Youssef Youssef Ayyad

Associate professor
Mathematics department - Section I - Hadath
Speciality: Mathematics
Specific Speciality: PDEs/ Control Theory

Teaching 5 Taught Courses
(2014-2015) Math 101 - Linear Algebra I (Matrix Algebra)

BS Mathematics

(2014-2015) Math 101 - Linear Algebra I (Matrix Algebra)

BS Mathematics

(2014-2015) Math 103 - Linear Algebra II (Vector Space)

BS Mathematics

(2014-2015) Math 105 - Integral Calculus

BS Mathematics

(2014-2015) Math 283 - Linear Algebra

BS Chemistry

Publications 5 publications
Youssef Ayyad & Ali Ayad & Ali Fares Parametric Euclidean Algorithm Journal of Theoretical Mathematics and Applications 2013

In this paper, we deal with the computation of generic greatest common divisors (gcd) of a finite set of parametric univariate polynomials. We will describe a parametric version of the well-known euclidean algorithm for computing gcds of univariate polynomials. We introduce the notion of parametric greatest common divisor in order to uniformly describe the gcd of univariate polynomials depending on parameters. The main algorithm of the paper decomposes the parameters space into a finite number of constructible sets such that a gcd of the parametric univariate polynomials is given uniformly in each constructible set.

Youssef Ayyad & Ali Ayad & Ali Fares An algorithm for solving zero-dimensional parametric systems of polynomial homogeneous equations The Journal of Nonlinear Science and Applications(JNSA) 2012

This paper presents a new algorithm for solving zero-dimensional parametric systems of polynomial homogeneous equations. This algorithm is based on the computation of what we call parametric U-resultants. The parameters space, i.e., the set of values of the parameters is decomposed into a nite number of constructible sets. The solutions of the input polynomial system are given uniformly in each constructible set by Polynomial Univariate Representations. The complexity of this algorithm is single exponential in the number n of the unknowns and the number r of the parameters.

• Youssef Ayyad, Mikaël Barboteu Formulation and analysis of two energy-consistent methods for nonlinear elastodynamic frictional contact problems Journal of Computational and applied Mathematics, CAM 2009

Energy-conserving algorithms are necessary to solve nonlinear elastodynamic problems in order to recover long term time integration accuracy and stability. Furthermore, some physical phenomena (such as friction) can generate dissipation; then in this work, we present and analyse two energy-consistent algorithms for hyperelastodynamic frictional contact problems which are characterised by a conserving behaviour for frictionless impacts but also by an admissible frictional dissipation phenomenon. The first approach permits one to enforce, respectively, the Kuhn–Tucker and persistency conditions during each time step by combining an adapted continuation of the Newton method and a Lagrangean formulation. In addition the second method which is based on the work in [P. Hauret, P. Le Tallec, Energy-controlling time integration methods for nonlinear elastodynamics and low-velocity impact, Comput. Methods Appl. Mech. Eng. 195 (2006) 4890–4916] represents a specific penalisation of the unilateral contact conditions. Some numerical simulations are presented to underscore the conservative or dissipative behaviour of the proposed methods.

• Youssef Ayyad & Mikaël Barboteu & J.R. Fernandez A frictionless elastodynamic contact problem with energy conservation properties : numerical analysis and computational aspects Computer Methods in Applied Mechanics and Engineering, CMAME 2009

A dynamic frictionless contact problem between a viscoelastic body and a rigid obstacle is numerically studied in this paper. The contact is modelled using an adapted unilateral contact law in terms of velocities in order to obtain some energy conservation properties. The variational formulation is briefly recalled. Then, a fully discrete scheme is introduced based on the finite element method to approximate the spatial variable and the midpoint scheme to discretize the time derivatives. Error estimates are derived on the approximative solutions from which the linear convergence of the algorithm is deduced under suitable regularity conditions. Furthermore, we focus our interest on the analysis of the discrete energy evolution and the presentation of an adapted numerical algorithm. Finally, a representative two-dimensional example is presented to demonstrate the accuracy and the energy consistent properties of the numerical scheme.

Youssef Ayyad, Mircea Sofonea Analysis of two dynamic frictionless contact problems for elastic-visco-plastic materials Electron. J. Diff Eqns 2007

We consider two mathematical models which describe the contact between an elastic-visco-plastic body and an obstacle, the so-called foundation. In both models the contact is frictionless and the process is assumed to be dynamic. In the first model the contact is described with a normal compliance condition and, in the second one, is described with a normal damped response condition. We derive a variational formulation of the models which is in the form of a system coupling an integro-differential equation with a second order variational equation for the displacement and the stress fields. Then we prove the unique weak solvability of the models. The proofs are based on arguments on nonlinear evolution equations with monotone operators and fixed point. Finally, we study the dependence of the solution with respect to a perturbation of the contact conditions and prove a convergence result.


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