Efficient numerical methods for computing stationary states of spherical Landau-Brazovskii model
For researchers studying pattern formation on spherical surfaces, this work provides faster computational tools for the Landau-Brazovskii model, though the methods are domain-specific and incremental in nature.
The paper develops efficient numerical methods for computing stationary states of the spherical Landau-Brazovskii model, achieving significant reductions in iteration count and computational time through a combination of spherical harmonic discretization, five optimization methods, and a principal mode analysis for initial estimation.
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