报告人：廖洪林 (南京航空航天大学)
报告时间：2025年10月30日（星期四）19:30-22:00
报告地点：腾讯会议：391 373 880
报告摘要：One of main obstacles in verifying the energy dissipation laws of implicit-explicit Runge-Kutta (IERK) methods for phase field equations is to establish the uniform boundedness of stage solutions without the global Lipschitz continuity assumption of nonlinear bulk. With the help of discrete orthogonal convolution kernels, an updated time-space splitting technique is developed to establish the uniform boundedness of stage solutions for a refined class of IERK methods in which the associated differentiation matrices and the average dissipation rates are always independent of the time-space discretization meshes. This makes the refined IERK methods highly advantageous in self-adaptive time-stepping procedures as some larger adaptive step-sizes in actual simulations become possible. From the perspective of optimizing the average dissipation rate, we construct some parameterized refined IERK methods up to third-order accuracy, in which the involved diagonally implicit Runge-Kutta methods for the implicit part have an explicit first stage and allow a stage-order of two such that they are not necessarily algebraically stable. Then we are able to establish, for the first time, the original energy dissipation law and the unconditional $L^2$ norm convergence. Extensive numerical tests are presented to support our theory.
报告人简介：廖洪林，应用数学博士，2018年至今任教于南京航空航天大学数学学院。2010年在东南大学获理学博士学位，2001-2017年任教于原解放军理工大学。长期从事偏微分方程数值解的研究和教学工作，形成了诸如离散互补卷积核、离散正交卷积核等离散分析工具，在非均匀以及高阶时间离散格式方面形成了一套独具特色的算法设计与理论分析方法。目前侧重于非线性相场、不可压Navier-Stokes模型和多相流耦合系统高阶时间自适应算法的设计与理论分析，在MCOM、SINUM、SISC、JCP、SCM等国内外计算数学高水平期刊上发表学术研究论文六十余篇。
邀请人：王季红
