Optimal extensions on tensor-product meshes

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 preco...

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Bibliographic Details
Published in:Applied numerical mathematics 2005-08, Vol.54 (3), p.391-405
Main Authors: Beuchler, Sven, Schöberl, Joachim
Format: Article
Language:English
Subjects:
Domain decomposition
Exact sciences and technology
Finite elements
Mathematical analysis
Mathematics
Numerical analysis
Numerical analysis. Scientific computation
Partial differential equations
Partial differential equations, boundary value problems
Partial differential equations, initial value problems and time-dependant initial-boundary value problems
Sciences and techniques of general use
Solution of discretized equations
Wavelets
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Summary: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.
ISSN:0168-9274
1873-5460
DOI:10.1016/j.apnum.2004.09.010