Domain Decomposition And Multilevel Methods

S.V.Nepomnyaschikh

Computing Center of Siberian Branch of Russian Academy of Sciences Lavrentiev Ave. 6, 630090 Novosibirsk, Russia, svnep@comcen.nsk.su

Abstract

Boundary value problems for elliptic equations with essentially disproportional parameters are considered. The main goal is the construction of a preconditioning operator for the resulting system of grid equestions. The method of the construction is based on three approaches: decomposition into sub-spaces, fictitious space method, and extension operators. The convergence rate of the preconditioned iterative process is independent of the grid size and the parameters.