An accelerated method for computing stationary states of multicomponent phase field crystal model
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Finding the stationary states of a free energy functional is an essential topic in multicomponent material systems. In this paper, we propose a class of efficient numerical algorithms to fast compute the stationary states of multicomponent phase field crystal model. Our approach formulates the problem as solving a constrained non-convex minimization problem. By using the block structure of multicomponent systems, we propose an adaptive block Bregman proximal gradient algorithm that updates each order parameter alternatively. The updating block can be chosen in a deterministic or random manner. The convergence property of the proposed algorithm is established without the requirement of global Lipschitz constant. The numerical results on computing stationary periodic crystals and quasicrystals in the multicomponent coupled-mode Swift-Hohenberg model have shown the significant acceleration over many existing methods.
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