Return to search

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:qucosa:18501
Date11 April 2006
CreatorsBeuchler, Sven
PublisherTechnische Universität Chemnitz
Source SetsHochschulschriftenserver (HSSS) der SLUB Dresden
LanguageEnglish
Detected LanguageEnglish
Typedoc-type:preprint, info:eu-repo/semantics/preprint, doc-type:Text
SourcePreprintreihe des Chemnitzer SFB 393, 03-04
Rightsinfo:eu-repo/semantics/openAccess

Page generated in 0.0024 seconds