Multigrid for anisotropic diffusion problems based on adaptive Chebyshev's smoothers

We propose an efficient multigrid algorithm for solving anisotropic elliptic difference equations. The algorithm is based on the explicit Chebyshev iterations for solution of the coarsest grid equations and for construction of smoothing procedures. We develop the adaptive smoothers for anisotropic problems, and show that it provides efficiency of the multigrid algorithm and scalability in parallel implementation.