Guy Bayada, Jalila Sabil, Taoufik Sassi (2008)
ESAIM: Mathematical Modelling and Numerical Analysis
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In this paper, the convergence of a Neumann-Dirichlet algorithm to approximate Coulomb's contact problem between two elastic bodies is proved in a continuous setting. In this algorithm, the natural interface between the two bodies is retained as a decomposition zone.
Todor Angelov, Asterios Liolios (2005)
International Journal of Applied Mathematics and Computer Science
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A class of contact problems with friction in elastostatics is considered. Under a certain restriction on the friction coefficient, the convergence of the two-step iterative method proposed by P.D. Panagiotopoulos is proved. Its applicability is discussed and compared with two other iterative methods, and the computed results are presented.
Luca Gerardo-Giorda, Mauro Perego (2013)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
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The propagation of the action potential in the heart chambers is accurately described by the Bidomain model, which is commonly accepted and used in the specialistic literature. However, its mathematical structure of a degenerate parabolic system entails high computational costs in the numerical solution of the associated linear system. Domain decomposition methods are a natural way to reduce computational costs, and Optimized Schwarz Methods have proven in the recent years their effectiveness...
Gassav S. Abdoulaev, Yves Achdou, Yuri A. Kuznetsov, Christophe Prud'homme (2010)
ESAIM: Mathematical Modelling and Numerical Analysis
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We discuss a parallel implementation of the domain decomposition method based on the macro-hybrid formulation of a second order elliptic equation and on an approximation by the mortar element method. The discretization leads to an algebraic saddle- point problem. An iterative method with a block- diagonal preconditioner is used for solving the saddle- point problem. A parallel implementation of the method is emphasized. Finally the results of numerical experiments are presented....
A. H. Osbaldestin, P. Shiu (1991)
Publications de l'Institut Mathématique
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Samir Akesbi (2010)
ESAIM: Mathematical Modelling and Numerical Analysis
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The aim of this work is to introduce and to analyze new algorithms for solving the transport neutronique equation in 2D geometry. These algorithms present the duplicate favors to be, on the one hand faster than some classic algorithms and easily to be implemented and naturally deviced for parallelisation on the other hand. They are based on a splitting of the collision operator holding amount of caracteristics of the transport operator. Some numerical results are given at the end...
Růžička, Adam, Horák, David
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This paper deals with the basic preconditioning and deflation variants of the FETI-1 and TFETI-1 methods, with (T)FETI-1 with deflation being called (T)FETI-2. It also presents the results of numerical experiments performed on a simple benchmark 2D problem of linear elasticity to compare the computational efficiency of FETI-1 and TFETI-1 and each variant of their preconditioning or deflation in terms of number of executed CG iterations.