Jingwei Sun

National University of Defense Technology | NUDT · Department of Mathematics and System Science

We consider the numerical approximations of the viscous Cahn–Hilliard equation with either the Ginzburg–Landau polynomial potential or Flory–Huggins logarithmic potential. One challenge in solving such a fourth-order-in-space system is to develop accurate temporal discretization to preserve the energy stability, mass conservation, and maximum princ...

In this work, we develop a class of up to eighth-order maximum-principle-preserving (MPP) methods for the Allen-Cahn equation. Beginning with the space-discrete system , we extend the integrating factor two-step Runge-Kutta (IFTSRK) methods and define sufficient conditions for the preservation of the discrete maximum principle. In particular, we co...

In this paper, we propose a novel energy dissipative method for the Allen-Cahn equation on nonuniform grids. For spatial discretization, the classical central difference method is utilized, while the average vector field method is applied for time discretization. Compared with the average vector field method on the uniform mesh, the proposed method...

Before proving (unconditional) energy stability for gradient flows, most existing studies either require a strong Lipschitz condition regarding the non-linearity or certain $L^{\infty}$ bounds on the numerical solutions (the maximum principle). However, proving energy stability without such premises is a very challenging task. In this paper, we aim...

相比于经典Allen--Cahn方程, 修正的Allen--Cahn方程由于加入了非局部拉格朗日乘子, 使得方程解的质量得以守恒. 本文针对守恒型Allen--Cahn方程构造一系列最高到八阶精度的保极值格式. 基于二阶有限差分空间离散, 我们提出一种高阶积分因子两步Runge--Kutta方法求解守恒型Allen--Cahn方程. 之后证明该格式可以保持守恒型Allen--Cahn方程的极值原理和质量守恒律, 并且给出数值格式的收敛性分析. 最后, 分别使用二维和三维数值实验来验证理论结果和数值格式的性能表现.