保守性Allen-Cahn方程的四阶保结构方法

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY Accounts of Chemical Research Pub Date : 2023-01-01 DOI:10.4208/aamm.oa-2021-0325

Xiaowei Chen, Xu Qian null, Songhe Song

{"title":"保守性Allen-Cahn方程的四阶保结构方法","authors":"Xiaowei Chen, Xu Qian null, Songhe Song","doi":"10.4208/aamm.oa-2021-0325","DOIUrl":null,"url":null,"abstract":". We propose a class of up to fourth-order maximum-principle-preserving and mass-conserving schemes for the conservative Allen-Cahn equation equipped with a non-local Lagrange multiplier. Based on the second-order ﬁnite-difference semi-discretization in the spatial direction, the integrating factor Runge-Kutta schemes are applied in the temporal direction. Theoretical analysis indicates that the proposed schemes conserve mass and preserve the maximum principle under reasonable time step-size restriction, which is independent of the space step size. Finally, the theoretical analysis is veriﬁed by several numerical examples.","PeriodicalId":1,"journal":{"name":"Accounts of Chemical Research","volume":null,"pages":null},"PeriodicalIF":16.4000,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Fourth-Order Structure-Preserving Method for the Conservative Allen-Cahn Equation\",\"authors\":\"Xiaowei Chen, Xu Qian null, Songhe Song\",\"doi\":\"10.4208/aamm.oa-2021-0325\",\"DOIUrl\":null,\"url\":null,\"abstract\":\". We propose a class of up to fourth-order maximum-principle-preserving and mass-conserving schemes for the conservative Allen-Cahn equation equipped with a non-local Lagrange multiplier. Based on the second-order ﬁnite-difference semi-discretization in the spatial direction, the integrating factor Runge-Kutta schemes are applied in the temporal direction. Theoretical analysis indicates that the proposed schemes conserve mass and preserve the maximum principle under reasonable time step-size restriction, which is independent of the space step size. Finally, the theoretical analysis is veriﬁed by several numerical examples.\",\"PeriodicalId\":1,\"journal\":{\"name\":\"Accounts of Chemical Research\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":16.4000,\"publicationDate\":\"2023-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Accounts of Chemical Research\",\"FirstCategoryId\":\"5\",\"ListUrlMain\":\"https://doi.org/10.4208/aamm.oa-2021-0325\",\"RegionNum\":1,\"RegionCategory\":\"化学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"CHEMISTRY, MULTIDISCIPLINARY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Accounts of Chemical Research","FirstCategoryId":"5","ListUrlMain":"https://doi.org/10.4208/aamm.oa-2021-0325","RegionNum":1,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"CHEMISTRY, MULTIDISCIPLINARY","Score":null,"Total":0}

引用次数: 1

摘要

．我们提出了一类具有非局部拉格朗日乘子的保守Allen-Cahn方程的最高四阶最大保原理和最大保质量方案。基于空间方向上的二阶有限差分半离散化，在时间方向上采用积分因子龙格-库塔格式。理论分析表明，所提方案在合理的时间步长限制下，与空间步长无关，能保持质量守恒和最大原则。最后，通过数值算例验证了理论分析的正确性。

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

Fourth-Order Structure-Preserving Method for the Conservative Allen-Cahn Equation

. We propose a class of up to fourth-order maximum-principle-preserving and mass-conserving schemes for the conservative Allen-Cahn equation equipped with a non-local Lagrange multiplier. Based on the second-order ﬁnite-difference semi-discretization in the spatial direction, the integrating factor Runge-Kutta schemes are applied in the temporal direction. Theoretical analysis indicates that the proposed schemes conserve mass and preserve the maximum principle under reasonable time step-size restriction, which is independent of the space step size. Finally, the theoretical analysis is veriﬁed by several 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

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.

期刊最新文献

Management of Cholesteatoma: Hearing Rehabilitation. Congenital Cholesteatoma. Evaluation of Cholesteatoma. Management of Cholesteatoma: Extension Beyond Middle Ear/Mastoid. Recidivism and Recurrence.