学术报告会：Average energy dissipation rates of explicit exponential Runge-Kutta methods for gradient flow problems

报告题目：Average energy dissipation rates of explicit exponential Runge-Kutta methods for gradient flow problems

报 告 人：廖洪林   （南京航空航天大学   教授）

报告时间：2026年3月13日周五09：30

报告地点：S3-502

Abstract：We propose a unified theoretical framework to examine the energy dissipation properties at all stages of explicit exponential Runge-Kutta (EERK) methods for gradient flow problems. The main part of the novel framework is to construct the differential form of EERK method by using the difference coefficients of method and the so-called discrete orthogonal convolution kernels. As the main result, we prove that an EERK method can preserve the original energy dissipation law unconditionally if the associated differentiation matrix is positive semi-definite. A simple indicator, namely average dissipation rate, is also introduced for these multi-stage methods to evaluate the overall energy dissipation rate of an EERK method such that one can choose proper parameters in some parameterized EERK methods or compare different kinds of EERK methods. Some existing EERK methods in the literature are evaluated from the perspective of preserving the original energy dissipation law and the energy dissipation rate. Some numerical examples are also included to support our theory.

个人简介：

廖洪林，应用数学博士、教授、博士生导师，2018年至今任教于南京航空航天大学数学学院。2010年获理学博士学位，2001-2017年任教于原解放军理工大学、陆军工程大学。学术研究方向为偏微分方程数值解，目前主要关注非线性偏微分方程的变步长时间离散与时间自适应算法，在Math Comp，SIAM J Numer Anal, SIAM J Sci Comput，IMA J Numer Anal，J Comput Phys，Sci China Math等国内外专业期刊上发表学术研究论文五十余篇。相关研究工作得到了国内外同行的广泛关注与认可、引发了很多后续研究工作，在WOS上他引3000余次。近年来有15篇研究论文入选ESI高被引论文，2024-2025连续入选Elsevier全球前2%顶尖科学家年度榜单、2025年入选Clarivate全球高被引研究者榜单。