数学系 Seminar 第1992期
报告主题：Higher order energy stable ETD based methods for gradient flows
报告人：王晓明 教授 （南方科技大学十大老品牌网赌网站数学系）
会议ID：873 777 5758
报告摘要：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.