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Keywords:
multilevel method; correction by aggregation; convergence acceleration; multigrid method; Jacobi relaxation; aggregation method; coarse grid correction
multilevel method; correction by aggregation; convergence acceleration; multigrid method; Jacobi relaxation; aggregation method; coarse grid correction
Summary:
The author studies the behaviour of a multi-level method that combines the Jacobi iterations and the correction by aggragation of unknowns. Our considerations are restricted to a simple one-dimensional example, which allows us to employ the technique of the Fourier analysis. Despite of this restriction we are able to demonstrate differences between the behaviour of the algorithm considered and of multigrid methods employing interpolation instead of aggregation.
References:
[1] W. Hackbusch U. Trottenberg, eds.: Multigrid methods. Lecture Notes in Math. 960, Springer-Verlag, Berlin 1982. MR 0685772
[2] K. Stüben U. Trottenberg: Multigrid Methods: Fundamental Algorithms. Model Problem Analysis and Applications, in [1]. MR 0685773
[3] W. Hackbusch: Multigrid Convergence Theory. in [1].
[4] A. Brondt: Algebraic Multigrid Theory: The Symmetric Case. Preliminary Proceedings of the International Multigrid Conference, Copper Mountain, Colorado, April 6-8, 1983.
[5] Z. Dostál, al.: Numerical Methods and Mathematical Modelling for Determination of the Stress Field in the Rock Mass. Res. report, Mining Institute of the Czech. Acad. Sci., Ostrava 1985 (in Czech).
[6] R. Blaheta: A Multi-Level Method with Correction by Aggregation for Solving Discrete Elliptic Problems. preliminary version, Ostrava 1984.
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