An Adaptive Block Bregman Proximal Gradient Method for Computing Stationary States of Multicomponent Phase-Field Crystal Model

In this paper, we compute the stationary states of multicomponent phase-field crystal model by formulating it as a block constrained minimization problem. The original infinite-dimensional non-convex problem is approximated finite-dimensional after an appropriate spatial discretization. To efficiently solve above optimization problem, propose so-called adaptive Bregman proximal gradient (AB-BPG) algorithm that fully exploits problem's structure. proposed method updates each order parameter alternatively, and update blocks can be chosen in deterministic or random manner. Besides, choose step size developing practical linear search approach such generated sequence either keeps energy dissipation has controllable subsequence with dissipation. convergence property established without requirement global Lipschitz continuity derivative bulk part using divergence. numerical results on computing ordered structures binary, ternary, quinary component coupled-mode Swift-Hohenberg models have shown significant acceleration over many existing methods.