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An efficient algebraic multigrid preconditioned conjugate gradient solver. (English) Zbl 1045.74047

Summary: We present a robust and efficient algebraic multigrid preconditioned conjugate gradient solver for systems of linear equations arising from the finite element discretization of a scalar elliptic partial differential equation of second order on unstructured meshes. The algebraic multigrid (AMG) method is one of most promising methods for solving large systems of linear equations arising from unstructured meshes. The conventional AMG method usually requires an expensive setup time, particularly for three-dimensional problems, so that generally it is not used for small and medium size systems or low-accuracy approximations. Our solver has a quick setup phase for the AMG method and a fast iteration cycle. These allow us to apply this solver not only to large systems, but also to small or medium systems of linear equations, and also to systems requiring low-accuracy approximations.

MSC:

74S05 Finite element methods applied to problems in solid mechanics
74K20 Plates
65F10 Iterative numerical methods for linear systems
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
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References:

[1] Ruge, J.; Stüben, K., Algebraic multigrid, (McCormick, S., Multigrid methods, Frontiers in Applied Mathematics (1987), Society for Industrial and Applied Mathematics: Society for Industrial and Applied Mathematics Philadelphia, PA)
[2] K. Stüben, Algebraic Multigrid (AMG): An Introduction with Applications, GMD Report 70, Sankt Augastin, Germany, 1999; K. Stüben, Algebraic Multigrid (AMG): An Introduction with Applications, GMD Report 70, Sankt Augastin, Germany, 1999
[3] Hageman, L.; Young, D., Applied Iterative Methods (1981), Academic Press: Academic Press New York · Zbl 0459.65014
[4] Briggs, W.; Henson, V.; McCormick, S., A Multigrid Tutorial (2000), Society for Industrial and Applied Mathematics: Society for Industrial and Applied Mathematics Philadelphia, PA · Zbl 0958.65128
[5] Hackbusch, W., Multi-grid Methods and Applications (1985), Springer-Verlag: Springer-Verlag Berlin · Zbl 0585.65030
[6] Jung, M.; Langer, U.; Meyer, A.; Queck, W.; Schneider, M., Multigrid preconditioners and their applications, (Telschow, G., Third Multigrid Seminar (1989), Akademie der Wissenschaften der Ddr: Akademie der Wissenschaften der Ddr Berlin) · Zbl 0699.65076
[7] Axelsson, O., Iterative Solution Methods (1994), Cambridge University Press: Cambridge University Press Cambridge · Zbl 0795.65014
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