报告题目：Fourth-order accurate energy dissipation schemes for solving gradient flows
报告人：张弘副教授（国防科技大学）
时间：2024年9月25日16:00-17:00
地点：数学学院207
报告摘要：
We propose and analyze a class of temporally up-to-fourth-order, unconditionally energy dissipation schemes for solving gradient flow equations, with Fourier pseudo-spectral spatial discretization. A linear stabilization term is introduced to the physical model, and an exponential-free Runge--Kutta (EFRK) framework is developed in the time direction. The EFRK framework replaces exponential functions in the integrating factor Runge--Kutta approach with carefully designed recursive approximations, exhibiting favorable properties such as the preservation of equilibria, absence of time step constraints, and computational convenience in the Fourier space. By employing a unified strategy with a sufficient large stabilization parameter, we prove that the original energy obtained by EFRK schemes, without any numerical correction term, is non-increasing for any time step. The provable dissipation of the original energy is the first such result for a fourth-order accurate scheme for a gradient flow. Numerical experiments are demonstrated, which validate the high-order accuracy, energy stability, and efficiency of the proposed schemes.
报告人简介：
张弘，国防科技大学数学系副教授，硕士生导师。2012年毕业于浙江大学数学系，2018年获荷兰乌特勒支大学数学博士学位。主要从事偏微分方程保结构算法、自适应移动网格方法的研究。在CMAME，SISC，JCP，JSC等期刊发表论文40余篇，入选国防科技大学高层次创新人才、湖南省荷尖人才、湖湘青年英才。主持国家自然科学基金面上项目、军科委173项目等。
