报告题目：Quadratic Auxiliary Variable Runge-Kutta Methods for the Camassa-Holm Equation
报告人：王雨顺
工作单位：南京师范大学数学科学学院 报告时间：2021-11-23 10:00-12:00；
腾讯会议ID：411 329 349
报告摘要：In this talk, we present a novel class of Runge-Kutta methods for the Camassa-Holm equation, which is named quadratic auxiliary variable Runge-Kutta (QAVRK) methods. We introduce an auxiliary variable that satisfies a quadratic equation and rewrite the original energy into a quadratic functional. With the aid of the energy variational principle, the original system is then reformulated into an equivalent form with two strong quadratic invariants, where one is induced by the quadratic auxiliary variable and the other is the modified energy. Staring from the equivalent model, we employ RK methods satisfying the symplectic condition for time discretization, which naturally conserve all strong quadratic invariants of the new system. The resulting methods are shown to inherit the relationship between the auxiliary variable and the original one, and thus can be simplified by eliminating the auxiliary variable, which leads to a new of QAVRK schemes. Furthermore, the QAVRK methods are proved rigorously to preserve the original energy conservation law. Numerical examples are presented to confirm the expected order of accuracy, conservative property and efficiency of the proposed schemes. This numerical strategy makes it possible to directly apply the symplectic RK methods to develop energy-preserving algorithms for general conservation systems with any polynomial energy.
报告人简介：王雨顺，南京师范大学教授。98-01年就读于中科院计算数学所，01-04年在中科院大气物理所作博士后研究，04年起在南京师范大学数科院工作。长期从事保结构算法及其应用研究，发表论文100多篇，入选江苏省“333”工程、青蓝工程学术带头人、江苏省“六大人才高峰”高层次人才；江苏省创新团队主持人；获得江苏省科技进步奖，江苏省数学成就奖。专著《偏微分方程保结构算法》获得中国政府图书奖。
