论文标题
耦合艾伦 - 卡恩和卡恩 - 希利亚德系统的平行能量稳定求解器
Parallel energy-stable solver for a coupled Allen-Cahn and Cahn-Hilliard system
论文作者
论文摘要
在本文中，我们研究了用于求解与对数类型的自由能函数相关的耦合的allen-cahn/cahn-hilliard系统的数值方法。为了应对特殊的自由能功能所带来的挑战，我们提出了一种方法，以近似多项式形式的离散变化衍生物，以使相应的有限差方案无条件的能量稳定，并维持了能量耗散定律。为了进一步提高算法的性能，采用了修改的自适应时间步进策略，以便可以根据问题的动态演变来灵活地控制时间步长。为了在并行计算机上实现高性能，我们引入了基于域分解的，平行的牛顿 - 克里洛夫 - 塞瓦尔兹方法，以求解每个时间步骤中离散化构建的非线性代数系统。数值实验表明，所提出的算法在空间和时间上都是二阶精确的，能量稳定，具有较大的时间步长，并且在Sunway Taihulight Supercuter上高度可扩展到超过一千多个处理器核心。
In this paper, we study numerical methods for solving the coupled Allen-Cahn/Cahn-Hilliard system associated with a free energy functional of logarithmic type. To tackle the challenge posed by the special free energy functional, we propose a method to approximate the discrete variational derivatives in polynomial forms, such that the corresponding finite difference scheme is unconditionally energy stable and the energy dissipation law is maintained. To further improve the performance of the algorithm, a modified adaptive time stepping strategy is adopted such that the time step size can be flexibly controlled based on the dynamical evolution of the problem. To achieve high performance on parallel computers, we introduce a domain decomposition based, parallel Newton-Krylov-Schwarz method to solve the nonlinear algebraic system constructed from the discretization at each time step. Numerical experiments show that the proposed algorithm is second-order accurate in both space and time, energy stable with large time steps, and highly scalable to over ten thousands processor cores on the Sunway TaihuLight supercomputer.
