Structure preserving numerical methods for phase-field equations
报告题目：Structure preserving numerical methods for phase-field equations
报告专家：杨将 教授（南方科技大学）
报告时间：2022年11月23日 16:00—17:00
报告地点：腾讯会议，317-532-445，无密码
报告摘要：Phase-field equations have intrinsic structures such as energy dissipation, maximum principle. It is desirable, sometimes necessary, to preserve these structures in a numerical scheme. 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.
专家简介：杨将，现为南方科技大学数学系副教授。分别于2010年和2014年在浙江大学和香港浸会大学取得学士学位和博士学位，并于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，随后在南方科技大学工作至今。从事计算数学方向的研究，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。主持广东省自然科学基金项目1项、国家自然科学基金面上项目2项。共发表论文30余篇，包括SIAM Review、SINUM、SISC、JCP、SIAP等计算数学领域国际知名期刊。
邀请人：贺巧琳