Schwarz methods for discrete elliptic and parabolic problems with an application to nuclear waste repository modelling

Authors:
R. Blaheta;R. Kohut;M. Neytcheva;J. Starý
Affiliations:
Institute of Geonics, Academy of Sciences of the Czech Republic, Studentská 1768, 708 00 Ostrava, Poruba, Czech Republic;Institute of Geonics, Academy of Sciences of the Czech Republic, Studentská 1768, 708 00 Ostrava, Poruba, Czech Republic;Department of Information Technology, Uppsala University, Box 337, SE-751 05 Uppsala, Sweden;Institute of Geonics, Academy of Sciences of the Czech Republic, Studentská 1768, 708 00 Ostrava, Poruba, Czech Republic
Venue:
Mathematics and Computers in Simulation
Year:
2007

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Abstract

The paper is devoted to the numerical solution of both elliptic and parabolic problems by overlapping Schwarz methods. It demonstrates that while the two-level Schwarz method is necessary for the efficient solution of discrete elliptic problems, the one-level Schwarz method can be sufficiently efficient in the parabolic case. The paper includes results from numerical simulations of a large-scale model of the performance of a nuclear waste repository.