated with the biharmonic equation\",\"authors\":\"\",\"doi\":\"10.1016/j.cam.2024.116285\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>In this paper, we propose a numerical algorithm that combines the fading regularization method with the method of fundamental solutions (MFS) to solve a Cauchy problem associated with the biharmonic equation. We introduce a new stopping criterion for the iterative process and compare its performance with previous criteria. Numerical simulations using MFS validate the accuracy of this stopping criterion for both compatible and noisy data and demonstrate the convergence, stability, and efficiency of the proposed algorithm, as well as its ability to deblur noisy data.</div></div>\",\"PeriodicalId\":50226,\"journal\":{\"name\":\"Journal of Computational and Applied Mathematics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":2.1000,\"publicationDate\":\"2024-09-18\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Computational and Applied Mathematics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0377042724005338\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Computational and Applied Mathematics","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0377042724005338","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}

引用次数: 0

摘要

在本文中，我们提出了一种结合消隐正则化方法和基本解法（MFS）的数值算法，用于解决与双谐波方程相关的柯西问题。我们为迭代过程引入了一个新的停止准则，并将其性能与之前的准则进行了比较。使用 MFS 进行的数值模拟验证了这一停止准则对于兼容数据和噪声数据的准确性，并证明了所提算法的收敛性、稳定性和效率，以及其消除噪声数据的能力。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Fading regularization method for an inverse boundary value problem associated with the biharmonic equation

In this paper, we propose a numerical algorithm that combines the fading regularization method with the method of fundamental solutions (MFS) to solve a Cauchy problem associated with the biharmonic equation. We introduce a new stopping criterion for the iterative process and compare its performance with previous criteria. Numerical simulations using MFS validate the accuracy of this stopping criterion for both compatible and noisy data and demonstrate the convergence, stability, and efficiency of the proposed algorithm, as well as its ability to deblur noisy data.

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

Journal of Computational and Applied Mathematics 数学-应用数学

CiteScore

5.40

自引率

4.20%

发文量

437

审稿时长

3.0 months

期刊介绍： The Journal of Computational and Applied Mathematics publishes original papers of high scientific value in all areas of computational and applied mathematics. The main interest of the Journal is in papers that describe and analyze new computational techniques for solving scientific or engineering problems. Also the improved analysis, including the effectiveness and applicability, of existing methods and algorithms is of importance. The computational efficiency (e.g. the convergence, stability, accuracy, ...) should be proved and illustrated by nontrivial numerical examples. Papers describing only variants of existing methods, without adding significant new computational properties are not of interest. The audience consists of: applied mathematicians, numerical analysts, computational scientists and engineers.