题目一：Geometric Integrators for Differential Equations with HighlyOscillatory Solutions
主讲人：吴新元教授、博士生导师
工作单位：南京大学数学系
时间：2021年5月14号10:00
地点：文理楼254
摘要：The idea of Geometric Numerical Integration appeared in the 1980’s. The new paradigm brought many innovative changes. The new paradigm wanted to identify the long-time behaviour of the solutions or perhaps the existence of conservation laws or some other qualitative feature of the dynamics. Another area that has kept growing in importance within Geometric Numerical Integration is the study of highly-oscillatory problems: problems where the solutions are periodic or quasiperiodic and have to be studied in time intervals that include an extremely large number of periods. As is known, these problems cannot be solved efficiently using conventional methods. A further study of novel geometric integrators has become increasingly important in recent years. The objective of this talk is to present geometric integrators for highly oscillatory problems that can be formulated as systems of ordinary and partial differential equations, and will focus on oscillation-preserving integrators for systems of second-order ordinary differential equations with highly oscillatory solutions.
题目二：From quadrature formulae for integrals to numerical schemes for differential equations
主讲人：吴新元教授、博士生导师
工作单位：南京大学数学系
时间：2021年5月14号14:00
地点：文理楼254
摘要：This talk focuses on applications of quadrature formulae for evaluating definite integrals to the design of numerical schemes for solving differential equations, also including the geometric numerical integrators in the sense of structure preservation. The presentation of this talk will provide some new perspectives concerning the relation between quadrature formulae for integrals and numerical schemes for differential equations.
报告人简介：
吴新元，南京大学教授、博士生导师、曾任中国计算数学会理事、中国仿真学会仿真算法专业委员会委员、江苏省计算数学会常务理事、《高等学校计算数学学报》编委。2002年1月—2003年1月德国图宾根大学数学院访问教授；2004年7月—8月新西兰奥克兰大学数学系访问教授；2014年7月—8月英国剑桥大学应用数学与理论物理系访问教授。主要从事微分方程几何算法研究，多次主持国家自然科学面上基金，教育部博士点博导类基金，自然科学基金委与英国皇家学会国际交流与合作基金项目，聘请外国专家重点项目（国批）。多次获得国家科学技术学术著作出版基金项目。在国际权威出版社Springer出版学术专著四部，并且赢得了美国数学会数学评论《Mathematical Reviews》的高度评价。在SIAM Numer. Anal.、SIAM Sci. Comput.、Found. Comput. Math. 等国际顶级SCI期刊上发表了一系列高质量的学术论文。多次应邀到英国剑桥大学、伦敦帝国理工学院、美国普渡大学、加拿大麦吉尔大学、德国图宾根大学、新西兰奥克兰大学等国际著名高等学府进行学术访问并作报告。2017年荣获欧洲科学与工程计算方法学会颁发的最高荣誉奖：“Honorary Fellowship”。2021年荣获Vebleo科学家奖。
理学院 科技处