报告题目 Discrete maximum principle of exponential time differencing schemes for nonlocal Allen-Cahn equations

报告人：乔中华教授

报告地点：郑州大学数学与统计学院金融实验室

报告时间：2018年4月3日16:00---17:00点

报告摘要

In this work, we construct exponential time differencing (ETD) schemes for solving the nonlocal Allen-Cahn (NAC) equation. Since the solution to the NAC equation satisfies the maximum principle, numerical approximations preserving the maximum principle in the discrete sense are highly desirable at both physical and mathematical levels. Our numerical schemes are obtained by using the quadrature-based finite difference method for the spatial discretization and applying ETD-based approximations on the temporal integration. We establish the discrete maximum principle by using the properties of matrix exponentials, and then the energy stability and the maximum-norm error estimates are obtained in the discrete sense. In addition, we also prove the asymptotic compatibility of the proposed scheme, which implies the robustness of numerical approximations to the NAC equation. The convergence rates are verified numerically with respect to the discretization and the nonlocal parameters. A further numerical investigation is carried out for the steady state solutions on the relationship between the discontinuities and the nonlocal parameters.

乔中华教授简介

·2006年香港浸会大学博士毕业，获得The 2013-2014 Early Career Award,（ The Research Grants Council of Hong Kong），从事数值分析和科学计算，在相场方程方面有很深造诣。