报告题目：Unconditionally energy-decreasing high-order stabilized Implicit-Explicit Runge--Kutta methods for phase-field models
报告人：杨将 副教授（南方科技大学）
邀请人：宋怀玲
时间：5月30日10:00-11:00
腾讯会议：381-857-427（无密码）
报告摘要：Phase field models attract much attention these years. The energy naturally decreases along the direction of gradient flows, so it is rather significant for numerical methods to preserve this intrinsic structure. In order to guarantee the energy dissipation, various numerical schemes have been developed and among them, a simple but vital approach is implicit-explicit (IMEX) Runge--Kutta (RK) method. In this paper we prove that a class of high-order stabilized IMEX RK schemes unconditionally preserve the energy dissipation law for phase-field models with Lipschitz nonlinearity. A simple systematic condition is established to determine the nonlinear energy decaying property. This is the first work to prove that a high-order linear scheme can guarantee the dissipation of the original energy unconditionally. We also obtain the error estimate to show the convergence and accuracy. In the end, we give some concrete IMEX RK schemes as examples.
报告人简介：
杨将，现为南方科技大学数学系副教授，2014年博士于毕业于香港浸会大学数学系，2014-2017年在宾夕法尼亚州立大学和哥伦比亚大学从事博士后研究工作；研究方向为计算数学，主要研究兴趣包括关于相场模型和非局部模型的建模、计算与应用。在计算数学领域发表论文30余篇，含SIAM Review, SIAM Journal on Scientific Computing, SIAM Journal on Numerical Analysis, Journal of Computational Physics等期刊。2018年入选了国家特聘青年专家。
