Owe Axelsson
Department of Information Technology, Uppsala University, Sweden
and
Institute of Geonics, Academy of Sciences, Ostrava, Czech Republic

A general approach to analyse preconditioners for two-by-two block matrices
Two-by-two block matrices arise in various applications, such as in domain decomposition methods or when solving boundary value problems discretised by finite elements from the separation of the node set of the mesh into 'fine' and 'coarse' nodes. Matrices with such a structure,in saddle point form arise also in mixed variable finite element methods and in constrained optimisation problems.

A general algebraic approach to construct, analyse and control the accuracy of preconditioners for matrices in two-by-two block form is presented. This includes both symmetric and nonsymmetric matrices, as well as indefinite matrices. The action of the preconditioners can involve element-by-element approximations and/or geometric or algebraic multigrid/multilevel methods.