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KIAM Preprint  113, Moscow, 2016
Authors: Zhukov V. T., Krasnov M. M., Novikova N. D., Feodoritova O. B.
Algebraic Multigrid Method with adaptive smoothers based on Chebyshev polynomials
We introduce an adaptive algebraic multigrid method (AMG) for numerical solution of three-dimensional elliptic equations. A new element is the integration of AMG technique with the smoothers based on optimal Chebyshev polynomials. The possibilities of automatic adaptation of smoothers to the bounds of the MG discrete operators are shown. The properties of two smoothers, the polynomial and the rational function, are discussed. The results of experimental verification of the AMG are given. Effective implementation of the smoothers and solver for the coarsest equations with the help of Chebyshev explicit-iterative algorithms enables the functioning of the parallel code on modern supercomputer architectures.
elliptic equations, algebraic multigrid method, Chebyshev polynomials, adaptive smoother
Publication language: russian,  pages: 32
Research direction:
Mathematical problems and theory of numerical methods
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About authors:
  • Zhukov Victor Timofeevich, RAS
  • Krasnov Mikhail Mikhailovich, RAS
  • Novikova Natalia Dmitrievna, RAS
  • Feodoritova Olga Borisovna, RAS