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Overlapping additive schwarz methods for nonlinear parabolic reaction-diffusion problems : dottorato di ricerca in matematica e statistica per le scienze computazionali : tesi di dottorato di ricerca

Munteanu, Marilena

Tesi o dissertazioni - 2007

Abstract
Overlapping Additive Schwarz Methods for Nonlinear Parabolic Reaction-Diffusion Problems Marilena Munteanu In this thesis, we study overlapping Schwarz methods for nonlinear parabolic problems, focusing in particular on reaction-diffusion problems of increasing complexity such as the scalar Nagumo equation, the FitzHugh-Nagumo system, the Monodomain and Bidomain - LR1 systems. We study fully implicit time discretizations (such as Backward Euler), linearly implicit Rosenbrock methods (such as Ros3P) and decoupled methods based on the separate time advancement of some variables of the system. We construct and study a scalable overlapping Additive Schwarz-\-Richardson (ASR) algorithm for monotone nonlinear parabolic problems discretized implicitly in time. We prove first an abstract convergence result and then convergence rate estimates showing the scalability of the ASR algorithm. The results of numerical experiments in the plane confirm the theoretical results obtained and illustrate the [...]
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Inventario
3761
Collocazione
D. 2007 0456
Note
Autorizzazione: si.