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.
 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.
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