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(xué)
講座時(shí)間：2019年12月7日（周六）下午16:10--16:50
講座地點(diǎn)：數(shù)學(xué)院341
主辦單位：煙臺(tái)大學(xué)數(shù)學(xué)與信息科學(xué)學(xué)院
內(nèi)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(xué)數(shù)學(xué)與統(tǒng)計(jì)學(xué)院副教授，碩士生導(dǎo)師。2012年獲香港浸會(huì)大學(xué)博士學(xué)位，2016-2017年獲國(guó)家留學(xué)基金委資助赴美國(guó)南卡羅來(lái)納大學(xué)進(jìn)行學(xué)術(shù)交流。目前主要從事相場(chǎng)模型和無(wú)界區(qū)域上偏微分方程數(shù)值解法的研究工作。近年來(lái)先后主持國(guó)家自然科學(xué)基金、山東省自然科學(xué)基金3項(xiàng)，在J. Sci. Comput., Phys. Review E等雜志上發(fā)表論文多篇。
