Convergence and Complexity of an Adaptive Planewave Method for Eigenvalue Computations

Convergence and Complexity of an Adaptive Planewave Method for Eigenvalue Computations

Year:    2024

Author:    Xiaoying Dai, Yan Pan, Bin Yang, Aihui Zhou

Advances in Applied Mathematics and Mechanics, Vol. 16 (2024), Iss. 3 : pp. 636–666

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.

You do not have full access to this article.

Already a Subscriber? Sign in as an individual or via your institution

Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/aamm.OA-2023-0099

Advances in Applied Mathematics and Mechanics, Vol. 16 (2024), Iss. 3 : pp. 636–666

Published online:    2024-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    31

Keywords:    Adaptive planewave method convergence rate complexity eigenvalue.

Author Details

Xiaoying Dai

Yan Pan

Bin Yang

Aihui Zhou