关于Allen-Cahn的对称性破缺

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2021-06-12 DOI:10.4208/csiam-am.so-2021-0030

Dong Li, Chaoyu Quan, T. Tang, Wen Yang

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引用次数: 1

摘要

我们考虑具有标准双阱势和周期边界条件的Allen-Cahn方程的数值解。令人惊讶的是，发现使用具有高精度计算解的标准数值离散可能会收敛到完全不正确的稳态。这种情况发生在非常平滑的初始数据和最先进的算法上。我们分析了这一现象，并展示了通过一种新的对称性保持滤波器技术来解决这一问题。我们建立了一个新的理论框架，并严格证明了滤波解的稳态收敛性。

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On Symmetry Breaking of Allen-Cahn

We consider numerical solutions for the Allen-Cahn equation with standard double well potential and periodic boundary conditions. Surprisingly it is found that using standard numerical discretizations with high precision computational solutions may converge to completely incorrect steady states. This happens for very smooth initial data and state-of-the-art algorithms. We analyze this phenomenon and showcase the resolution of this problem by a new symmetry-preserving filter technique. We develop a new theoretical framework and rigorously prove the convergence to steady states for the filtered solutions.

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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.