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Algebraic multi-grid for discrete elliptic second-order problems. (English) Zbl 0926.65128

Hackbusch, Wolfgang (ed.) et al., Multigrid methods V. Proceedings of the 5th European multigrid conference, held in Stuttgart, Germany, October 1–4, 1996. Berlin: Springer. Lect. Notes Comput. Sci. Eng. 3, 157-172 (1998).
Summary: This paper is devoted to the construction of algebraic multi-grid (AMG) methods, which are especially suited for the solution of large sparse systems of algebraic equations arising from the finite element discretization of second-order elliptic boundary value problems on unstructured, fine meshes in two or three dimensions. The only information needed is recovered from the stiffness matrix.
We present two types of coarsening algorithms based on the graph of the stiffness matrix. In some special cases of nested mesh refinement, we observe, that some geometrical version of the multi-grid method turns out to be a special case of our AMG algorithms. Finally, we apply our algorithms on two- and three-dimensional heat conduction problems in domains with complicated geometry (e.g. micro-scales), as well as to plane strain elasticity problems with jumping coefficients.
For the entire collection see [Zbl 0899.00038].

MSC:

65N55 Multigrid methods; domain decomposition for boundary value problems involving PDEs
65N50 Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
35J25 Boundary value problems for second-order elliptic equations
65F10 Iterative numerical methods for linear systems
74B05 Classical linear elasticity
74S05 Finite element methods applied to problems in solid mechanics
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