Convergence and Complexity of an Adaptive Planewave Method for Eigenvalue Computations

2021/06/02 by Xiaoying Dai, Dai, Xiaoying, Pan Yan +5 · 1 citation
Computer Science · Engineering · Physics and Astronomy · #Advanced Numerical Methods in Computational Mathematics #Electromagnetic Scattering and Analysis #FOS: Mathematics #Matrix Theory and Algorithms #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.2106.01008

openalex publication_date 2021/06/02 · openalex created_date 2022/11/03 · openalex updated_date 2026/07/28

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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• Convergence of the adaptive finite element discretization based parallel orbital-updating method for eigenvalue problems

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