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Fast solvers for degenerated problems

In this paper, finite element discretizations of the
degenerated operator
-&omega;<sup>2</sup>(y) u<sub>xx</sub>-&omega;<sup>2</sup>(x)u<sub>yy</sub>=g
in the unit square are investigated, where the
weight function satisfies &omega;(&xi;)=&xi;<sup>&alpha;</sup>
with &alpha; &ge; 0.
We propose two multi-level methods in order to
solve the resulting system of linear algebraic
equations. The first method is a multi-grid
algorithm with line-smoother.
A proof of the smoothing property is given.
The second method is a BPX-like preconditioner
which we call MTS-BPX preconditioner.
We show that the upper eigenvalue bound of the
MTS-BPX preconditioned system matrix grows
proportionally to the level number.

Identiferoai:union.ndltd.org:DRESDEN/oai:qucosa.de:swb:ch1-200600611
Date11 April 2006
CreatorsBeuchler, Sven
ContributorsTU Chemnitz, SFB 393
PublisherUniversitätsbibliothek Chemnitz
Source SetsHochschulschriftenserver (HSSS) der SLUB Dresden
LanguageEnglish
Detected LanguageEnglish
Typedoc-type:preprint
Formattext/html, text/plain, image/png, image/gif, text/plain, image/gif, application/pdf, application/x-gzip, text/plain, application/zip
SourcePreprintreihe des Chemnitzer SFB 393, 03-04

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