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Economical cascadic multigrid method (ECMG). (English) Zbl 1153.65046

Summary: An economical cascadic multigrid method is proposed. Compared with the usual cascadic multigrid method developed by F. A. Bornemann and P. Deuflhard [Numer. Math. 75, No. 2, 135–152 (1996; Zbl 0873.65107)], the new one requires less iterations on each level, especially on the coarser grids. Many operations can be saved in the new cascadic multigrid algorithms. The main ingredient is the control of the iteration numbers on the each level to preserve the accuracy without over iterations. The theoretical justification is based on the observations that the error reduction rate of an iteration scheme in terms of the smoothing property is no longer accurate while the iteration number is big enough. A new formulae of the error reduction rate is employed in our new algorithm. Numerical experiments are reported to support our theory.

MSC:

65F50 Computational methods for sparse matrices
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs

Citations:

Zbl 0873.65107
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References:

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