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 Average energy dissipation rates of explicit exponential Runge-Kutta methods for gradient flow problems

主讲人：廖洪林

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.

主讲人简介：廖洪林，理学博士，南京航空航天大学教授、博士生导师。2001年硕士毕业于解放军理工大学，2010年博士毕业于东南大学，2001-2017年在解放军理工大学任教。学术研究方向为偏微分积分方程数值解， 目前主要关注线性和非线性偏微分方程的时间变步长离散与时间自适应算法。 在 《Mathematics of Computation》, 《SIAM Journal on Numerical Analysis》,  《SIAM Journal on Scientific Computing》, 《IMA Journal of Numerical Analysis》、《Journal of Computational Physics》,《Science in China》等国内外重要期刊上发表学术论文50余篇。

邀请人：张诚坚

时间：2024年9月19日晚19:00--21:00

地点：线下：科技楼南楼706室；线上：腾讯会议号232819885