An Adaptive Block Bregman Proximal Gradient Method for Computing Stationary States of Multicomponent Phase-Field Crystal Model
Year: 2022
Author: Chenglong Bao, Chang Chen, Kai Jiang
CSIAM Transactions on Applied Mathematics, Vol. 3 (2022), Iss. 1 : pp. 133–171
Abstract
In this paper, we compute the stationary states of the multicomponent phase-field crystal model by formulating it as a block constrained minimization problem. The original infinite-dimensional non-convex minimization problem is approximated by a finite-dimensional constrained non-convex minimization problem after an appropriate spatial discretization. To efficiently solve the above optimization problem, we propose a so-called adaptive block Bregman proximal gradient (AB-BPG) algorithm that fully exploits the problem’s block structure. The proposed method updates each order parameter alternatively, and the update order of blocks can be chosen in a deterministic or random manner. Besides, we choose the step size by developing a practical linear search approach such that the generated sequence either keeps energy dissipation or has a controllable subsequence with energy dissipation. The convergence property of the proposed method is established without the requirement of global Lipschitz continuity of the derivative of the bulk energy part by using the Bregman divergence. The numerical results on computing stationary ordered structures in binary, ternary, and quinary component coupled-mode Swift-Hohenberg models have shown a significant acceleration over many existing methods.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/csiam-am.SO-2021-0002
CSIAM Transactions on Applied Mathematics, Vol. 3 (2022), Iss. 1 : pp. 133–171
Published online: 2022-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 39
Keywords: Multicomponent coupled-mode Swift-Hohenberg model stationary states adaptive block Bregman proximal gradient algorithm convergence analysis adaptive step size.
Author Details
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Convergence Analysis for Bregman Iterations in Minimizing a Class of Landau Free Energy Functionals
Bao, Chenglong
Chen, Chang
Jiang, Kai
Qiu, Lingyun
SIAM Journal on Numerical Analysis, Vol. 62 (2024), Iss. 1 P.476
https://doi.org/10.1137/22M1517664 [Citations: 2]