TY - JOUR
T1 - An Adaptive Block Bregman Proximal Gradient Method for Computing Stationary States of Multicomponent Phase-Field Crystal Model
AU - Bao , Chenglong
AU - Chen , Chang
AU - Jiang , Kai
JO - CSIAM Transactions on Applied Mathematics
VL - 1
SP - 133
EP - 171
PY - 2022
DA - 2022/03
SN - 3
DO - http://doi.org/10.4208/csiam-am.SO-2021-0002
UR - https://global-sci.org/intro/article_detail/csiam-am/20292.html
KW - Multicomponent coupled-mode Swift-Hohenberg model, stationary states, adaptive block Bregman proximal gradient algorithm, convergence analysis, adaptive step size.
AB - <p style="text-align: justify;">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.</p>