Approximate inverse computations and algebraic multigrid

Jane Cullum

MS B250, Los Alamos National Laboratory, Los Alamos, NM 87544, USA


An algebraic multigrid algorithm consists of a hierarchy of problems, typically nested, and mappings to transfer information between the levels in the hierarchy. In this talk we focus on the construction of these mappings, the prolongation and the restriction operators. We extend the notation of approximate inverses to the computation of the product of a matrix inverse times a specified block of vectors. We examine the use of this extension within an algebraic multigrid framework to compute these mappings at each level of an algebraic multigrid hierarchy. We apply these ideas to several test problems and compare the convergence behavior of these new AMG algorithms with that obtained using a basic Ruge-Stuben AMG algorithm. This is joint work with Miroslav Tuma.