A multi-level method with correction by aggregation for solving discrete elliptic problems.

*(English)*Zbl 0615.65103This paper studies the behavior of a multigrid method that combines Jacobi relaxation with a correction scheme based on a fixed interpolation process. The author refers to the latter as an aggregation method because interpolation is chosen without regard to the differential operator and the coarse grid correction is constructed variationally from this choice. The analysis considers only the model problem in one dimension with no numerical results reported. However, the apparent aim of this work is to show that a simple aggregation process can substantially accelerate simple iteration.

Reviewer: S.F.McCormick

##### MSC:

65N22 | Numerical solution of discretized equations for boundary value problems involving PDEs |

65F10 | Iterative numerical methods for linear systems |

35J25 | Boundary value problems for second-order elliptic equations |

##### Keywords:

multilevel method; correction by aggregation; convergence acceleration; multigrid method; Jacobi relaxation; aggregation method; coarse grid correction
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##### References:

[1] | W. Hackbusch U. Trottenberg: Multigrid methods. Lecture Notes in Math. 960, Springer-Verlag, Berlin 1982. · Zbl 0497.00015 |

[2] | K. Stüben U. Trottenberg: Multigrid Methods: Fundamental Algorithms. Model Problem Analysis and Applications, in [1]. · Zbl 0562.65071 |

[3] | W. Hackbusch: Multigrid Convergence Theory. in [1]. · Zbl 0505.65036 |

[4] | A. Brondt: Algebraic Multigrid Theory: The Symmetric Case. Preliminary Proceedings of the International Multigrid Conference, Copper Mountain, Colorado, April 6-8, 1983. |

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[6] | R. Blaheta: A Multi-Level Method with Correction by Aggregation for Solving Discrete Elliptic Problems. preliminary version, Ostrava 1984. |

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