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Structure preserving numerical methods for phase-field equations

主讲人：杨将

摘要：Phase-field equations have intrinsic structures, such as energy dissipation, maximum principle. It is desirable, sometimes necessary, to preserve these structures in numerical schemes. In the first part of this talk, the SAV approach is present to deal with nonlinear terms in a large class of gradient flows. It leads to linear and unconditionally energy stable schemes which only require to solve decoupled linear equations with constant coefficients. We also present several one-step methods to preserve the original energy decaying property, including second-order ETDRK and high-order IMEX-RK.  In the second part, we establish a framework of monotone schemes for the Allen-Cahn equations, in which only several concise and reasonable conditions are assumed. These conditions can guarantee both the unique solvability and the maximum principle. A cut-off technique is also introduced to preserve the maximum principle. In the end, we apply these structure preserving numerical schemes to shape optimization. Several numerical examples demonstrate the efficiency and effectiveness of these numerical schemes.

主讲人简介：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。

邀请人：李东方

时间：：2022年8月22日（星期一）15:00-17:00

地点：腾讯会议室     ID:346 187 426