The nonlocal Cahn-Hilliard (NCH) equation with nonlocal diffusion operator is more suitable for the simulation of microstructure phase transition than the local Cahn-Hilliard (LCH) equation. In this paper, based on the exponential semi-implicit scalar auxiliary variable (ESI-SAV) method, the highly effcient and accurate schemes in time with unconditional energy stability for solving the NCH equation are proposed. On the one hand, we have demostrated the unconditional energy stability for the NCH equation with its high-order semi-discrete schemes carefully and rigorously. On the other hand, in order to reduce the calculation and storage cost in numerical simulation, we use the fast solver based on FFT and FCG for spatial discretization. Some numerical simulations involving the Gaussian kernel are presented and show the stability, accuracy, efficiency and unconditional energy stability of the proposed schemes.

翻译：非局部扩散算子的非局部Cahn-Hilliard（NCH）方程相较于局部Cahn-Hilliard（LCH）方程更适用于微观结构相变模拟。本文基于指数半隐式标量辅助变量（ESI-SAV）方法，提出了求解NCH方程的高效高精度时间离散格式，该格式具有无条件能量稳定性。一方面，我们严谨且严格地证明了NCH方程的高阶半离散格式满足无条件能量稳定性；另一方面，为降低数值模拟中的计算与存储成本，采用基于快速傅里叶变换（FFT）和预处理共轭梯度法（FCG）的快速求解器进行空间离散。数值算例包含高斯核函数，结果验证了所提方法的稳定性、精度、效率及无条件能量稳定性。