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Volume 16, Issue 3
Convergence and Complexity of an Adaptive Planewave Method for Eigenvalue Computations

Xiaoying Dai, Yan Pan, Bin Yang & Aihui Zhou

DOI: 10.4208/aamm.OA-2023-0099

Adv. Appl. Math. Mech., 16 (2024), pp. 636-666.

Published online: 2024-02

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  • 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.

  • Keywords

Adaptive planewave method, convergence rate, complexity, eigenvalue.

  • AMS Subject Headings

65N15, 65N25, 65N35, 65T40

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAMM-16-636, author = {Dai , XiaoyingPan , YanYang , Bin and Zhou , Aihui}, title = {Convergence and Complexity of an Adaptive Planewave Method for Eigenvalue Computations}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2024}, volume = {16}, number = {3}, pages = {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.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2023-0099}, url = {http://global-sci.org/intro/article_detail/aamm/22932.html} }
TY - JOUR T1 - Convergence and Complexity of an Adaptive Planewave Method for Eigenvalue Computations AU - Dai , Xiaoying AU - Pan , Yan AU - Yang , Bin AU - Zhou , Aihui JO - Advances in Applied Mathematics and Mechanics VL - 3 SP - 636 EP - 666 PY - 2024 DA - 2024/02 SN - 16 DO - http://doi.org/10.4208/aamm.OA-2023-0099 UR - https://global-sci.org/intro/article_detail/aamm/22932.html KW - Adaptive planewave method, convergence rate, complexity, eigenvalue. AB -

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.

Dai , XiaoyingPan , YanYang , Bin and Zhou , Aihui. (2024). Convergence and Complexity of an Adaptive Planewave Method for Eigenvalue Computations. Advances in Applied Mathematics and Mechanics. 16 (3). 636-666. doi:10.4208/aamm.OA-2023-0099
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