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The nonlocal Cahn-Hilliard (NCH) equation with nonlocal diffusion operator ismore suitable for the simulation of microstructure phase transition than thelocal Cahn-Hilliard (LCH) equation. In this paper, based on the exponentialsemi-implicit scalar auxiliary variable (ESI-SAV) method, the highly effcientand accurate schemes in time with unconditional energy stability for solvingthe NCH equation are proposed. On the one hand, we have demostrated theunconditional energy stability for the NCH equation with its high-ordersemi-discrete schemes carefully and rigorously. On the other hand, in order toreduce the calculation and storage cost in numerical simulation, we use thefast solver based on FFT and FCG for spatial discretization. Some numericalsimulations involving the Gaussian kernel are presented and show the stability,accuracy, efficiency and unconditional energy stability of the proposedschemes.

The high-order exponential semi-implicit scalar auxiliary variable approach for nonlocal Cahn-Hilliard equation