Superconvergence of projection integrators for conservative system

报告题目：Superconvergence of projection integrators for conservative system

报 告 人：王雨顺  南京师范大学教授博导

报告时间：4月13日  16:00-18:00

报告地点：明理楼C302B

报告人简介：

王雨顺，南京师范大学二级教授。长期从事保结构算法及其应用研究，主持7项国家基金委项目，同时作为主要成员参加科技部“863”课题、“973”项目、“863”计划、基金委重点等项目，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；获江苏省科技进步二等奖，江苏省数学成就奖、教育部自然科学二等奖，江苏省教学成果一等奖等奖项。专著《偏微分方程保结构算法》获得第三届中国政府出版奖-图书奖。现任期刊International Journal of Computer Mathematics、《计算数学》编委、大规模复杂系统数值模拟教育部重点实验室主任、江苏省“大数据建模、分析与计算”国际联合实验室常务副主任、江苏省数学学会计算数学分会理事长、江苏省工业与应用数学学会副理事长等。。

报告内容摘要：

Projection methods are applicable in many fields. It is a natural and practical approach to devise the invariant-preserving schemes for conservative systems. The idea is to project the solution of any underlying numerical scheme onto the manifold determined

by the invariant, and this process will be referred to as the projection integrator. Generally, the projection integrator chooses the gradient of invariant as its projection direction and has the same order as the underlying method. In this paper, we propose a different projection direction to construct a new projection integrator whose order is higher than the underlying method. According to this novel direction, we further summarize high-order projection integrators with superconvergence and rigorously prove the truncation error by utilizing the linear integral method as a central tool. Apart from the invariant-preserving property, symmetry is an important geometric property for reversible differential equations. The design and analysis of another high-order projection integrators with symmetry and superconvergence are also presented in this paper. Numerical experiments are provided to verify our theoretical results and illustrate that our proposed projection integrators have superior behaviors in a long time numerical simulation.

主办单位：理学院、人工智能研究院

非线性动力系统研究所、数理力学研究中心 

科学技术发展研究院