SHORT COURSE ON MULTIGRID METHODS AND APPLICATIONS
Prof. Dr. Ludmil Zikatanov (Penn State University, University Park, USA) will give a short
course on multigrid methods and their applications at the State Key Laboratory of Scientific and
Engineering Computing (LSEC) in 2015. Prof. Zikatanov is a well-known expert in multilevel
iterative methods, especially in geometric and algebraic multigrid methods. The short course will
cover the following topics:
- Basic facts from linear algebra. Stationary iterative methods.
- The two-grid method and its convergence rate.
- Subspace corrections theory. Main convergence theorem.
- Introduction to basic graph theory.
- Algebraic multigrid (AMG) methods: Coarse spaces, interpolation and convergence.
- Convergence theory for the smoothed aggregation AMG.
- Auxiliary space method and uniform preconditioning.
- Multigrid methods for convection-diffusion problems.
- A subspace correction method for eigenvalue problems on graphs.
- Applications of subspace correction methods to spectral graph drawing.
Time: August 5, 6, and 7, 2015 (W Th F, 9am–12pm).
Location: Room 311, Lan Bai Lou, LSEC, Beijing.
Direction (Maps in English and Chinese): http://lsec.cc.ac.cn/~zhangcs/
If you have questions, feel free to contact Chensong Zhang (firstname.lastname@example.org).
 Jinchao Xu. Iterative methods by space decomposition and subspace correction. SIAM Rev.,
 Jinchao Xu and Ludmil Zikatanov. The method of alternating projections and the method of subspace
corrections in Hilbert space. J. Amer. Math. Soc., 15(3):573–597, 2002.
 Panayot S. Vassilevski. Multilevel block factorization preconditioners. Springer, New York, 2008.
Matrix-based analysis and algorithms for solving finite element equations.
 Panayot S. Vassilevski. Lecture notes on multigrid methods. Technical Report LLNL-TR-439511,
Lawrence Livermore National Laboratory, July 1 2010. Available at http://people.llnl.gov/vassilevski1.