Optimal extensions on tensor-product meshes

Authors:
Sven Beuchler;Joachim Schöberl
Affiliations:
Institute for Numerical Mathematics, Kepler-University Linz, Altenberger Strasse, Linz, Austria;Institute for Numerical Mathematics, Kepler-University Linz, Altenberger Strasse, Linz, Austria
Venue:
Applied Numerical Mathematics - Selected papers from the 16th Chemnitz finite element symposium 2003
Year:
2005

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Abstract

In this paper, a uniformly elliptic second order boundary value problem in 2D is discretized by the p-version of the finite element method. An inexact Dirichlet-Dirichlet domain decomposition preconditioner for the system of linear algebraic equations is investigated. The ingredients of such a preconditioner are a preconditioner for the Schur complement, a preconditioner for the subdomains and an extension operator operating from the edges of the elements into their interior. Using methods of multi-resolution analysis, we propose a new method in order to compute the extension efficiently. Numerical experiments show the optimal performance of the described extension.