讲座主题：An efficient second-order linear scheme for the phase field model of corrosive dissolution

主持人：李宏伟

工作单位：山东师范大学

讲座时间：2019年12月7日（周六）下午16:10--16:50

讲座地点：数学院341

主办单位：烟台大学数学与信息科学学院

内容摘要：

We propose an efficient numerical scheme for solving the phase field model (PFM) of corrosive dissolution that is linear and second-order accurate in both time and space. The PFM of corrosion is based on the gradient flow of a free energy functional depending on a phase field variable and a single concentration variable. While classic backward differentiation formula (BDF) schemes have been used for time discretization in the literature, they require very small time step sizes owing to the strong numerical stiffness and nonlinearity of the parabolic partial differential equation (PDE) system defining the PFM. Based on the observation that the governing equation corresponding to the phase field variable is very stiff due to the reaction term, the key idea of this paper is to employ an exponential time integrator that is more effective for stiff dynamic PDEs. By combining the exponential integrator based Rosenbrock--Euler scheme with the classic Crank--Nicolson scheme for temporal integration of the spatially semi-discretized system, we develop a decoupled linear numerical scheme that alleviates the time step size restriction due to high stiffness. Several numerical examples are presented to demonstrate accuracy, efficiency and robustness of the proposed scheme in two-dimensions, and we find that a time step size of $10^{-3}$ second for meshes with the typical spatial resolution $1~\mu$m is stable. Additionally, the proposed scheme is robust and does not suffer from any convergence issues often encountered by nonlinear Newton methods.

主讲人介绍：

山东师范大学数学与统计学院副教授，硕士生导师。2012年获香港浸会大学博士学位，2016-2017年获国家留学基金委资助赴美国南卡罗来纳大学进行学术交流。目前主要从事相场模型和无界区域上偏微分方程数值解法的研究工作。近年来先后主持国家自然科学基金、山东省自然科学基金3项，在J. Sci. Comput., Phys. Review E等杂志上发表论文多篇。