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.

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):

If you have questions, feel free to contact Chensong Zhang (


[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