講座主題：An efficient second-order linear scheme for the phase field model of corrosive dissolution
主持人：李宏偉
工作單位：山東師范大學
講座時間：2019年12月7日（周六）下午16:10--16:50
講座地點：數學院341
主辦單位：煙臺大學數學與信息科學學院
內容摘要：
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.
主講人介紹：
山東師范大學數學與統計學院副教授，碩士生導師。2012年獲香港浸會大學博士學位，2016-2017年獲國家留學基金委資助赴美國南卡羅來納大學進行學術交流。目前主要從事相場模型和無界區域上偏微分方程數值解法的研究工作。近年來先后主持國家自然科學基金、山東省自然科學基金3項，在J. Sci. Comput., Phys. Review E等雜志上發表論文多篇。
