用于特征值计算的自适应平面波方法的收敛性和复杂性

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-02-01 DOI:10.4208/aamm.oa-2023-0099

Xiaoying Dai,Yan Pan,Bin Yang, Aihui Zhou

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引用次数: 0

摘要

本文研究了二阶椭圆偏微分方程特征值群的自适应平面波离散化。我们首先设计了一个后验误差估计器，并证明了上界和下界。在后验误差估计器的基础上，我们提出了一种自适应平面波方法。然后，我们证明了自适应平面波近似具有线性收敛速率和准最优复杂度。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Convergence and Complexity of an Adaptive Planewave Method for Eigenvalue Computations

In this paper, we study the adaptive planewave discretization for a cluster of eigenvalues of second-order elliptic partial differential equations. We first design an a posteriori error estimator and prove both the upper and lower bounds. Based on the a posteriori error estimator, we propose an adaptive planewave method. We then prove that the adaptive planewave approximations have the linear convergence rate and quasi-optimal complexity

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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.