论文标题
用于空间分数Cahn-Hilliard方程的有效的二阶能量稳定BDF方案
An efficient second-order energy stable BDF scheme for the space fractional Cahn-Hilliard equation
论文作者
论文摘要
与经典的cahn-hilliard模型相比，空间分数Cahn-Hilliard相位模型在形成和相变机理的描述中更为充分，更准确。在本文中，我们为空间分数Cahn-Hilliard模型提出了一个时间二阶能量稳定方案。该方案基于时间上的二阶向后分化公式和空间中有限的差异方法。分析了该方案的能量稳定性和收敛性，并在数值上说明了时间和空间中的最佳收敛顺序。请注意，该方案的系数矩阵是$ 2 \ times 2 $块矩阵，每个块中具有类似于toeplitz的结构。将这种特殊结构的优势与Krylov子空间方法相结合，旨在有效地解决该系统。据报道，数值示例说明了预处理的性能。
The space fractional Cahn-Hilliard phase-field model is more adequate and accurate in the description of the formation and phase change mechanism than the classical Cahn-Hilliard model. In this article, we propose a temporal second-order energy stable scheme for the space fractional Cahn-Hilliard model. The scheme is based on the second-order backward differentiation formula in time and a finite difference method in space. Energy stability and convergence of the scheme are analyzed, and the optimal convergence orders in time and space are illustrated numerically. Note that the coefficient matrix of the scheme is a $2 \times 2$ block matrix with a Toeplitz-like structure in each block. Combining the advantages of this special structure with a Krylov subspace method, a preconditioning technique is designed to solve the system efficiently. Numerical examples are reported to illustrate the performance of the preconditioned iteration.
