報(bào)告題目：Superconvergence of projection integrators for conservative system

報(bào) 告 人：王雨順  南京師范大學(xué)教授博導(dǎo)

報(bào)告時(shí)間：4月13日  16:00-18:00

報(bào)告地點(diǎn)：明理樓C302B

報(bào)告人簡介：

王雨順，南京師范大學(xué)二級教授。長期從事保結(jié)構(gòu)算法及其應(yīng)用研究，主持7項(xiàng)國家基金委項(xiàng)目，同時(shí)作為主要成員參加科技部“863”課題、“973”項(xiàng)目、“863”計(jì)劃、基金委重點(diǎn)等項(xiàng)目，入選江蘇省“333”工程、青藍(lán)工程學(xué)術(shù)帶頭人、江蘇省“六大人才高峰”高層次人才；江蘇省創(chuàng)新團(tuán)隊(duì)主持人；獲江蘇省科技進(jìn)步二等獎(jiǎng)，江蘇省數(shù)學(xué)成就獎(jiǎng)、教育部自然科學(xué)二等獎(jiǎng)，江蘇省教學(xué)成果一等獎(jiǎng)等獎(jiǎng)項(xiàng)。專著《偏微分方程保結(jié)構(gòu)算法》獲得第三屆中國政府出版獎(jiǎng)-圖書獎(jiǎng)。現(xiàn)任期刊International Journal of Computer Mathematics、《計(jì)算數(shù)學(xué)》編委、大規(guī)模復(fù)雜系統(tǒng)數(shù)值模擬教育部重點(diǎn)實(shí)驗(yàn)室主任、江蘇省“大數(shù)據(jù)建模、分析與計(jì)算”國際聯(lián)合實(shí)驗(yàn)室常務(wù)副主任、江蘇省數(shù)學(xué)學(xué)會(huì)計(jì)算數(shù)學(xué)分會(huì)理事長、江蘇省工業(yè)與應(yīng)用數(shù)學(xué)學(xué)會(huì)副理事長等。。

報(bào)告內(nèi)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.

主辦單位：理學(xué)院、人工智能研究院

非線性動(dòng)力系統(tǒng)研究所、數(shù)理力學(xué)研究中心 

科學(xué)技術(shù)發(fā)展研究院