清华主页 EN
导航菜单

动力系统几何算法

来源: 03-15

时间:09:50 - 12:15, every Tuesday, 3/15/2022 - 7/5/2022

地点:1110&Zoom ID:361 038 6975,密码:BIMSA

组织者:尚在久

主讲人:尚在久

 要:

Geometric numerical integration of dynamical systems or structure-preserving method for ordinary differential equations has become a vital area of numerical analysis since 1980’s. The key idea is that one should discretize a continuous system of differential equations with some geometric structure or physical invariant by preserving the structure or invariant properly, as Kang Feng proposed. The course introduces some basic geometric numerical methods including the symplectic method for Hamiltonian systems, the volume-preserving method for divergence-free systems, the contact method for contact systems and the Lie-group method for systems of differential equations defined on a Lie-group. We will also introduce some applications of the various structure-preserving methods to some typical problems.


预备知识:

Differential equations, classical mechanics,exterior differential calculus


主讲人简介:

尚在久,中国科学院数学与系统科学研究院研究员、博士生导师,中国科学院大学岗位教师。曾任中国科学院数学与系统科学研究院数学研究所副所长(2003-2011)、所长(2012-2016)。 《中国科学:数学》(中、英文版)、 《数学学报》(中、英文版)、 《应用数学学报》(中、英文版)等期刊编委。从事动力系统及其几何数值方法的研究,曾获国家教委科技进步二等奖(1993),是“冯康等国家自然科学一等奖获奖项目“哈密尔顿系统的辛几何算法“(1997)的主要骨干成员,代表性成果有“辛算法的稳定性理论”、“保体积算法”等。


返回顶部
相关文章
  • 计算共形几何

    摘要计算共形几何是现代数学与计算机科学交叉的学科,在课程设置上采用基础数学理论与计算机算法并重的路线。课程涵盖基础数学本科的代数拓扑、黎曼几何、黎曼面理论和微分几何课程。同时,为了解释计算方法,我们也介绍一些研究生水平的数学课程,包括调和映照理论、Teichmuller空间理论、曲面Ricci 流理论。近年来,依随AI的蓬勃发展,我们系统地介绍了凸微分几何中的Minkowski-Alexandrov理论,以及等价的Monge-Kantorovich-...

  • 周二代数与复动力系统讨论班:奥斯陆大学Fei Hu主讲

    An upper bound for polynomial log-volume growth of automorphisms of zero entropyAbstractLet f by an automorphism of zero entropy of a smooth projective variety X. The polynomial log-volume growth plov(f) of f is a natural analog of Gromov's log-volume growth of automorphisms (of positive entropy), formally introduced by Cantat and Paris-Romaskevich for slow dynamics in 2020. A surprising fact n...