报告题目：Average energy dissipation rates of explicit exponential Runge-Kutta methods for gradient flow problems
报告人：王旭平
报告摘要：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.
报告人简介：王旭平，博士后，2023年至今就职于南京航空航天大学数学学院。2023年于东南大学获理学博士学位。学术研究方向为微分方程数值解，目前主要关注相场模型的时间变步长离散与自适应算法、基于指数积分的Runge-Kutta方法, 在Advances in Computational Mathematics, Numerical Methods for Partial Differential Equations, Applied Mathematics Letters等期刊上发表学术研究论文六篇。
时间：2024年5月23日19:30
地点：教科楼B座863
邀请人：任金城
主办单位：数学与信息科学学院
