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Algebraic multigrid by smoothed aggregation for second and fourth order elliptic problems. (English) Zbl 0851.65087

The authors develop an algebraic multigrid algorithm for symmetric positive definite linear systems based on a concept of smoothed aggregation relying on a suitable decomposition of the set of nodes and a corresponding tentative interpolation. The coarsening is governed by abstract multigrid theory and by requirements reflecting practical experience. Favorable behaviour of the algorithm is demonstrated on eleven real-world examples from solid elasticity, plate bending, and shells. The code is available via internet on the address given in the paper.

MSC:

65N55 Multigrid methods; domain decomposition for boundary value problems involving PDEs
74B05 Classical linear elasticity
74S05 Finite element methods applied to problems in solid mechanics
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65F10 Iterative numerical methods for linear systems
35J40 Boundary value problems for higher-order elliptic equations
74K20 Plates
74K15 Membranes
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