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 Original energy dissipation preserving corrections of integrating factor Runge-Kutta methods for gradient flow problems

主讲人：廖洪林

摘要：Explicit integrating factor Runge-Kutta methods are attractive and popular in developing high-order maximum bound principle preserving time-stepping schemes for Allen-Cahn type gradient flows. However, they always suffer from the non-preservation of steady-state solution and original energy dissipation law. To overcome these disadvantages, some new integrating factor methods are developed by using two classes of difference correction, including the telescopic correction and nonlinear-term translation correction, enforcing the preservation of steady-state solution. Then the original energy dissipation properties of the new methods are examined by using the associated differential forms and the differentiation matrices. As applications, some new integrating factor Runge-Kutta methods up to third-order maintaining the original energy dissipation law are constructed by applying the difference correction strategies to some popular explicit integrating factor methods in the literature. Extensive numerical experiments are presented to support our theory and to demonstrate the improved performance of new methods.

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21:00--23:00

地点：线下：科技楼南楼706室；线上：腾讯会议号232819885