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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 (zhangcs@lsec.cc.ac.cn).

### References

[1] Jinchao Xu. Iterative methods by space decomposition and subspace correction. SIAM Rev.,
34(4):581–613, 1992.

[2] 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.

[3] Panayot S. Vassilevski. Multilevel block factorization preconditioners. Springer, New York, 2008.
Matrix-based analysis and algorithms for solving finite element equations.

[4] 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.