Series of Academic Activities of School and Institute of Mathematics in 2020（the 206th）：
Wang Xiaoming Professor Southern University of Science and Technology
Report title: Higher Order Energy Stable ETD Based Methods for Gradient Flows
Reporter: Professor Wang Xiaoming, Southern University of Science and Technology
Report time: September 11, 2020 10:00
Report location: Conference room on the third floor of the School of Mathematics
School contact: Zhang Ran zhangran@jlu.edu.cn
Report summary：
Many natural and engineering problems follow gradient flow structures in the sense that systems evolve to decrease certain energy. The dynamics of most of these gradient systems are complicated and hence numerical methods are called for. There are at least two desirable features for numerical algorithms for gradient flows with long evolution process: efficient higher oder in time, and long-time stability. We present a class of efficient higher-order energy stable methods for a class of gradient flows based on the exponential time differencing (ETD) method combined with multi-step methods and interpolation. As a specific example, we present a third order ETD based scheme for thin film epitaxial growth model together with numerical results establishing the convergence and stability of the scheme, and the ability of the scheme to capture long-time scaling properties of the system.
Brief introduction of the speaker:
Wang Xiaoming graduated from Fudan University with a bachelor and master degree and a Ph.D. from Indiana University Bloomington. His main research direction is the application of partial differential equations and numerical methods. He has published more than 90 papers in journals such as CPAM, JFM, SINUM, etc. He is also a national talent recognized by the Ministry, who previously worked at New York Courant Institute, Princeton Institute for Advanced Study, Iowa State University, Fudan University. Before returning to China, he was appointed full professor and dean of the Department of Mathematics as the Dean of Florida State University. He is currently the dean and chair professor of the Department of Mathematics at Southern University of Science and Technology.
