TY - JOUR
T1 - Efficient Numerical Methods for Computing Stationary States of Spherical Landau-Brazovskii Model
AU - Qiu , Qun
AU - Si , Wei
AU - Ji , Guanghua
AU - Jiang , Kai
JO - CSIAM Transactions on Applied Mathematics
VL - 3
SP - 435
EP - 467
PY - 2025
DA - 2025/09
SN - 6
DO - http://doi.org/10.4208/csiam-am.SO-2023-0038
UR - https://global-sci.org/intro/article_detail/csiam-am/24371.html
KW - Spherical Landau-Brazovskii model, stationary states, spherical harmonic expansion, optimization methods, principal mode analysis.
AB - <p style="text-align: justify;">In this paper, we develop a set of efficient methods to compute stationary
states of the spherical Landau-Brazovskii (LB) model in a discretization-then-optimization way. First, we discretize the spherical LB energy functional into a finite-dimensional energy function by the spherical harmonic expansion. Then five optimization
methods are developed to compute stationary states of the discretized energy function, including the accelerated adaptive Bregman proximal gradient, Nesterov, adaptive Nesterov, adaptive nonlinear conjugate gradient and adaptive gradient descent
methods. To speed up the convergence, we propose a principal mode analysis (PMA)
method to estimate good initial configurations and sphere radius. The PMA method
also reveals the relationship between the optimal sphere radius and the dominant degree of spherical harmonics. Numerical experiments show that our approaches significantly reduce the number of iterations and the computational time.</p>