Kickinger, Ferdinand 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]. Cited in 19 Documents 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 Keywords:discrete elliptic second-order problems; algebraic multi-grid methods; large sparse systems; finite element; coarsening algorithms; nested mesh refinement; heat conduction problems; plane strain elasticity problems PDFBibTeX XMLCite \textit{F. Kickinger}, Lect. Notes Comput. Sci. Eng. 3, 157--172 (1998; Zbl 0926.65128)