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43 results on '"Assous, F."'

1. A new second order Taylor-like theorem with an optimized reduced remainder

Author

Chaskalovic, J. and Assous, F.

Subjects
Mathematics - Numerical Analysis, 65D30, 65N15, 65N30, 65N75, 41A05
Abstract

In this paper, we derive a variant of the Taylor theorem to obtain a new minimized remainder. For a given function $f$ defined on the interval $[a,b]$, this formula is derived by introducing a linear combination of $f'$ computed at $n+1$ equally spaced points in $[a,b]$, together with $f''(a)$ and $f''(b)$. We then consider two classical applications of this Taylor-like expansion: the interpolation error and the numerical quadrature formula. We show that using this approach improves both the Lagrange $P_2$ - interpolation error estimate and the error bound of the Simpson rule in numerical integration.

Published
2023

18. A characterization of singular electromagnetic fields by an inductive approach

Author

Assous, F., Patrick Ciarlet, Garcia, E., Ariel University Center (AUC), Propagation des Ondes : Étude Mathématique et Simulation (POEMS), Inria Saclay - Ile de France, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Unité de Mathématiques Appliquées (UMA), École Nationale Supérieure de Techniques Avancées (ENSTA Paris)-École Nationale Supérieure de Techniques Avancées (ENSTA Paris)-Centre National de la Recherche Scientifique (CNRS), Astrium Space Transportation (AST), and ASTRIUM

Subjects
polyhedral domains, [SPI.ELEC]Engineering Sciences [physics]/Electromagnetism, Maxwell's equations, singular geometries
Abstract

International audience; In this article, we are interested in the mathematical modeling of singular electromagnetic fields, in a non-convex polyhedral domain. We first describe the local trace (i. e. defined on a face) of the normal derivative of an L2 function, with L2 Laplacian. Among other things, this allows us to describe dual singularities of the Laplace problem with homogeneous Neumann boundary condition. We then provide generalized integration by parts formulae for the Laplace, divergence and curl operators. With the help of these results, one can split electromagnetic fields into regular and singular parts, which are then characterized. We also study the particular case of divergence-free and curl-free fields, and provide non-orthogonal decompositions that are numerically computable. © 2008 Institute for Scientific Computing and Information.

Published
2008

26. Numerical method for stress fields calculation in dissimilar elastic material with initial crack in axially symmetrical geometry.

Author

Michaeli, M., Assous, F., and Golubchik, A.

Abstract

This work deals with the crack problem simulation in dissimilar material. We propose a new numerical approach, based on a modified Nitsche's variational formulation, to handle the interface conditions in the Navier-Lame equations between two or more axially symmetrical sub domains, characterized by different material constants. This gives a numerical method easy to implement, that is able to solve problems in domains with cracks, where the stress fields tend to infinity. We present the variational formulation which provides the solution in terms of displacements field in the case of a crack existence for axisymmetric plate domain Ω made of several different layers characterized by different material properties. [ABSTRACT FROM AUTHOR]

Published
2013
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33. A Variational Approach to Compute Singular Axisymmetric Electromagnetic Fields.

Author

Assous, F. and Raichik, I.

Subjects
MAXWELL equations, ELECTRIC fields, ELECTROMAGNETIC fields, CARTESIAN coordinates, ELECTROMAGNETIC induction, SOBOLEV spaces
Abstract

We propose a new variational approach to solve the axisymmetric Maxwell equations in singular domains, as for example in non convex polygonal domains. We focus on the computation of the electric field E = (Er, Ez). We show that the key point is to solve axisymmetric Laplace-like operators in the singular domain. This can not be performed by a standard finite element method, which would give a solution identically equal to zero. To get the true non-vanishing solution, we decompose the computational domain into several subdomains, then we derive an ad hoc variational formulation, in which the interface conditions are imposed through a method deduced from a Nitsche approach. Numerical examples are shown. [ABSTRACT FROM AUTHOR]

Published
2013

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