Mesh Independent Convergence Rates Via Differential Operator Pairs

Authors:
Owe Axelsson;János Karátson
Affiliations:
Department of Information Technology, Uppsala University, Sweden and Institute of Geonics AS CR, Ostrava, Czech Republic;Department of Applied Analysis, ELTE University, Budapest, Hungary
Venue:
Large-Scale Scientific Computing
Year:
2009

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Abstract

In solving large linear systems arising from the discretization of elliptic problems by iteration, it is essential to use efficient preconditioners. The preconditioners should result in a mesh independent linear or, possibly even superlinear, convergence rate. It is shown that a general way to construct such preconditioners is via equivalent pairs or compactequivalent pairs of elliptic operators.