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56 results on '"Taoufik Sassi"'

1. Error estimates for Stokes problem with Tresca friction condition

Author: Mekki, Ayadi, Khaled, Gdoura Mohamed, and Taoufik, Sassi
Subjects: Mathematics - Numerical Analysis
Abstract: In this work we propose and study a three field mixed formulation for solving the Stokes problem with Tresca-type non-linear boundary conditions. Two Lagrange multipliers are used to enforce div(u)=0 constraint and to regularize the energy functional. The resulting problem is discretised using "P1 bubble/P1-P1" finite elements. Error estimates are derived and several numerical studies are achieved.
Published: 2010
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2. Continued enteral nutrition until extubation compared with fasting before extubation in patients in the intensive care unit: an open-label, cluster-randomised, parallel-group, non-inferiority trial

Author: Mickaël Landais, Mai-Anh Nay, Johann Auchabie, Noemie Hubert, Aurélien Frerou, Aihem Yehia, Alain Mercat, Maud Jonas, Frédéric Martino, Mikael Moriconi, Anne Courte, Vincent Robert-Edan, Alexandre Conia, Florent Bavozet, Pierre-Yves Egreteau, Cédric Bruel, Anne Renault, Olivier Huet, Marc Feller, Nicolas Chudeau, Martine Ferrandiere, Anne Rebion, Alain Robert, Bruno Giraudeau, Jean Reignier, Arnaud W Thille, Elsa Tavernier, Stephan Ehrmann, Satar MORTAZA, Julien DEMISELLE, Taoufik SASSI, Charles DELALE, Julien GROUILLE, Anne DE TINTENIAC, Marie GESLAIN, Herve FLOCH, Pierre BAILLY, Laetitia BODENES, Gwenaël PRAT, Pierre KALFON, Gaetan BADRE, Cecile JOURDAIN, Thierry MAZZONI, Anthony LE MEUR, Pierre Marie FAYOLLE, Anne HERON, Odile MAILLET, Nelly LEDOUX, Amélie ROLLE, Régine RICHARD, Marc VALETTE, Marie-Ange AZAIS, Caroline POUPLET, Konstantinos BACHOUMAS, Jean Christophe CALLAHAN, Christophe GUITTON, Cedric DARREAU, Montaine LEFEVRE, Guillaume LELOUP, Mélanie BERTEL, Jerome DAUVERGNE, Laurence PACAUD, Karim LAKHAL, Maelle MARTIN, Charlotte GARRET, Jean-Baptiste LASCARROU, Thierry BOULAIN, Armelle MATHONNET, Grégoire MULLER, François PHILIPPART, Marc TRAN, Julien FOURNIER, Jean-Pierre FRAT, Remi COUDROY, Delphine CHATELLIER, Guillaume HALLEY, Arnaud GACOUIN, Jerome HOFF, Servane VASTAL, Anne-Charlotte TELLIER, Mathilde BARBAZ, Charlotte SALMON GANDONNIERE, Emmanuelle MERCIER, and Walid DARWICHE
Subjects: Pulmonary and Respiratory Medicine
Published: 2023

3. Domain Decomposition Method for Stokes Problem with Tresca Friction.

Author: Mohamed Khaled Gdoura, Jonas Koko, and Taoufik Sassi
Published: 2013
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4. Existence of a weak solution to a steady 2D fluid-1D elastic structure interaction problem with Tresca slip boundary condition

Author: Hela Ayed, Taoufik Sassi, and Leonardo Baffico
Subjects: Physics, Numerical Analysis, General Computer Science, Applied Mathematics, Weak solution, Mathematical analysis, Slip (materials science), Theoretical Computer Science, Physics::Fluid Dynamics, Nonlinear system, Modeling and Simulation, Fluid–structure interaction, Compressibility, Newtonian fluid, Boundary value problem, Displacement (fluid)
Abstract: We study a steady state fluid–structure interaction problem between an incompressible viscous Newtonian fluid and an elastic structure using a nonlinear boundary condition of friction type on the fluid–structure interface. This condition, also known as Tresca slip boundary condition, allows the fluid to slip on the interface when the tangential component of the fluid shear stress attains a certain threshold function. The governing equations are the 2 D Stokes equations for the fluid, written in an unknown domain depending on the structure displacement, and the 1 D Euler–Bernoulli model for the structure. We prove that there exists a weak solution of this nonlinear coupled problem by designing a proof based on the Schauder fixed-point theorem. The theoretical result will be illustrated with a numerical example.
Published: 2021

5. Dual strategies for solving the Stokes problem with stick–slip boundary conditions in 3D

Author: Václav Šátek, Jaroslav Haslinger, Radek Kučera, and Taoufik Sassi
Subjects: Numerical Analysis, General Computer Science, Applied Mathematics, Mathematical analysis, 010103 numerical & computational mathematics, 02 engineering and technology, Mixed finite element method, Slip (materials science), Stokes flow, 01 natural sciences, Theoretical Computer Science, symbols.namesake, Modeling and Simulation, Lagrange multiplier, 0202 electrical engineering, electronic engineering, information engineering, symbols, 020201 artificial intelligence & image processing, Boundary value problem, 0101 mathematics, Algebraic number, Newton's method, Interior point method, Mathematics
Abstract: The paper deals with the numerical realization of the 3D Stokes flow subject to threshold slip boundary conditions. The weak velocity–pressure formulation leads to an inequality type problem that is approximated by a mixed finite element method. The resulting algebraic system is non-smooth. Besides the pressure, three additional Lagrange multipliers are introduced: the discrete normal stress releasing the impermeability condition and two discrete shear stresses regularizing the non-smooth slip term. Eliminating the discrete velocity component we obtain the minimization problem for the smooth functional, expressed in terms of the pressure, the normal, and the shear stresses. This problem is solved either by a path following variant of the interior point method or by the semi-smooth Newton method. Numerical scalability is illustrated by computational experiments.
Published: 2021

6. Stokes system with solution-dependent threshold slip boundary conditions: Analysis, approximation and implementation

Author: Václav Šátek, Radek Kučera, Jaroslav Haslinger, and Taoufik Sassi
Subjects: General Mathematics, Mathematical analysis, 010103 numerical & computational mathematics, Slip (materials science), 01 natural sciences, 010101 applied mathematics, symbols.namesake, Classical mechanics, Mechanics of Materials, Stokes' law, symbols, General Materials Science, Boundary value problem, 0101 mathematics, Mathematics
Abstract: The paper analyzes the Stokes system with threshold slip boundary conditions of Navier type. Based on the fixed-point formulation we prove the existence of a solution for a class of solution-dependent slip functions g satisfying an appropriate growth condition and its uniqueness provided that g is one-sided Lipschitz continuous. Further we study under which conditions the respective fixed-point mapping is contractive. To discretize the problem we use P1-bubble/P1 elements. Properties of discrete models in dependence on the discretization parameter are analysed and convergence results are established. In the second part of the paper we briefly describe the duality approach used in computations and present results of a model example.
Published: 2017

7. Stokes Problem with Slip Boundary Conditions of Friction Type: Error Analysis of a Four-Field Mixed Variational Formulation

Author: Mekki Ayadi, Leonardo Baffico, Hela Ayed, Taoufik Sassi, Université de Sousse, Laboratoire de Mathématiques Nicolas Oresme (LMNO), Centre National de la Recherche Scientifique (CNRS)-Université de Caen Normandie (UNICAEN), and Normandie Université (NU)-Normandie Université (NU)
Subjects: Numerical Analysis, Applied Mathematics, Mathematical analysis, General Engineering, Slip (materials science), Lambda, 01 natural sciences, Finite element method, Theoretical Computer Science, 010101 applied mathematics, Computational Mathematics, symbols.namesake, Computational Theory and Mathematics, Lagrange multiplier, Stokes problem, symbols, Vector field, Uniqueness, Boundary value problem, 0101 mathematics, Software, ComputingMilieux_MISCELLANEOUS, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA], Mathematics
Abstract: In this work, a finite element approximation of the Stokes problem under a slip boundary condition of friction type, known as the Tresca boundary condition, is considered. We treat the approximate problem of a four field mixed formulation using the $${\mathbb {P}}^{1}$$ -bubble element for the velocity field, $${\mathbb {P}}^{1}$$ element for the pressure field and the $${\mathbb {P}}^{1}$$ element for the Lagrange multipliers $$\lambda _{n}$$ and $$\lambda _{t}$$ defined on the slip boundary. The multiplier $$\lambda _{t}$$ is introduced to regularize the non-differentiable problem, whereas $$\lambda _{n}$$ treats the impermeability condition. Existence and uniqueness results for both continuous and discrete problems are proven and an a priori error estimate is established. Numerical realization of such problem is discussed and some numerical tests are provided.
Published: 2019

8. The semi-smooth Newton method for solving the Stokes flow under the leak boundary condition

Author: Taoufik Sassi, Radek Kučera, Václav Šátek, Kristina Motyčková, and Jaroslav Haslinger
Subjects: Set (abstract data type), symbols.namesake, Discretization, symbols, Applied mathematics, Point (geometry), Boundary value problem, Stokes flow, Newton's method, Interior point method, Finite element method, Mathematics
Abstract: The article deals with the Stokes flow under the leak boundary conditions. The problem is discretized using the mixed finite element approximation and solved as algebraic optimization problem. The respective optimality conditions are the starting point for the algorithm based on an active set implementation of the semi-smooth Newton method. Numerical experiments compare performance of the algorithm with the path-following interior point method.
Published: 2019

9. The semi-smooth Newton method for solving the Stokes problem with the stick-slip boundary condition

Author: Kristina Motyčková, Jan Pacholek, Radek Kučera, and Taoufik Sassi
Subjects: Physics::Fluid Dynamics, symbols.namesake, Preconditioner, Diagonal, Stokes problem, symbols, Applied mathematics, Boundary value problem, Slip (materials science), Stokes flow, Newton's method, Finite element method, Mathematics
Abstract: The Stokes flow with the stick-slip boundary condition combining the Navier and Tresca laws is considered. The finite element approximation leads to an algebraic optimization problem. Its optimality condition is the starting point for an active set implementation of the semi-smooth Newton method. Numerical experiments demonstrate computational efficiency of an adaptive diagonal preconditioner.
Published: 2018

10. Numerical modelling of the Stokes flow with threshold slip boundary conditions

Author: Václav Šátek, Jonas Koko, František Pochylý, Taoufik Sassi, Radek Kučera, and Jaroslav Haslinger
Subjects: Physics, symbols.namesake, Stokes' law, symbols, Mechanics, Boundary value problem, Slip (materials science), Stokes flow, Stokes number
Published: 2017

11. Shape optimization for Stokes problem with threshold slip

Author: Jan Stebel, Jaroslav Haslinger, and Taoufik Sassi
Subjects: Large class, Planar, Shape design, Applied Mathematics, Bounded function, Mathematical analysis, Stokes problem, Shape optimization, Boundary value problem, Slip (materials science), Mathematics
Abstract: We study the Stokes problems in a bounded planar domain Ω with a friction type boundary condition that switches between a slip and no-slip stage. Our main goal is to determine under which conditions concerning the smoothness of Ω solutions to the Stokes system with the slip boundary conditions depend continuously on variations of Ω. Having this result at our disposal, we easily prove the existence of a solution to optimal shape design problems for a large class of cost functionals. In order to release the impermeability condition, whose numerical treatment could be troublesome, we use a penalty approach. We introduce a family of shape optimization problems with the penalized state relations. Finally we establish convergence properties between solutions to the original and modified shape optimization problems when the penalty parameter tends to zero.
Published: 2014

12. Existence result for a fluid structure interaction problem with friction type slip boundary condition

Author: Taoufik Sassi and Leonardo Baffico
Subjects: Applied Mathematics, 010102 general mathematics, Mathematical analysis, Computational Mechanics, Slip (materials science), Viscous liquid, Stokes flow, 01 natural sciences, Physics::Fluid Dynamics, 010101 applied mathematics, Algebraic equation, 11. Sustainability, Variational inequality, Fluid–structure interaction, No-slip condition, Boundary value problem, 0101 mathematics, Mathematics
Abstract: We study the stationary interaction between a 2D viscous fluid, governed by the Stokes equation, and a rigid structure that can move following rigid displacements. The displacements of the structure are determined using an algebraic equation. A slip boundary condition of friction type is used on the fluid–solid interface. An existence result is proved and numerical tests are presented.
Published: 2014

13. A domain decomposition method for two-body contact problems with Tresca friction

Author: Taoufik Sassi, Julien Riton, Radek Kučera, and Jaroslav Haslinger
Subjects: Computational Mathematics, Mathematical optimization, Body contact, Applied Mathematics, Domain decomposition algorithm, Mathematical analysis, Linear elasticity, A domain, Computational Science and Engineering, Domain decomposition methods, Decomposition method (constraint satisfaction), Mathematics
Abstract: The paper analyzes a continuous and discrete version of the Neumann-Neumann domain decomposition algorithm for two-body contact problems with Tresca friction. Each iterative step consists of a linear elasticity problem for one body with displacements prescribed on a contact part of the boundary and a contact problem with Tresca friction for the second body. To ensure continuity of contact stresses, two auxiliary Neumann problems in each domain are solved. Numerical experiments illustrate the performace of the proposed approach.
Published: 2013

14. Domain Decomposition Methods in Science and Engineering XXI

Author: Olof B. Widlund, Taoufik Sassi, Jocelyne Erhel, Martin J. Gander, Géraldine Pichot, Laurence Halpern, Simulations and Algorithms on Grids for Environment (SAGE), Inria Rennes – Bretagne Atlantique, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-SYSTÈMES LARGE ÉCHELLE (IRISA-D1), Institut de Recherche en Informatique et Systèmes Aléatoires (IRISA), CentraleSupélec-Télécom Bretagne-Université de Rennes 1 (UR1), Université de Rennes (UNIV-RENNES)-Université de Rennes (UNIV-RENNES)-Institut National de Recherche en Informatique et en Automatique (Inria)-École normale supérieure - Rennes (ENS Rennes)-Université de Bretagne Sud (UBS)-Centre National de la Recherche Scientifique (CNRS)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA)-CentraleSupélec-Télécom Bretagne-Université de Rennes 1 (UR1), Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA)-Institut de Recherche en Informatique et Systèmes Aléatoires (IRISA), Université de Rennes (UNIV-RENNES)-Université de Rennes (UNIV-RENNES)-École normale supérieure - Rennes (ENS Rennes)-Université de Bretagne Sud (UBS)-Centre National de la Recherche Scientifique (CNRS)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA), Section de mathématiques [Genève], Université de Genève (UNIGE), Laboratoire Analyse, Géométrie et Applications (LAGA), Université Paris 8 Vincennes-Saint-Denis (UP8)-Centre National de la Recherche Scientifique (CNRS)-Institut Galilée-Université Paris 13 (UP13), Laboratoire de Mathématiques Nicolas Oresme (LMNO), Centre National de la Recherche Scientifique (CNRS)-Université de Caen Normandie (UNICAEN), Normandie Université (NU)-Normandie Université (NU), Courant Institute of Mathematical Sciences [New York] (CIMS), New York University [New York] (NYU), NYU System (NYU)-NYU System (NYU), Jocelyne Erhel and Martin Gander and Laurence Halpern and Géraldine Pichot and Taoufik Sassi and Olof Widlund, Université de Rennes (UR)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université de Bretagne Sud (UBS)-École normale supérieure - Rennes (ENS Rennes)-Institut National de Recherche en Informatique et en Automatique (Inria)-Télécom Bretagne-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS)-Université de Rennes (UR)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université de Bretagne Sud (UBS)-École normale supérieure - Rennes (ENS Rennes)-Institut National de Recherche en Informatique et en Automatique (Inria)-Télécom Bretagne-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS)-Institut de Recherche en Informatique et Systèmes Aléatoires (IRISA), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université de Bretagne Sud (UBS)-École normale supérieure - Rennes (ENS Rennes)-Télécom Bretagne-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS), Université de Genève = University of Geneva (UNIGE), Université Paris 8 Vincennes-Saint-Denis (UP8)-Université Paris 13 (UP13)-Institut Galilée-Centre National de la Recherche Scientifique (CNRS), Université de Caen Normandie (UNICAEN), Normandie Université (NU)-Normandie Université (NU)-Centre National de la Recherche Scientifique (CNRS), Université de Rennes 1 (UR1), Université de Rennes (UNIV-RENNES)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA)-Université de Bretagne Sud (UBS)-École normale supérieure - Rennes (ENS Rennes)-Institut National de Recherche en Informatique et en Automatique (Inria)-Télécom Bretagne-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS)-Université de Rennes 1 (UR1), Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA)-Université de Bretagne Sud (UBS)-École normale supérieure - Rennes (ENS Rennes)-Institut National de Recherche en Informatique et en Automatique (Inria)-Télécom Bretagne-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS)-Institut de Recherche en Informatique et Systèmes Aléatoires (IRISA), and Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA)-Université de Bretagne Sud (UBS)-École normale supérieure - Rennes (ENS Rennes)-Télécom Bretagne-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS)
Subjects: Computer science, Scale (chemistry), Numerical analysis, Domain decomposition methods, 010103 numerical & computational mathematics, 02 engineering and technology, 01 natural sciences, Field (computer science), Computational science, Development (topology), Scalability, 0202 electrical engineering, electronic engineering, information engineering, 020201 artificial intelligence & image processing, Domain analysis, 0101 mathematics, Massively parallel, ComputingMilieux_MISCELLANEOUS, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]
Abstract: This volume contains a selection of papers presented at the 21st international conference on domain decomposition methods in science and engineering held in Rennes, France, June 25-29, 2012. Domain decomposition is an active and interdisciplinary research discipline, focusing on the development, analysis and implementation of numerical methods for massively parallel computers. Domain decomposition methods are among the most efficient solvers for large scale applications in science and engineering. They are based on a solid theoretical foundation and shown to be scalable for many important applications. Domain decomposition techniques can also naturally take into account multiscale phenomena. This book contains the most recent results in this important field of research, both mathematically and algorithmically and allows the reader to get an overview of this exciting branch of numerical analysis and scientific computing.
Published: 2014

15. Mixed formulation for Stokes problem with Tresca friction

Author: Mekki Ayadi, Taoufik Sassi, and Mohamed Khaled Gdoura
Subjects: Mathematical optimization, Field (physics), Discretization, Bubble, General Medicine, Finite element method, Constraint (information theory), symbols.namesake, Lagrange multiplier, symbols, Stokes problem, Applied mathematics, Energy functional, Mathematics
Abstract: In this Note we propose and study a three field mixed formulation for solving the Stokes problem with Tresca-type nonlinear boundary conditions. Two Lagrange multipliers are used to enforce div ( u ) = 0 constraint and to regularize the energy functional. The resulting problem is discretized using P1 bubble/P1-P1 finite elements. Optimal error estimate is derived and a numerical validation test is achieved.
Published: 2010

16. A Domain Decomposition Algorithm for Contact Problems: Analysis and Implementation

Author: Radek Kučera, Taoufik Sassi, and Jaroslav Haslinger
Subjects: Dirichlet problem, Banach fixed-point theorem, Iterative method, Modeling and Simulation, Applied Mathematics, Convergence (routing), Mathematical analysis, Scalability, Neumann–Dirichlet method, Decomposition (computer science), Relaxation (iterative method), Algorithm, Mathematics
Abstract: 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
Published: 2009

17. Convergence of a Neumann-Dirichlet algorithm for two-body contact problems with non local Coulomb's friction law

Author: Jalila Sabil, Taoufik Sassi, and Guy Bayada
Subjects: Numerical Analysis, Applied Mathematics, Numerical analysis, Domain decomposition methods, Non local, Dirichlet distribution, Computational Mathematics, symbols.namesake, Body contact, Modeling and Simulation, Convergence (routing), Coulomb, symbols, Decomposition method (constraint satisfaction), Algorithm, Analysis, Mathematics
Abstract: 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.
Published: 2008

18. Un algorithme de type Robin pour des problèmes de contact unilatéral

Author: Mohamed Ipopa and Taoufik Sassi
Subjects: General Medicine, Humanities, Mathematics
Abstract: Resume Dans cette Note, nous proposons un algorithme de decomposition de domaine de type Robin pour resoudre numeriquement un probleme de contact unilateral sans frottement entre deux corps elastiques. Cet algorithme combine sur l'interface Γ c des conditions aux limites de type Dirichlet et de Neumann (condition de Robin). L'originalite de cet algorithme est la resolution de la meme inequation variationnelle sur chaque sous-domaine. Pour citer cet article : M. Ipopa, T. Sassi, C. R. Acad. Sci. Paris, Ser. I 346 (2008).
Published: 2008

19. Domain Decomposition Methods in Science and Engineering XXI

Author: Jocelyne Erhel, Martin J. Gander, Laurence Halpern, Géraldine Pichot, Taoufik Sassi, Olof Widlund, Jocelyne Erhel, Martin J. Gander, Laurence Halpern, Géraldine Pichot, Taoufik Sassi, and Olof Widlund
Subjects: Differential equations, Partial--Congresses, Decomposition method--Congresses
Abstract: This volume contains a selection of papers presented at the 21st international conference on domain decomposition methods in science and engineering held in Rennes, France, June 25-29, 2012. Domain decomposition is an active and interdisciplinary research discipline, focusing on the development, analysis and implementation of numerical methods for massively parallel computers. Domain decomposition methods are among the most efficient solvers for large scale applications in science and engineering. They are based on a solid theoretical foundation and shown to be scalable for many important applications. Domain decomposition techniques can also naturally take into account multiscale phenomena. This book contains the most recent results in this important field of research, both mathematically and algorithmically and allows the reader to get an overview of this exciting branch of numerical analysis and scientific computing.
Published: 2014

20. A Posteriori Estimates for a Natural Neumann–Neumann Domain Decomposition Algorithm on a Unilateral Contact Problem

Author: Taoufik Sassi, L. Gallimard, D. Choï, Laboratoire de Mathématiques Nicolas Oresme (LMNO), Centre National de la Recherche Scientifique (CNRS)-Université de Caen Normandie (UNICAEN), Normandie Université (NU)-Normandie Université (NU), Laboratoire Energétique Mécanique Electromagnétisme (LEME), Université Paris Nanterre (UPN), Laboratoire de Mathématiques Nicolas Oresme ( LMNO ), Université de Caen Normandie ( UNICAEN ), Normandie Université ( NU ) -Normandie Université ( NU ) -Centre National de la Recherche Scientifique ( CNRS ), Laboratoire Energétique Mécanique Electromagnétisme ( LEME ), Université Paris Nanterre ( UPN ), Université de Caen Normandie (UNICAEN), and Normandie Université (NU)-Normandie Université (NU)-Centre National de la Recherche Scientifique (CNRS)
Subjects: Contact problem, Mathematical optimization, Truncation error, Discretization, Unilateral contact, Theoretical Computer Science, Error estimation, [SPI]Engineering Sciences [physics], Approximation error, Convergence (routing), [ SPI ] Engineering Sciences [physics], Applied mathematics, Algebraic error, Discretization error, ComputingMilieux_MISCELLANEOUS, Mathematics, Numerical Analysis, Applied Mathematics, General Engineering, Estimator, Computational Mathematics, Computational Theory and Mathematics, A priori and a posteriori, Round-off error, Domain decomposition algorithm, Software
Abstract: International audience; In this paper we present an error estimator for unilateral contact problems solved by a Neumann–Neumann Domain Decomposition algorithm. This error estimator takes into account both the spatial error due to the ﬁnite element discretization and the algebraic error due to the domain decomposition algorithm. To differentiate speciﬁcally the contribution of these two error sources to the global error, two quantities are introduced: a discretization error indicator and an algebraic error indicator. The effectivity indices and the convergence of both the global error estimator and the error indicators are shown on several examples.
Published: 2015

21. A posteriori error estimates and domain decomposition with nonmatching grids

Author: Taoufik Sassi and Jérôme Pousin
Subjects: Applied Mathematics, Mathematical analysis, Hilbert space, Estimator, Domain decomposition methods, Residual, Finite element method, Computational Mathematics, Nonlinear system, symbols.namesake, symbols, A priori and a posteriori, Decomposition method (constraint satisfaction), Mathematics
Abstract: Let F be a nonlinear mapping defined from a Hilbert space X into its dual X′, and let x be in X the solution of F(x)=0. Assume that, a priori, the zone where the gradient of the function x has a large variation is known. The aim of this article is to prove a posteriori error estimates for the problem F(x)=0 when it is approximated with a Petrov–Galerkin finite element method combined with a domain decomposition method with nonmatching grids. A residual estimator for a model semi-linear problem is proposed. We prove that this estimator is asymptotically equivalent to a simplified one adapted to parallel computing. Some numerical results are presented, showing the practical efficiency of the estimator.
Published: 2005

22. Mixed finite element approximation of 3D contact problems with given friction: Error analysis and numerical realization

Author: Taoufik Sassi and Jaroslav Haslinger
Subjects: Numerical Analysis, Mathematical optimization, Applied Mathematics, Numerical analysis, Regularization (mathematics), Finite element method, Piecewise linear function, Computational Mathematics, Rate of convergence, Error analysis, Modeling and Simulation, Piecewise, Applied mathematics, Constant function, Analysis, Mathematics
Abstract: This contribution deals with a mixed variational formulation of 3D contact problems with the simplest model involving friction. This formulation is based on a dualization of the set of admissible displacements and the regularization of the non-differentiable term. Displacements are approximated by piecewise linear elements while the respective dual variables by piecewise constant functions on a dual partition of the contact zone. The rate of convergence is established provided that the solution is smooth enough. The numerical realization of such problems will be discussed and results of a model example will be shown.
Published: 2004

23. A Neumann-Neumanndomain decomposition algorithm for the Signorini problem

Author: Guy Bayada, Taoufik Sassi, and Jalila Sabil
Subjects: Dirichlet problem, Mathematics::Operator Algebras, Applied Mathematics, Mathematical analysis, Parallel algorithm, Domain decomposition methods, Mathematics::Spectral Theory, Contact problems, Domain (mathematical analysis), Variational inequality, Convergence (routing), Neumann boundary condition, Signorini problem, Algorithm, Mathematics
Abstract: In this paper, we propose a Neumann-Neumann algorithm to approximate a frictionless static Signorini contact problem between two elastic bodies and we prove its convergence. The Neumann-Neumann algorithm is a parallel one, in which we have to solve a Dirichlet problem and then a Neumann one, simultaneously on each domain. The primary feature of this new algorithm is the retention the natural interface between the two bodies as a numerical interface for the domain decomposition.
Published: 2004
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24. Méthode d'éléments finis avec hybridisation frontière pour les problèmes de contact avec frottement

Author: Laurent Baillet and Taoufik Sassi
Subjects: General Medicine, Humanities, Mathematics
Abstract: Resume Dans cette Note, nous proposons une methode d'elements finis avec hybridisation frontiere pour les problemes de contact avec frottement. Dans le probleme de point-selle discret, les cones convexes associes aux contraintes normale et tangentielle sont constitues de fonctions continues et affines par morceaux verifiant des conditions affaiblies de negativite sur la zone de contact. Une estimation a priori optimale est etablie dans ce cas. Des essais numeriques confirmant les resultats theoriques sont presentes. Pour citer cet article : L. Baillet, T. Sassi, C. R. Acad. Sci. Paris, Ser. I 334 (2002) 917–922.
Published: 2002

25. Algorithme de Neumann–Dirichlet pour des problèmes de contact unilatéral : Résultat de convergence

Author: Guy Bayada, Jalila Sabil, and Taoufik Sassi
Subjects: General Medicine, Humanities, Mathematics
Abstract: Resume Dans cette Note, nous proposons et nous demontrons la convergence d'un algorithme de decomposition de domaine de type Neumann–Dirichlet. Celui-ci permet d'approcher un probleme de contact unilateral sans frottement entre deux materiaux elastiques en gardant les interfaces (physiques) de contact comme interfaces (numeriques) de decomposition. L'idee est de remplacer dans l'approche proposee par [4], le probleme de Dirichlet par une inequation variationnelle. Pour citer cet article : G. Bayada et al., C. R. Acad. Sci. Paris, Ser. I 335 (2002) 381–386.
Published: 2002

26. A Posteriori Error Estimates for a Neumann-Neumann Domain Decomposition Algorithm Applied to Contact Problems

Author: Daniel Choï, Taoufik Sassi, and Laurent Gallimard
Subjects: Mathematical optimization, Frictionless contact, Domain decomposition algorithm, A priori and a posteriori, Estimator, Applied mathematics, Global error, Finite element method, Mathematics, Resolution (algebra)
Abstract: We consider a Neumann-Neumann Domain Decomposition algorithm associated to a finite element method to approximate a unilateral frictionless contact problem between two elastic bodies. We present a global error estimator that takes into acount as well of the error introduced by finite element analysis as the error committed by the iterative resolution of the domain decomposition algorithm. The control of these errors sources is based on errors indicators that estimate the contribution of each source of error. Numerical results are presented, showing the practical efficiency of the estimator.
Published: 2014

27. A Domain Decomposition Algorithm for Contact Problems with Coulomb’s Friction

Author: Jaroslav Haslinger, Radek Kučera, and Taoufik Sassi
Subjects: Classical mechanics, Domain decomposition algorithm, Mathematical analysis, Linear elasticity, A domain, Decomposition (computer science), Coulomb, Boundary (topology), Coulomb friction, Domain (mathematical analysis), Mathematics
Abstract: The paper analyzes a continuous and discrete version of the Neumann–Neumann domain decomposition algorithm for two-body contact problems with Coulomb friction. Each iterative step consists of a linear elasticity problem for one body with displacements prescribed on a contact part of the boundary and a contact problem with Coulomb friction for the second body. To ensure continuity of contact stresses, two auxiliary Neumann problems in each domain are solved. Numerical experiments illustrate the performance of the proposed approach.
Published: 2014

28. Domain Decomposition with Nesterov’s Method

Author: Taoufik Sassi, Jonas Koko, and Firmin Andzembe
Subjects: Matrix (mathematics), Applied mathematics, ComputerApplications_COMPUTERSINOTHERSYSTEMS, Domain decomposition methods, Minification, Gradient projection, Gradient method, Computer Science::Databases, Poisson problem, Mathematics
Abstract: We apply the Nesterov minimization method to the domain decomposition of a Poisson problem. The resulting domain decomposition method can be viewed as a projected gradient method and needs only matrix/vector multiplications. Preliminary numerical experiments show that significant speed-up can be obtained with the method.
Published: 2014

29. Mixed finite element methods for unilateral problems: convergence analysis and numerical studies

Author: Patrice Coorevits, Taoufik Sassi, Khalid Lhalouani, and Patrick Hild
Subjects: Mathematical optimization, Algebra and Number Theory, Discretization, Applied Mathematics, Numerical analysis, Finite element method, Piecewise linear function, Computational Mathematics, symbols.namesake, Lagrange multiplier, Saddle point, Piecewise, symbols, Applied mathematics, Signorini problem, Mathematics
Abstract: In this paper, we propose and study different mixed variational methods in order to approximate with finite elements the unilateral problems arising in contact mechanics. The discretized unilateral conditions at the candidate contact interface are expressed by using either continuous piecewise linear or piecewise constant Lagrange multipliers in the saddle-point formulation. A priori error estimates are established and several numerical studies corresponding to the different choices of the discretized unilateral conditions are achieved.
Published: 2001

30. Estimateurs d'erreur a posteriori et formulation variationnelle de l'équation de transport

Author: Ouaténi Diallo, Jérôme Pousin, and Taoufik Sassi
Subjects: Partial differential equation, Optimal estimation, Rate of convergence, Variational equation, Applied mathematics, General Medicine, Galerkin method, Convection–diffusion equation, Mathematics
Abstract: Resume Dans cette Note, nous proposons un estimateur d'erreur de type residuel pour deux formulations variationnelles de l'equation de transport, l'une de Galerkin, l'autre de Petrov-Galerkin. Nous montrons qu'un des estimateurs est optimal pour une norme appropriee et nous comparons notre estimateur a celui propose dans [7].
Published: 1999

31. Méthode d'éléments finis hybrides en décomposition de domaines pour des problèmes de contact unilatéral

Author: Taoufik Sassi and Khalid Lhalouani
Subjects: Numerical analysis, Mathematical analysis, Unilateral contact, Geometry, Domain decomposition methods, General Medicine, Finite element method, symbols.namesake, Lagrange multiplier, Piecewise, symbols, Decomposition method (constraint satisfaction), Constant function, Mathematics
Abstract: In this Note, we deal with the domain decomposition method with non-matching grids for solving unilateral contact problem without friction between two deformable bodies. The unilateral contact conditions at the interface are expressed with a mixed formulation. The space of Lagrange multiplier defined on the contact zone is approximated by piecewise constant functions. Optimal error bound of h3/4 is obtained.
Published: 1998

32. Eléments finis avec joints pour des problèmes de contact avec frottement de Coulomb non local

Author: Michèle Chambat, Khalid Lhalouani, Guy Bayada, and Taoufik Sassi
Subjects: General Medicine, Mathematics, Mathematical physics
Abstract: Resume On considere deux problemes de contact unilateral avec frottement de Coulomb non local pour lesquels on introduit une discretisation en elements finis non conformes. Dans le cas classique du contact entre deux solides elastiques, l'estimation d'erreur est en h3/4. Le deuxieme cas correspond a un couplage entre un solide elastique et un revetement mince ≪ mou ≫. L'operateur d'elasticite dans le revetement n'est plus coercif au sens habituel, ceci entraine une perte de regularite sur les traces. On introduit un element fini specifique qui permet d'obtenir une estimation d'erreur en h1/2.
Published: 1997

33. Block thresholding for wavelet-based estimation of function derivatives from a heteroscedastic multichannel convolution model

Author: Fabien Navarro, Christophe Chesneau, Jalal M. Fadili, Taoufik Sassi, Laboratoire de Mathématiques Nicolas Oresme (LMNO), Centre National de la Recherche Scientifique (CNRS)-Université de Caen Normandie (UNICAEN), Normandie Université (NU)-Normandie Université (NU), Equipe Image - Laboratoire GREYC - UMR6072, Groupe de Recherche en Informatique, Image et Instrumentation de Caen (GREYC), Centre National de la Recherche Scientifique (CNRS)-École Nationale Supérieure d'Ingénieurs de Caen (ENSICAEN), Normandie Université (NU)-Normandie Université (NU)-Université de Caen Normandie (UNICAEN), Normandie Université (NU)-Centre National de la Recherche Scientifique (CNRS)-École Nationale Supérieure d'Ingénieurs de Caen (ENSICAEN), and Normandie Université (NU)
Subjects: Statistics and Probability, minimax, Mathematics - Statistics Theory, multichannel observations, Statistics Theory (math.ST), 02 engineering and technology, deconvolution, 01 natural sciences, wavelets, Convolution, 010104 statistics & probability, symbols.namesake, block thresholding, [MATH.MATH-ST]Mathematics [math]/Statistics [math.ST], 62G07, FOS: Mathematics, 0202 electrical engineering, electronic engineering, information engineering, Applied mathematics, 0101 mathematics, 62G20, Mathematics, Smoothness (probability theory), Estimator, 020206 networking & telecommunications, Function (mathematics), [STAT.TH]Statistics [stat]/Statistics Theory [stat.TH], Minimax, derivative estimation, Gaussian noise, Product (mathematics), Adaptive estimator, symbols, 62G07,62G20,62F12, Statistics, Probability and Uncertainty, 62F12
Abstract: 27p, 4 fig; International audience; We observe $n$ heteroscedastic stochastic processes $\{Y_v(t)\}_{v}$, where for any $v\in\{1,\ldots,n\}$ and $t \in [0,1]$, $Y_v(t)$ is the convolution product of an unknown function $f$ and a known blurring function $g_v$ corrupted by Gaussian noise. Under an ordinary smoothness assumption on $g_1,\ldots,g_n$, our goal is to estimate the $d$-th derivatives (in weak sense) of $f$ from the observations. We propose an adaptive estimator based on wavelet block thresholding, namely the "BlockJS estimator". Taking the mean integrated squared error (MISE), our main theoretical result investigates the minimax rates over Besov smoothness spaces, and shows that our block estimator can achieve the optimal minimax rate, or is at least nearly-minimax in the least favorable situation. We also report a comprehensive suite of numerical simulations to support our theoretical findings. The practical performance of our block estimator compares very favorably to existing methods of the literature on a large set of test functions.
Published: 2013

34. Domain Decomposition Method for Stokes Problem with Tresca Friction

Author: Jonas Koko, Mohamed Khaled Gdoura, and Taoufik Sassi
Subjects: Physics::Fluid Dynamics, Nonlinear system, Numerical analysis, Mathematical analysis, Stokes problem, Domain decomposition methods, Boundary value problem, Slip (materials science), Mathematics
Abstract: Development of numerical methods for the solution of Stokes system with slip boundary conditions (Tresca friction conditions) is a challenging task whose difficulty lies in the nonlinear conditions. Such boundary conditions have to be taken into account in many situations arising in practice, in flow of polymers (see [10] and references therein).
Published: 2013

35. On Domain Decomposition Algorithms for Contact Problems with Tresca Friction

Author: Radek Kučera, Taoufik Sassi, and Julien Riton
Subjects: Multigrid method, Computer science, Augmented Lagrangian method, Numerical analysis, Domain decomposition methods, Development (differential geometry), Boundary value problem, Elasticity (physics), Algorithm, Active set method
Abstract: Development of numerical methods for the solution of contact problems is a challenging task whose difficulty lies in the non-linear conditions for non-penetration and friction. Recently, many authors proposed to use various numerical algorithms combined with multigrid or domain decomposition techniques; see, e.g., the primal-dual active set algorithm [8], the non-smooth multiscale method [10], or the augmented Lagrangian based algorithm [3]. Another alternative consists in the formulation of suitable iterations solving the elasticity equations for each sub-body separately with certain boundary conditions [5]. In [1], the authors proposed a Dirichlet-Neumann algorithm which takes into account the natural interface for frictionless contact problems. Another improvement has led to a Neumann–Neumann algorithm in which they added two Neumann sub-problems in order to ensure the continuity of normal stresses [2]. Later, various numerical implementations of this approach was given in [7, 9].
Published: 2010

36. An Uzawa Domain Decomposition Method for Stokes Problem

Author: Jonas Koko and Taoufik Sassi
Subjects: Discretization, Scale (ratio), business.industry, Mathematics::Analysis of PDEs, Domain decomposition methods, Computational fluid dynamics, Space (mathematics), Physics::Fluid Dynamics, symbols.namesake, Lagrange multiplier, Conjugate gradient method, Compressibility, symbols, Applied mathematics, business, Mathematics
Abstract: The Stokes problem plays an important role in computational fluid dynamics since it is encountered in the time discretization of (incompressible) Navier-Stokes equations by operator-splitting methods [2, 3]. Space discretization of the Stokes problem leads to large scale ill-conditioned systems. The Uzawa (preconditioned) conjugate gradient method is an efficient method for solving the Stokes problem. The Uzawa conjugate gradient method is a decomposition coordination method with coordination by a Lagrange multiplier.
Published: 2010

37. A posteriori error analysis of a domain decomposition algorithm for unilateral contact problem

Author: Taoufik Sassi, Laurent Gallimard, Laboratoire Energétique Mécanique Electromagnétisme (LEME), Université Paris Nanterre (UPN), Laboratoire de Mathématiques Nicolas Oresme (LMNO), Université de Caen Normandie (UNICAEN), Normandie Université (NU)-Normandie Université (NU)-Centre National de la Recherche Scientifique (CNRS), Centre National de la Recherche Scientifique (CNRS)-Université de Caen Normandie (UNICAEN), Normandie Université (NU)-Normandie Université (NU), Laboratoire Energétique Mécanique Electromagnétisme ( LEME ), Université Paris Nanterre ( UPN ), Laboratoire de Mathématiques Nicolas Oresme ( LMNO ), Université de Caen Normandie ( UNICAEN ), and Normandie Université ( NU ) -Normandie Université ( NU ) -Centre National de la Recherche Scientifique ( CNRS )
Subjects: Truncation error, Unilateral contact, Iterative method, 010103 numerical & computational mathematics, 01 natural sciences, Error estimation, [SPI]Engineering Sciences [physics], Algorithm error indicator, [ SPI ] Engineering Sciences [physics], General Materials Science, Domain decomposition, 0101 mathematics, ComputingMilieux_MISCELLANEOUS, Civil and Structural Engineering, Mathematics, Mechanical Engineering, Estimator, Domain decomposition methods, Discretization error indicator, Finite element method, Computer Science Applications, 010101 applied mathematics, Modeling and Simulation, A priori and a posteriori, Round-off error, Algorithm
Abstract: International audience; In this paper, we consider a domain decomposition algorithm associated to a finite element method to approximate a unilateral frictionless contact problem between two elastic bodies. We present a global error estimator that takes into account of the error introduced by finite element analysis as well as the error introduced by the iterative resolution of the domain decomposition algorithm. The control of these error sources is a key point in order to introduce adaptive techniques and we propose error indicators that estimate the contribution of each source of error.
Published: 2010

38. Error estimates for Stokes problem with Tresca friction condition

Author: Mekki Ayadi, Leonardo Baffico, Mohamed Khaled Gdoura, Taoufik Sassi, Université de Sousse, Laboratoire de Mathématiques Nicolas Oresme (LMNO), Centre National de la Recherche Scientifique (CNRS)-Université de Caen Normandie (UNICAEN), and Normandie Université (NU)-Normandie Université (NU)
Subjects: Work (thermodynamics), Field (physics), Bubble, 01 natural sciences, symbols.namesake, FOS: Mathematics, Applied mathematics, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], 35, 65, 76, Boundary value problem, Mathematics - Numerical Analysis, 0101 mathematics, ComputingMilieux_MISCELLANEOUS, Energy functional, Mathematics, Numerical Analysis, Applied Mathematics, 010102 general mathematics, Numerical Analysis (math.NA), Finite element method, 010101 applied mathematics, Constraint (information theory), Computational Mathematics, Modeling and Simulation, Lagrange multiplier, symbols, Analysis, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]
Abstract: In this work we propose and study a three field mixed formulation for solving the Stokes problem with Tresca-type non-linear boundary conditions. Two Lagrange multipliers are used to enforce div(u)=0 constraint and to regularize the energy functional. The resulting problem is discretised using "P1 bubble/P1-P1" finite elements. Error estimates are derived and several numerical studies are achieved.
Published: 2010

39. A Robin Domain Decomposition Algorithm for Contact Problems: Convergence Results

Author: Mohamed Ipopa and Taoufik Sassi
Subjects: Mathematical optimization, Domain decomposition algorithm, Mathematics::Spectral Theory, Resolution (logic), Robin boundary condition, Dirichlet distribution, symbols.namesake, Feature (computer vision), Convergence (routing), Variational inequality, symbols, Contact zone, Applied mathematics, Mathematics
Abstract: In this paper, we propose and study a Robin domain decomposition algorithm to approximate a frictionless unilateral problem between two elastic bodies. Indeed this algorithm combines, in the contact zone, the Dirichlet and Neumann boundaries conditions (Robin boundary condition). The primary feature of this algorithm is the resolution on each sub-domain of variational inequality.
Published: 2009

40. Generalization of Lions' Nonoverlapping Domain Decomposition Method for Contact Problems

Author: François Xavier Roux, Mohamed Ipopa, and Taoufik Sassi
Subjects: Nonlinear system, Generalization, Preconditioner, Mathematical analysis, Variational inequality, Linear elasticity, Degrees of freedom (statistics), Domain decomposition methods, Type (model theory), Mathematics
Abstract: Contact problems take an important place in computational structural mechanics (see [8, 10, 13] and the references therein). Many numerical procedures have been proposed in the literature. They are based on standard numerical solvers for the solution of global problem in combination with a special implementation of the nonlinear contact conditions (see [5, 4]). The numerical treatment of such nonclassical contact problems leads to very large (due to the large ratio of degrees of freedom concerned by contact conditions) and illconditioned systems. Domain decomposition methods are good alternative to overcome this difficulties (see [2, 3, 15, 11, 14]). The aim of this paper is to present and study an efficient iterative schemes based on domain decomposition techniques for a nonlinear problem modeling the frictionless contact of linear elastic bodies. The present method is a generalization to variational inequality of the method described in [17, 9]. It can be interpreted as a nonlinear Robin-Robin type preconditioner.
Published: 2008

41. Mixed finite element methods for the Signorini problem with friction

Author: Laurent Baillet, Taoufik Sassi, Laboratoire de Mécanique des Contacts et des Structures [Villeurbanne] ( LaMCoS ), Institut National des Sciences Appliquées de Lyon ( INSA Lyon ), Université de Lyon-Institut National des Sciences Appliquées ( INSA ) -Université de Lyon-Institut National des Sciences Appliquées ( INSA ) -Centre National de la Recherche Scientifique ( CNRS ), Tribologie et Mécanique des Interfaces ( TMI ), Université de Lyon-Institut National des Sciences Appliquées ( INSA ) -Université de Lyon-Institut National des Sciences Appliquées ( INSA ) -Centre National de la Recherche Scientifique ( CNRS ) -Institut National des Sciences Appliquées de Lyon ( INSA Lyon ), Laboratoire de Mathématiques Nicolas Oresme ( LMNO ), Université de Caen Normandie ( UNICAEN ), Normandie Université ( NU ) -Normandie Université ( NU ) -Centre National de la Recherche Scientifique ( CNRS ), Laboratoire de Mécanique des Contacts et des Structures [Villeurbanne] (LaMCoS), Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Université de Lyon-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS), Tribologie et Mécanique des Interfaces (TMI), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Université de Lyon-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Laboratoire de Mathématiques Nicolas Oresme (LMNO), Centre National de la Recherche Scientifique (CNRS)-Université de Caen Normandie (UNICAEN), and Normandie Université (NU)-Normandie Université (NU)
Subjects: Numerical Analysis, Discretization, Applied Mathematics, Mathematical analysis, 010103 numerical & computational mathematics, Mixed finite element method, 01 natural sciences, mixed finite element methods • unilateral contact problems with friction • a priori error estimates, Finite element method, 010101 applied mathematics, Piecewise linear function, Computational Mathematics, symbols.namesake, [SPI]Engineering Sciences [physics], Lagrange multiplier, Piecewise, symbols, [ SPI ] Engineering Sciences [physics], Partial derivative, 0101 mathematics, Signorini problem, Analysis, Mathematics
Abstract: In this article, we propose and study different mixed variational methods in order to approximate the Signorini problem with friction using finite elements. The discretized normal and tangential constraints at the contact interface are expressed by using either continuous piecewise linear or piecewise constant Lagrange multipliers in the saddle−point formulation. A priori error estimates are established and several numerical examples corresponding to the different choices of the discretized normal and tangential constraints are carried out. © 2006 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2006
Published: 2006

42. Mixed finite element formulation in large deformation frictional contact problem

Author: Laurent Baillet, Taoufik Sassi, Laboratoire de Mécanique des Contacts et des Structures [Villeurbanne] ( LaMCoS ), Institut National des Sciences Appliquées de Lyon ( INSA Lyon ), Université de Lyon-Institut National des Sciences Appliquées ( INSA ) -Université de Lyon-Institut National des Sciences Appliquées ( INSA ) -Centre National de la Recherche Scientifique ( CNRS ), Tribologie et Mécanique des Interfaces ( TMI ), Université de Lyon-Institut National des Sciences Appliquées ( INSA ) -Université de Lyon-Institut National des Sciences Appliquées ( INSA ) -Centre National de la Recherche Scientifique ( CNRS ) -Institut National des Sciences Appliquées de Lyon ( INSA Lyon ), Laboratoire de Mathématiques Nicolas Oresme ( LMNO ), Université de Caen Normandie ( UNICAEN ), Normandie Université ( NU ) -Normandie Université ( NU ) -Centre National de la Recherche Scientifique ( CNRS ), Laboratoire de Mécanique des Contacts et des Structures [Villeurbanne] (LaMCoS), Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Université de Lyon-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS), Tribologie et Mécanique des Interfaces (TMI), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Université de Lyon-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Laboratoire de Mathématiques Nicolas Oresme (LMNO), Centre National de la Recherche Scientifique (CNRS)-Université de Caen Normandie (UNICAEN), Normandie Université (NU)-Normandie Université (NU), and Institut National des Sciences Appliquées (INSA)-Université de Lyon-Institut National des Sciences Appliquées (INSA)-Université de Lyon-Centre National de la Recherche Scientifique (CNRS)
Subjects: Large deformation, friction, Computational Mechanics, [SDU.STU]Sciences of the Universe [physics]/Earth Sciences, Geometry, 02 engineering and technology, 01 natural sciences, Constraint algorithm, 65N30, 74M15, 0203 mechanical engineering, FOS: Mathematics, mixed finite element, Mathematics - Numerical Analysis, 0101 mathematics, ComputingMilieux_MISCELLANEOUS, Mathematics, dynamic explicit, Mechanical Engineering, Mathematical analysis, [ SDU.STU ] Sciences of the Universe [physics]/Earth Sciences, Mixed finite element method, Numerical Analysis (math.NA), Finite element method, 010101 applied mathematics, mortar elements, Computational Mathematics, 020303 mechanical engineering & transports, Mechanics of Materials, Modeling and Simulation, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA], contact, contac problems
Abstract: In this paper, we propose an efficient numerical treatment for solving contact problems with friction between deformable bodies. The discretized normal and tangential constraints at the candidate contact interface are expressed by using either continuous piecewise linear or piecewise constant Lagrange multipliers. Several numerical studies corresponding to this choice are achieved in the PLAST2 code., r\'{e}daction : septembre 2004
Published: 2005

43. Finite element analysis of a contact with friction between an elastic body and a thin soft layer

Author: Jalila Sabil, Vannina Linck, Guy Bayada, Laurent Baillet, Taoufik Sassi, Laboratoire de Mécanique des Contacts et des Structures [Villeurbanne] (LaMCoS), Institut National des Sciences Appliquées de Lyon (INSA Lyon), Institut National des Sciences Appliquées (INSA)-Université de Lyon-Institut National des Sciences Appliquées (INSA)-Université de Lyon-Centre National de la Recherche Scientifique (CNRS), Tribologie et Mécanique des Interfaces (TMI), Institut National des Sciences Appliquées (INSA)-Université de Lyon-Institut National des Sciences Appliquées (INSA)-Université de Lyon-Centre National de la Recherche Scientifique (CNRS)-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Colin, Anne-Marie, Université de Lyon-Institut National des Sciences Appliquées (INSA)-Université de Lyon-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Université de Lyon-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Laboratoire de Mathématiques Appliquées de Lyon (MAPLY), École Centrale de Lyon (ECL), Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Centre National de la Recherche Scientifique (CNRS)-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA), Laboratoire de Mathématiques Nicolas Oresme (LMNO), Centre National de la Recherche Scientifique (CNRS)-Université de Caen Normandie (UNICAEN), and Normandie Université (NU)-Normandie Université (NU)
Subjects: Engineering, Scale (ratio), [SDU.STU.GP]Sciences of the Universe [physics]/Earth Sciences/Geophysics [physics.geo-ph], [PHYS.PHYS.PHYS-GEO-PH]Physics [physics]/Physics [physics]/Geophysics [physics.geo-ph], 02 engineering and technology, Brake pad, [SPI]Engineering Sciences [physics], 0203 mechanical engineering, Dynamic problem, Simulation, ComputingMilieux_MISCELLANEOUS, Thin layers, business.industry, Mechanical Engineering, Surfaces and Interfaces, Mechanics, 021001 nanoscience & nanotechnology, Finite element method, Surfaces, Coatings and Films, Mechanical system, 020303 mechanical engineering & transports, Mechanics of Materials, 0210 nano-technology, Contact area, business, Layer (electronics)
Abstract: International audience; When studying a mechanical system involving contact between two bodies such as a disc and brake pad system, finite element simulations are often used to predict the phenomena involved. However, due to model size and calculation time problems, when modeling this type of mechanical system on a scale of about 100 mm, it is difficult to model as well a layer (for example a third body layer) on a scale of approximately 10 µm. In quasi-static problems it is possible to simulate the contact between an elastic body and a thin elastic layer bonded to a rigid surface, by considering the contact between this elastic body and a rigid surface with a specific contact law. This paper shows that it is possible to implement this specific contact law in a dynamic finite element code to simulate thin layers undergoing quasi-static and dynamic problems without physical contact instabilities. This specific contact law saves a large amount of calculation time. Once the specific contact law has been validated, the influence of the layer thickness is studied.
Published: 2005

44. Simulations numériques de différentes méthodes d'éléments finis pour les problèmes de contact avec frottement

Author: Laurent Baillet, Taoufik Sassi, Laboratoire de Mécanique des Contacts et des Structures [Villeurbanne] (LaMCoS), Institut National des Sciences Appliquées de Lyon (INSA Lyon), Institut National des Sciences Appliquées (INSA)-Université de Lyon-Institut National des Sciences Appliquées (INSA)-Université de Lyon-Centre National de la Recherche Scientifique (CNRS), Tribologie et Mécanique des Interfaces (TMI), Institut National des Sciences Appliquées (INSA)-Université de Lyon-Institut National des Sciences Appliquées (INSA)-Université de Lyon-Centre National de la Recherche Scientifique (CNRS)-Institut National des Sciences Appliquées de Lyon (INSA Lyon), and Université de Lyon-Institut National des Sciences Appliquées (INSA)-Université de Lyon-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)
Subjects: 010101 applied mathematics, Marketing, [SDU.STU.GP]Sciences of the Universe [physics]/Earth Sciences/Geophysics [physics.geo-ph], Strategy and Management, Media Technology, General Materials Science, [PHYS.PHYS.PHYS-GEO-PH]Physics [physics]/Physics [physics]/Geophysics [physics.geo-ph], 010103 numerical & computational mathematics, 0101 mathematics, 01 natural sciences, ComputingMilieux_MISCELLANEOUS
Abstract: Resume Nous proposons une etude numerique de differentes methodes d'elements finis avec multiplicateurs de Lagrange pour les problemes de contact avec frottement de Coulomb. Le probleme de point-selle correspondant est approche par des elements finis lineaires ou quadratiques. Les conditions de contact et de frottement discretisees sont exprimees au sens faible (raccord integral). La mise en œuvre de ces approches est realisee dans la nouvelle version d'un code de calcul par elements finis en deux dimensions (PLAST2). Pour citer cet article : L. Baillet, T. Sassi, C. R. Mecanique 331 (2003).
Published: 2003

45. Domain Decomposition with Nonmatching Grids: Augmented Lagrangian Approach

Author: Patrick Le Tallec and Taoufik Sassi
Subjects: Algebra and Number Theory, Partial differential equation, Discretization, Augmented Lagrangian method, Preconditioner, Applied Mathematics, Mathematical analysis, Domain decomposition methods, Finite element method, Computational Mathematics, Rate of convergence, Applied mathematics, Decomposition method (constraint satisfaction), Mathematics
Abstract: We propose and study a domain decomposition method which treats the constraint of displacement continuity at the interfaces by augmented Lagrangian techniques and solves the resulting problem by a parallel version of the Peaceman-Rachford algorithm. We prove that this algorithm is equivalent to the fictitious overlapping method introduced by P.L. Lions. We also prove its linear convergence independently of the discretization step h, even if the finite element grids do not match at the interfaces. A new preconditioner using fictitious overlapping and well adapted to three-dimensional elasticity problems is also introduced and is validated on several numerical examples.
Published: 1995

46. Convergence of a Neumann-Dirichlet algorithm for tow-body contact problems with non local Coulomb's friction law.

Author: Guy Bayada, Jalila Sabil, and Taoufik Sassi
Abstract: 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. [ABSTRACT FROM AUTHOR]
Published: 2008
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47. Mixed finite element methods for unilateral problems: convergence analysis and numerical studies.

Author: Patrice Coorevits, Patrick Hild, Khalid Lhalouani, and Taoufik Sassi
Published: 2002

48. Distributed Nonsmooth Contact Domain Decomposition (NSCDD): Algorithmic Structure and Scalability

Author: Vincent Visseq, David Dureisseix, Alexandre Martin, Frédéric Dubois, Pierre Alart, Laboratoire de Mécanique et Génie Civil (LMGC), Université de Montpellier (UM)-Centre National de la Recherche Scientifique (CNRS), Laboratoire de Mécanique des Structures Industrielles Durables (LAMSID - UMR 8193), EDF R&D (EDF R&D), EDF (EDF)-EDF (EDF)-Centre National de la Recherche Scientifique (CNRS)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA), Laboratoire de Mécanique des Contacts et des Structures [Villeurbanne] (LaMCoS), Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Université de Lyon-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS), Réseaux, Moyens Informatiques, Calcul Scientifique (Remics), Université de Montpellier (UM)-Centre National de la Recherche Scientifique (CNRS)-Université de Montpellier (UM)-Centre National de la Recherche Scientifique (CNRS), Modélisation Mathématique en Mécanique (M3), This work was partly supported by OSEO, FEDER and the region of Languedoc-Roussillon (Degrip project), Jocelyne Erhel, Martin J. Gander, Laurence Halpern, Géraldine Pichot, Taoufik Sassi, Olof Widlund, Laboratoire de Mécanique et Génie Civil ( LMGC ), Université de Montpellier ( UM ) -Centre National de la Recherche Scientifique ( CNRS ), Laboratoire de Mécanique des Structures Industrielles Durables ( LAMSID - UMR 8193 ), EDF R&D ( EDF R&D ), EDF ( EDF ) -EDF ( EDF ) -Centre National de la Recherche Scientifique ( CNRS ) -Commissariat à l'énergie atomique et aux énergies alternatives ( CEA ), Laboratoire de Mécanique des Contacts et des Structures [Villeurbanne] ( LaMCoS ), Institut National des Sciences Appliquées de Lyon ( INSA Lyon ), Université de Lyon-Institut National des Sciences Appliquées ( INSA ) -Université de Lyon-Institut National des Sciences Appliquées ( INSA ) -Centre National de la Recherche Scientifique ( CNRS ), Réseaux, Moyens Informatiques, Calcul Scientifique ( Remics ), Université de Montpellier ( UM ) -Centre National de la Recherche Scientifique ( CNRS ) -Université de Montpellier ( UM ) -Centre National de la Recherche Scientifique ( CNRS ), Modélisation Mathématique en Mécanique ( M3 ), Jocelyne Erhel, Martin J. Gander, Laurence Halpern, Géraldine Pichot, Taoufik Sassi, Olof Widlund, Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Centre National de la Recherche Scientifique (CNRS)-EDF R&D (EDF R&D), and EDF (EDF)-EDF (EDF)
Subjects: Mathematical optimization, Computer science, Interface (Java), Computation, Structure (category theory), [ SPI.MECA.STRU ] Engineering Sciences [physics]/Mechanics [physics.med-ph]/Mechanics of the structures [physics.class-ph], Domain decomposition methods, Granular media, 02 engineering and technology, [ PHYS.MECA.STRU ] Physics [physics]/Mechanics [physics]/Mechanics of the structures [physics.class-ph], 01 natural sciences, Discrete element method, Computational science, 010101 applied mathematics, [PHYS.MECA.STRU]Physics [physics]/Mechanics [physics]/Structural mechanics [physics.class-ph], [SPI.MECA.STRU]Engineering Sciences [physics]/Mechanics [physics.med-ph]/Structural mechanics [physics.class-ph], Scalability, 0202 electrical engineering, electronic engineering, information engineering, 020201 artificial intelligence & image processing, Parallel detection, 0101 mathematics
Abstract: A draft (preprint) version of the publication is available at http://dd21.inria.fr/pdf/visseqv_contrib.pdf; International audience; Numerical simulations of the dynamics of discrete structures in presence of numerous impacts with frictional contacts leads to CPU-intensive large time computations. To deal with these problems, numerical tools have been developed, such as the nonsmooth contact domain decomposition (NSCDD). We present further a distributed version of its algorithm with parallel detection of fine contacts and discuss two possible communication schemes to solve the interface problem. Those improvements allow to study scalability and numerical performances of the method for 2D and 3D granular media.
Published: 2012

49. An Adaptive Parallel-in-Time Method with application to a membrane problem

Author: Jocelyne Erhel, Noha Makhoul Karam, Nabil Nassif, Institut de Recherche en Informatique et Systèmes Aléatoires (IRISA), Université de Rennes (UR)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université de Bretagne Sud (UBS)-École normale supérieure - Rennes (ENS Rennes)-Institut National de Recherche en Informatique et en Automatique (Inria)-Télécom Bretagne-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS), Department of mathematics [Beirut], American University of Beirut [Beyrouth] (AUB), Simulations and Algorithms on Grids for Environment (SAGE), Inria Rennes – Bretagne Atlantique, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-SYSTÈMES LARGE ÉCHELLE (IRISA-D1), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université de Bretagne Sud (UBS)-École normale supérieure - Rennes (ENS Rennes)-Institut National de Recherche en Informatique et en Automatique (Inria)-Télécom Bretagne-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS)-Université de Rennes (UR)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université de Bretagne Sud (UBS)-École normale supérieure - Rennes (ENS Rennes)-Institut National de Recherche en Informatique et en Automatique (Inria)-Télécom Bretagne-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS)-Institut de Recherche en Informatique et Systèmes Aléatoires (IRISA), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université de Bretagne Sud (UBS)-École normale supérieure - Rennes (ENS Rennes)-Télécom Bretagne-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS), Jocelyne Erhel and Martin Gander and Laurence Halpern and Géraldine Pichot and Taoufik Sassi and Olof Widlund, Université de Rennes 1 (UR1), Université de Rennes (UNIV-RENNES)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA)-Université de Bretagne Sud (UBS)-École normale supérieure - Rennes (ENS Rennes)-Institut National de Recherche en Informatique et en Automatique (Inria)-Télécom Bretagne-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS), Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA)-Université de Bretagne Sud (UBS)-École normale supérieure - Rennes (ENS Rennes)-Institut National de Recherche en Informatique et en Automatique (Inria)-Télécom Bretagne-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS)-Université de Rennes 1 (UR1), Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA)-Université de Bretagne Sud (UBS)-École normale supérieure - Rennes (ENS Rennes)-Institut National de Recherche en Informatique et en Automatique (Inria)-Télécom Bretagne-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS)-Institut de Recherche en Informatique et Systèmes Aléatoires (IRISA), Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA)-Université de Bretagne Sud (UBS)-École normale supérieure - Rennes (ENS Rennes)-Télécom Bretagne-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS), and SAGE team, Inria Rennes and LMNO, Caen
Subjects: Discrete mathematics, Sequence, Work (thermodynamics), [SDU.STU.GP]Sciences of the Universe [physics]/Earth Sciences/Geophysics [physics.geo-ph], Value (computer science), 010103 numerical & computational mathematics, 02 engineering and technology, Function (mathematics), Grid, 01 natural sciences, Data model, Feature (computer vision), 020204 information systems, 0202 electrical engineering, electronic engineering, information engineering, Initial value problem, 0101 mathematics, [INFO.INFO-DC]Computer Science [cs]/Distributed, Parallel, and Cluster Computing [cs.DC], ComputingMilieux_MISCELLANEOUS, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]
Abstract: In a previous work (Nassif et al., In: V.A. al (ed.) ICCS 06. Computer Science, pp. 148–155. Springer, New York, 2006), we introduced an approach for solving the initial value problem $\frac{\mathit{dY}} {\mathit{dt}} = F(t,Y ),\,Y (0) = Y _{0}$ in a time-parallel way. The main feature of the method is its capacity to automatically generate a non-regular time grid, adapted to the behavior of the solution. Parallel integration is made possible by introducing a “shooting function” that partitions the problem into a sequence of shooting value problems, each defined on a time slice of the coarse grid. After rescaling the variables on each slice, a prediction data model that permits accurate predictions of the solution at the beginning of every slice, leads to an Adaptive Parallel Time Integration (APTI) algorithm. In this paper, the method is applied to a membrane problem having oscillatory and unbounded solutions on (0, ∞).
Published: 2014

50. A Mortar BDD method for solving flow in stochastic discrete fracture networks

Author: Jean-Raynald de Dreuzy, Jocelyne Erhel, Géraldine Pichot, Baptiste Poirriez, Pichot, Géraldine, Calcul intensif et simulation - Modelling and Intensive Computation for Aquifer Simulations - - MICAS2007 - ANR-07-CIS7-0004 - CIS - VALID, Jocelyne Erhel and Martin Gander and Laurence Halpern and Géraldine Pichot and Taoufik Sassi, Erhel, Jocelyne, Simulations and Algorithms on Grids for Environment (SAGE), Inria Rennes – Bretagne Atlantique, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-SYSTÈMES LARGE ÉCHELLE (IRISA-D1), Institut de Recherche en Informatique et Systèmes Aléatoires (IRISA), CentraleSupélec-Télécom Bretagne-Université de Rennes 1 (UR1), Université de Rennes (UNIV-RENNES)-Université de Rennes (UNIV-RENNES)-Institut National de Recherche en Informatique et en Automatique (Inria)-École normale supérieure - Rennes (ENS Rennes)-Université de Bretagne Sud (UBS)-Centre National de la Recherche Scientifique (CNRS)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA)-CentraleSupélec-Télécom Bretagne-Université de Rennes 1 (UR1), Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA)-Institut de Recherche en Informatique et Systèmes Aléatoires (IRISA), Université de Rennes (UNIV-RENNES)-Université de Rennes (UNIV-RENNES)-École normale supérieure - Rennes (ENS Rennes)-Université de Bretagne Sud (UBS)-Centre National de la Recherche Scientifique (CNRS)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA), Université de Rennes 1 (UR1), Université de Rennes (UNIV-RENNES)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS), Géosciences Rennes (GR), Centre National de la Recherche Scientifique (CNRS)-Observatoire des Sciences de l'Univers de Rennes (OSUR)-Institut national des sciences de l'Univers (INSU - CNRS)-Université de Rennes 1 (UR1), Université de Rennes (UNIV-RENNES)-Université de Rennes (UNIV-RENNES), GEOFRAC, ANR-07-CIS7-0004,MICAS,Modelling and Intensive Computation for Aquifer Simulations(2007), SAGE team, Inria Rennes and LMNO, Caen, Université de Rennes (UR)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université de Bretagne Sud (UBS)-École normale supérieure - Rennes (ENS Rennes)-Institut National de Recherche en Informatique et en Automatique (Inria)-Télécom Bretagne-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS)-Université de Rennes (UR)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université de Bretagne Sud (UBS)-École normale supérieure - Rennes (ENS Rennes)-Institut National de Recherche en Informatique et en Automatique (Inria)-Télécom Bretagne-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS)-Institut de Recherche en Informatique et Systèmes Aléatoires (IRISA), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université de Bretagne Sud (UBS)-École normale supérieure - Rennes (ENS Rennes)-Télécom Bretagne-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS), Université de Rennes (UR)-Institut national des sciences de l'Univers (INSU - CNRS)-Observatoire des Sciences de l'Univers de Rennes (OSUR), Université de Rennes (UR)-Institut national des sciences de l'Univers (INSU - CNRS)-Université de Rennes 2 (UR2)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE)-Institut national des sciences de l'Univers (INSU - CNRS)-Université de Rennes 2 (UR2)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE)-Centre National de la Recherche Scientifique (CNRS), and Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)
Subjects: Discrete fracture, Discretization, Balancing domain decomposition method, [SDU.STU.GP]Sciences of the Universe [physics]/Earth Sciences/Geophysics [physics.geo-ph], ComputingMethodologies_SIMULATIONANDMODELING, Linear system, 010103 numerical & computational mathematics, Solver, [MATH.MATH-NA] Mathematics [math]/Numerical Analysis [math.NA], 01 natural sciences, Finite element method, 010101 applied mathematics, Flow (mathematics), [INFO.INFO-DC] Computer Science [cs]/Distributed, Parallel, and Cluster Computing [cs.DC], [SDU.STU.GP] Sciences of the Universe [physics]/Earth Sciences/Geophysics [physics.geo-ph], 0101 mathematics, Mortar, [INFO.INFO-DC]Computer Science [cs]/Distributed, Parallel, and Cluster Computing [cs.DC], Algorithm, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA], ComputingMilieux_MISCELLANEOUS, Mathematics
Abstract: International audience; In this paper, flow in Discrete Fracture Networks (DFN) is solved using a Mortar Mixed Hybrid Finite Element Method. To solve large linear systems derived from a nonconforming discretization of stochastic fractured networks, a Balancing Domain Decomposition is used. Tests on three stochastically generated DFN are proposed to show the ability of the iterative solver SIDNUR to solve the flow problem.
Published: 2014

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