In this article, we present an unconditional energy stable numerical method for the coupled Cahn–Hilliard system for homopolymer and copolymer mixtures in two- and three-dimensional spaces. By combining a Crank–Nicolson-type method with a nonlinearly stabilized splitting method, a second-order accurate numerical scheme is constructed. To efficiently solve the discrete system, we use a fast iterative Fourier transform method. We prove the unconditional energy stability of the proposed method. Therefore, a large time step can be adopted. Various numerical experiments are performed to prove the performance of the proposed scheme.

中文翻译：

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共聚物/均聚物混合物中耦合 Cahn-Hilliard 系统的无条件能量稳定二阶时间精确数值方案

在本文中，我们针对二维和三维空间中的均聚物和共聚物混合物的耦合 Cahn-Hilliard 系统提出了一种无条件能量稳定数值方法。通过将 Crank-Nicolson 型方法与非线性稳定分裂方法相结合，构建了二阶精确数值方案。为了有效地求解离散系统，我们使用快速迭代傅立叶变换方法。我们证明了所提出方法的无条件能量稳定性。因此，可以采用大的时间步长。进行了各种数值实验以证明所提出方案的性能。