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On the convergence of multilevel methods for elliptic problems

Ludmil Zikatanov
PSU Department of Mathematics


In this talk we present results related to the convergenceof multilevel/multigrid methods, applied to symmetric positivedefinite linear systems. The presentation is based on the subspacecorrection framework. The abstract theory is applied to examplescoming from finite element discretizations of scalar elliptic partialdifferential equations and we show how some of the known estimates ofthe convergence rate of the multigrid method can be obtained in astraightforward fashion. We also discuss some relations between amultiplicative Schwarz method convergence and the condition number ofthe corresponding additive Schwarz preconditioner.

Thursday, May 4, 2006
11:00AM AP&M 7421