講座主題：Superconvergence of projection integrators for conservative system
專家姓名：王雨順
工作單位：南京師范大學
講座時間：2024年06月30日10:30-12:00
講座地點：數學院大會議室341
主辦單位：煙臺大學數學與信息科學學院
內容摘要：
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.
主講人介紹：
王雨順，南京師范大學二級教授。長期從事保結構算法及其應用研究，主持7項國家基金委項目，同時作為主要成員參加科技部“863”課題、“973”項目、“863”計劃、基金委重點等項目，入選江蘇省“333”工程、青藍工程學術帶頭人、江蘇省“六大人才高峰”高層次人才；江蘇省創新團隊主持人；獲江蘇省科技進步二等獎，江蘇省數學成就獎、教育部自然科學二等獎，江蘇省教學成果一等獎等獎項。專著《偏微分方程保結構算法》獲得第三屆中國政府出版獎-圖書獎。現任期刊International Journal of Computer Mathematics、《計算數學》編委、大規模復雜系統數值模擬教育部重點實驗室主任、江蘇省“大數據建模、分析與計算”國際聯合實驗室常務副主任、江蘇省數學學會計算數學分會理事長、江蘇省工業與應用數學學會副理事長等。
