Speaker: Prof. Xiaoming Wang (王晓明教授)

Time: 11:00-12:00, 22 Octorber 2021 (Friday) (Beijing time)

Venue: 华信书院，CC126

Abstract

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 several desirable features for numerical algorithms for gradient flows with long evolution process: 1. efficiency; 2. higher-order accuracy; and 3. long-time stability. We present a class of efficient higher-order energy stable variable step 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.

About Prof. Wang

王晓明本科及硕士毕业于复旦大学，博士毕业于印第安纳大学布卢明顿分校，主要研究方向为应用偏微分方程及其数值方法，在CPAM、JFM、SINUM、JCP等杂志发表论文90多篇，系中组部认定的国家级人才 。曾任职纽约库朗研究所、普林斯顿高等研究院、爱荷华州立大学、复旦大学。回国前为美国佛罗里达州立大学长聘正教授和数学系系主任，现任南方科技大学数学系系主任、讲席教授、深圳国家应数中心执行主任。