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Multilevel preconditioning operators on locally modified grids

Systems of grid equations that approximate elliptic boundary value problems on locally modified grids are considered. The triangulation, which approximates the boundary with second order of accuracy, is generated from an initial uniform triangulation by shifting nodes near the boundary according to special rules. This "locally modified" grid possesses several significant features: this triangulation has a regular structure, the generation of the triangulation is rather fast, this construction allows to use multilevel preconditioning (BPX-like) methods. The proposed iterative methods for solving elliptic boundary value problems approximately are based on two approaches: The fictitious space method, i.e. the reduction of the original problem to a problem in an auxiliary (fictitious) space, and the multilevel decomposition method, i.e. the construction of preconditioners by decomposing functions on hierarchical grids. The convergence rate of the corresponding iterative process with the preconditioner obtained is independent of the mesh size. The construction of the grid and the preconditioning operator for the three dimensional problem can be done in the same way.

Identiferoai:union.ndltd.org:DRESDEN/oai:qucosa.de:swb:ch1-200601671
Date11 September 2006
CreatorsJung, Michael, Matsokin, Aleksandr M., Nepomnyaschikh, Sergey V., Tkachov, Yu. A.
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, 05-14

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