Cahn-Hilliard方程多子域的线性和非线性Dirichlet-Neumann方法

IF 1.7 4区数学 Q2 MATHEMATICS, APPLIED

International Journal of Computer Mathematics Pub Date : 2023-09-29 DOI:10.1080/00207160.2023.2266068

Gobinda Garai, Bankim C. Mandal

{"title":"Cahn-Hilliard方程多子域的线性和非线性Dirichlet-Neumann方法","authors":"Gobinda Garai, Bankim C. Mandal","doi":"10.1080/00207160.2023.2266068","DOIUrl":null,"url":null,"abstract":"AbstractIn this paper, we propose and present a non-overlapping substructuring type iterative algorithm for the Cahn-Hilliard (CH) equation, which is a prototype for phase-field models. It is of great importance to develop efficient numerical methods for the CH equation, given the range of applicability of CH equation has. Here we present a formulation for the linear and non-linear Dirichlet-Neumann (DN) method applied to the CH equation and study the convergence behaviour in one and two spatial dimension in multiple subdomains. We show numerical experiments to illustrate our theoretical findings and effectiveness of the method.Keywords: Dirichlet-NeumannCahn-Hilliard equationParallel computingDomain decompositionConvergence analysisAMS subject classifications: 65M5565Y0565M15DisclaimerAs a service to authors and researchers we are providing this version of an accepted manuscript (AM). Copyediting, typesetting, and review of the resulting proofs will be undertaken on this manuscript before final publication of the Version of Record (VoR). During production and pre-press, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal relate to these versions also. AcknowledgmentsThe authors would like to thank the CSIR India (File No:09/1059(0019)/2018-EMR-I) and DST-SERB (File No: SRG/2019/002164) for the financial assistance and IIT Bhubaneswar for research facility.","PeriodicalId":13911,"journal":{"name":"International Journal of Computer Mathematics","volume":null,"pages":null},"PeriodicalIF":1.7000,"publicationDate":"2023-09-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Linear and Nonlinear Dirichlet-Neumann Method in Multiple Subdomains for the Cahn-Hilliard Equation\",\"authors\":\"Gobinda Garai, Bankim C. Mandal\",\"doi\":\"10.1080/00207160.2023.2266068\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"AbstractIn this paper, we propose and present a non-overlapping substructuring type iterative algorithm for the Cahn-Hilliard (CH) equation, which is a prototype for phase-field models. It is of great importance to develop efficient numerical methods for the CH equation, given the range of applicability of CH equation has. Here we present a formulation for the linear and non-linear Dirichlet-Neumann (DN) method applied to the CH equation and study the convergence behaviour in one and two spatial dimension in multiple subdomains. We show numerical experiments to illustrate our theoretical findings and effectiveness of the method.Keywords: Dirichlet-NeumannCahn-Hilliard equationParallel computingDomain decompositionConvergence analysisAMS subject classifications: 65M5565Y0565M15DisclaimerAs a service to authors and researchers we are providing this version of an accepted manuscript (AM). Copyediting, typesetting, and review of the resulting proofs will be undertaken on this manuscript before final publication of the Version of Record (VoR). During production and pre-press, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal relate to these versions also. AcknowledgmentsThe authors would like to thank the CSIR India (File No:09/1059(0019)/2018-EMR-I) and DST-SERB (File No: SRG/2019/002164) for the financial assistance and IIT Bhubaneswar for research facility.\",\"PeriodicalId\":13911,\"journal\":{\"name\":\"International Journal of Computer Mathematics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.7000,\"publicationDate\":\"2023-09-29\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"International Journal of Computer Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1080/00207160.2023.2266068\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Journal of Computer Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1080/00207160.2023.2266068","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}

引用次数: 0

摘要

摘要本文提出并提出了一种求解Cahn-Hilliard (CH)方程的非重叠子结构型迭代算法，这是相场模型的一个原型。考虑到CH方程的适用范围，开发有效的数值方法对求解CH方程具有重要意义。本文给出了用于CH方程的线性和非线性Dirichlet-Neumann (DN)方法的一个公式，并研究了CH方程在多子域中的一维和二维空间收敛性。通过数值实验来说明我们的理论发现和方法的有效性。关键词:Dirichlet-NeumannCahn-Hilliard方程并行计算域分解收敛分析ams主题分类:65m5565y0565m15免责声明作为对作者和研究人员的服务，我们提供此版本的接受稿件(AM)。在最终出版版本记录(VoR)之前，将对该手稿进行编辑、排版和审查。在制作和印前，可能会发现可能影响内容的错误，所有适用于期刊的法律免责声明也与这些版本有关。作者要感谢CSIR印度(文件号:09/1059(0019)/2018-EMR-I)和st -塞族(文件号:SRG/2019/002164)的资助和IIT Bhubaneswar的研究设施。

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

Linear and Nonlinear Dirichlet-Neumann Method in Multiple Subdomains for the Cahn-Hilliard Equation

AbstractIn this paper, we propose and present a non-overlapping substructuring type iterative algorithm for the Cahn-Hilliard (CH) equation, which is a prototype for phase-field models. It is of great importance to develop efficient numerical methods for the CH equation, given the range of applicability of CH equation has. Here we present a formulation for the linear and non-linear Dirichlet-Neumann (DN) method applied to the CH equation and study the convergence behaviour in one and two spatial dimension in multiple subdomains. We show numerical experiments to illustrate our theoretical findings and effectiveness of the method.Keywords: Dirichlet-NeumannCahn-Hilliard equationParallel computingDomain decompositionConvergence analysisAMS subject classifications: 65M5565Y0565M15DisclaimerAs a service to authors and researchers we are providing this version of an accepted manuscript (AM). Copyediting, typesetting, and review of the resulting proofs will be undertaken on this manuscript before final publication of the Version of Record (VoR). During production and pre-press, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal relate to these versions also. AcknowledgmentsThe authors would like to thank the CSIR India (File No:09/1059(0019)/2018-EMR-I) and DST-SERB (File No: SRG/2019/002164) for the financial assistance and IIT Bhubaneswar for research facility.

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

International Journal of Computer Mathematics 数学-应用数学

CiteScore

3.60

自引率

0.00%

发文量

审稿时长

5 months

期刊介绍： International Journal of Computer Mathematics (IJCM) is a world-leading journal serving the community of researchers in numerical analysis and scientific computing from academia to industry. IJCM publishes original research papers of high scientific value in fields of computational mathematics with profound applications to science and engineering. IJCM welcomes papers on the analysis and applications of innovative computational strategies as well as those with rigorous explorations of cutting-edge techniques and concerns in computational mathematics. Topics IJCM considers include: • Numerical solutions of systems of partial differential equations • Numerical solution of systems or of multi-dimensional partial differential equations • Theory and computations of nonlocal modelling and fractional partial differential equations • Novel multi-scale modelling and computational strategies • Parallel computations • Numerical optimization and controls • Imaging algorithms and vision configurations • Computational stochastic processes and inverse problems • Stochastic partial differential equations, Monte Carlo simulations and uncertainty quantification • Computational finance and applications • Highly vibrant and robust algorithms, and applications in modern industries, including but not limited to multi-physics, economics and biomedicine. Papers discussing only variations or combinations of existing methods without significant new computational properties or analysis are not of interest to IJCM. Please note that research in the development of computer systems and theory of computing are not suitable for submission to IJCM. Please instead consider International Journal of Computer Mathematics: Computer Systems Theory (IJCM: CST) for your manuscript. Please note that any papers submitted relating to these fields will be transferred to IJCM:CST. Please ensure you submit your paper to the correct journal to save time reviewing and processing your work. Papers developed from Conference Proceedings Please note that papers developed from conference proceedings or previously published work must contain at least 40% new material and significantly extend or improve upon earlier research in order to be considered for IJCM.