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Abstract: |
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: ：
1. Basic facts from linear algebra. Stationary iterative methods.
2. The two-grid method and its convergence rate.
3. Subspace corrections theory. Main convergence theorem.
4. Introduction to basic graph theory.
5. Algebraic multigrid (AMG) methods: Coarse spaces, interpolation and convergence.
6. Convergence theory for the smoothed aggregation AMG.
7. Auxiliary space method and uniform preconditioning.
8. Multigrid methods for convection-diffusion problems.
9. A subspace correction method for eigenvalue problems on graphs.
10.Applications of subspace correction methods to spectral graph drawing.
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. |
