来自美国布朗大学应用数学系的乔治.卡尼亚达克斯（George Karniadakis）教授将于2013年11月到6163am银河线路能源与资源工程系进行学术访问。访问期间将开设研究生选修课程《谱方法与谱元法》（Spectral & Spectral Element Methods）。该课程适用于能源与资源工程专业、力学与空天技术专业的研究生及高年级本科生，课程将采取英文授课的方式，考核方式为平时作业。 授课时间：2013年11月13日---12月4日，每周一、周三上午10:00—12:00 授课地点：6163am银河线路1号楼212会议室 学分：1学分 教学大纲：Fourier methods; Galerkin and collocation projections; Polynomial spectral methods (Chebyshev, Legendre, general Jacobi; Hermite); Domain decomposition in complex geometries; spectral elements. 课程教材：G.E. Karniadakis & S.J. Sherwin, Spectral/hp Element Methods for CFD, Oxford University Press, 2 nd edition, 2005. 其他参考书： (1) D.I.. Gottlieb & S.A. Orszag, Numerical analysis of spectral methods: theory and applications, SIAM-CMBS, 1977 (2) J. Boyd, Chebyshev and Fourier Spectral Methods, Springer-Verlag, New York, 1989.   课程主要内容安排：

序号	课程内容
1	Fourier series; convergence
2	Singular Sturm-Liouville eigen-problem
3	Method of weighted residuals and multi-domains
4	Discrete trigonometric expansions and aliasing
5	Fourier Galerkin and collocation methods
6	Orthogonal polynomials and their properties
7	Polynomial spectral methods for PDEs
8	Spectral methods for non-smooth problems
9	Time stepping and stability of spectral methods
10	Spectral elements and discontinous Galerkin methods

授课人简介： George Karniadakis is the Charles Pitts Robinson and John Palmer Barstow Professor of Applied Mathematics, Brown University. He is also Research Scientist at MIT (Mechanical Engineering) and the Director of the new Collaboratory on Mathematics for Mesoscopic Modelimg of Materials (CM4) – a Department of Energy Center at USA. He has published three books and more than 200 research papers on computational mathematics, stochastic modeling, uncertainty quantification, microfluidics, turbulence, biophysics, and parallel computing. He is fellow of SIAM, APS and ASME. He received the CFD award (2007) and the J. Tinsley Oden Medal (2013) by the US Association in Computational Mechanics. His h-index is 59 and he has been cited more than 17,000 times.    有意选课的同学请发邮件至：6163am银河线路张老师 zhangshanshan@pku.edu.cn