报告人：徐岩教授 中国科学技术大学数学科学学院
报告时间：2024年11月22日15:30-16:30
报告地点：红瓦楼726室
报告内容简介：In this talk, we will discuss port-Hamiltonian formulations and their numerical discretization for several classes of hyperbolic partial differential equations. Firstly, based on the classical formulations, we derive generalized Hamiltonian formulations of the incompressible Euler equations with a free surface using the language of differential forms. Three sets of variables, including velocity, solenoidal velocity, potential, vorticity, and free surface, are used to represent the incompressible Euler equations with a free surface. Additionally, we derive the corresponding Poisson bracket for these sets of variables and express the Hamiltonian systems using these Poisson brackets. Our main results are the construction and proof of Dirac structures in suitable Sobolev spaces of differential forms for each variable set, which provides the core of any port-Hamiltonian formulation. We obtain discontinuous Galerkin (DG) finite element discretizations of a class for linear hyperbolic port-Hamiltonian dynamical systems. The accuracy and capabilities of the methods developed in this chapter are demonstrated by presenting several numerical experiments.
报告人简介：徐岩，中国科学技术大学数学科学学院教授。2005年于中国科学技术大学数学系获计算数学博士学位。2005-2007年在荷兰Twente大学从事博士后研究工作。2009年获得德国洪堡基金会的支持在德国Freiburg大学访问工作一年。主要研究领域为高精度数值计算方法。2008年度获全国优秀博士学位论文奖，2017年获国家自然科学基金委“优秀青年基金”, 2017年获中国数学会计算数学分会第二届“青年创新奖”。徐岩教授入选了教育部新世纪优秀人才计划，主持国家自然科学基金面上项目、德国洪堡基金会研究组合作计划(Research Group Linkage Programme)、霍英东青年教师基础研究课题等科研项目。徐岩教授担任中国数学会计算数学分会理事，担任SIAM Journal on Scientific Computing, Journal of Scientific Computing, Advances in Applied Mathematics and Mechanics, Communication on Applied Mathematics and Computation、计算物理等杂志的编委。
报告邀请人：黄学海