论文标题
基于Ni的合金系统的平行能量稳定相场模拟
Parallel energy stable phase field simulations of Ni-based alloys system
论文作者
论文摘要
在本文中，我们研究了用于求解与自由能有关的基于镍的相位磁场系统的数值方法，包括弹性能量和对数型功能。为了应对特定自由能功能的挑战，我们提出了一个基于离散的变分衍生方法的半平滑方案，该方案无条件的能量稳定，并保持能量耗散法和群众保护法。由于半径方案的良好稳定性，采用自适应时间步长策略，可以根据问题的动态演变灵活地控制时间步长。引入了基于域分解的基于域分解的牛顿 - 克里洛夫 - 史克瓦尔兹方法，以解决每个时间步骤的离散化构建的非线性代数系统。数值实验表明，所提出的算法具有较大时间步长的能量稳定，并且高度可扩展到六千个处理器核心。
In this paper, we investigate numerical methods for solving Nickel-based phase field system related to free energy, including the elastic energy and logarithmic type functionals. To address the challenge posed by the particular free energy functional, we propose a semi-implicit scheme based on the discrete variational derivative method, which is unconditionally energy stable and maintains the energy dissipation law and the mass conservation law. Due to the good stability of the semi-implicit scheme, the adaptive time step strategy is adopted, which can flexibly control the time step according to the dynamic evolution of the problem. A domain decomposition based, parallel Newton--Krylov--Schwarz method is introduced to solve the nonlinear algebraic system constructed by the discretization at each time step. Numerical experiments show that the proposed algorithm is energy stable with large time steps, and highly scalable to six thousand processor cores.
