Convergence and Complexity of an Adaptive Planewave Method for Eigenvalue Computations

IF 1.5 4区工程技术 Q2 MATHEMATICS, APPLIED

Advances in Applied Mathematics and Mechanics Pub Date : 2024-02-01 DOI:10.4208/aamm.oa-2023-0099

Xiaoying Dai,Yan Pan,Bin Yang, Aihui Zhou

引用次数: 0

Abstract

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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用于特征值计算的自适应平面波方法的收敛性和复杂性

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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来源期刊

Advances in Applied Mathematics and Mechanics MATHEMATICS, APPLIED-MECHANICS

CiteScore

2.60

自引率

7.10%

发文量

审稿时长

6 months

期刊介绍： Advances in Applied Mathematics and Mechanics (AAMM) provides a fast communication platform among researchers using mathematics as a tool for solving problems in mechanics and engineering, with particular emphasis in the integration of theory and applications. To cover as wide audiences as possible, abstract or axiomatic mathematics is not encouraged. Innovative numerical analysis, numerical methods, and interdisciplinary applications are particularly welcome.