Acceleration and stabilization properties of minimal residual smoothing technique in multigrid

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Abstract

We analyze the standard multigrid method accelerated by a minimal residual smoothing (MRS) technique. We show that MRS can accelerate the convergence of the slow residual components, thus accelerates the overall multigrid convergence. We prove that, under certain hypotheses, MRS stabilizes the divergence of certain slow residual components and thus stabilizes the divergent multigrid iteration. The analysis is customarily conducted on the two-level method.

References (35)

  • A. Brandt

    Multi-level adaptive solution to boundary-value problems

    Math. Comput.

    (1977)
  • P. Wesseling

    An Introduction to Multigrid Methods

    (1992)
  • A. Brandt et al.

    Accelerated multigrid convergence and high-Reynolds recirculating flows

    SIAM J. Sci. Comput.

    (1993)
  • J. Zhang

    On convergence and performance of iterative method for fourth-order compact schemes, Numer

    Methods Partial Differential Equations

    (1998)
  • A. Brandt et al.

    On recombining iterants in multigrid algorithms and problems with small islands

    SIAM J. Sci. Comput.

    (1995)
  • J. Zhang

    Multigrid Acceleration Techniques and Applications to the Numerical Solution of Partial Differential Equations

  • A. Reusken

    Fourier analysis of a robust multigrid method for convection-diffusion equation

    Numer. Math.

    (1995)
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