The Stabilized Exponential-SAV Approach Preserving Maximum Bound Principle For Nonlocal Allen-Cahn Equation

The nonlocal Allen-Cahn equation with nonlocal diffusion operator is a generalization of the classical Allen-Cahn equation,which also satisfies the energy dissipation law and the maximum bound principle.This model can more accurately describe the mechanism of phase transition of microstructure and is of great significance for simulating a series of physical and biological phenomena involving long-distance interactions in space.The appearance of nonlocal operators obviously increases the calculation cost,therefore it is necessary to establish an efficient and stable numerical algorithm for this system.The main content of this paper is to construct first order and second order temporal accuracy numerical schemes for nonlocal Allen-Cahn model based on the stabilized exponential scalar auxiliary variable method.On the one hand,by implicit approximation of linear terms and explicit treatment of nonlinear terms,a decoupled system of linear equations is obtained,which avoids iterative calculation.On the other hand,we carry out numerical theoretical analysis at the fully discrete level.We not only carefully and strictly prove the maximum bound principle and unconditional energy stability of the two schemes at discrete level,but also give the optimal error estimation under the L∞ norm.Finally,several typical numerical experiments are carried out with a Gaussian kernel nonlocal operator as example,and different typical numerical examples are used to verify the accuracy and effectiveness of the proposed algorithm.