Daněk, Josef
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The paper presents some results on mathematical simulations of a total knee joint replacement. The finite element method and the non-overlapping decomposition technique for the contact problem in elasticity are applied. Numerical experiments are presented.
Roman Kohut (2018)
Applications of Mathematics
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The finite element (FE) solution of geotechnical elasticity problems leads to the solution of a large system of linear equations. For solving the system, we use the preconditioned conjugate gradient (PCG) method with two-level additive Schwarz preconditioner. The preconditioning is realised in parallel. A coarse space is usually constructed using an aggregation technique. If the finite element spaces for coarse and fine problems on structural grids are fully compatible, relations between...
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....
J. Haslinger, R. Kučera, T. Sassi (2009)
Mathematical Modelling of Natural Phenomena
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The paper deals with an iterative method for numerical solving frictionless contact problems for two elastic bodies. Each iterative step consists of a Dirichlet problem for the one body, a contact problem for the other one and two Neumann problems to coordinate contact stresses. Convergence is proved by the Banach fixed point theorem in both continuous and discrete case. Numerical experiments indicate scalability of the algorithm for some choices of the relaxation parameter. ...
Laitinen, E., Lapin, A. V., Pieskä, J. (2003)
Lobachevskii Journal of Mathematics
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Laura Anania, Antonio Badalá, Giuseppe D’Agata (2016)
Curved and Layered Structures
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In this work the attention is focused to the numerical simulation of the experimental bending tests carried out on a total of six reinforced concrete r.c. plates the latter aimed to provide a basic understanding of the its performance when strengthened by Fiber Reinforced Cementitius Matrix (FRCM) Composites. Three of those were used as control specimens. The numerical simulation was carried out by LUSAS software. A good correlation between the FE results and data obtained from the test,...