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15 results on '"Henda El Fekih"'

1. Progress and impact of the publications of the Faculty of Medicine of Tunis: A 55 years study

Author

Rim, Charfi, Mouna, Mlika, Sarra, Cheikhrouhou, Henda, El Fekih, Fathi, Sellaouti, Lilia, Zakhama, Iheb, Labbene, and Mohamed, Jouini

Subjects
Adult, Male, Publishing, Biomedical Research, Faculty, Medical, Education, Medical, Publications, History, 20th Century, Middle Aged, History, 21st Century, Cross-Sectional Studies, Bibliometrics, Humans, Female
Abstract

Over the past few years, efforts have been made to ensure that the teachers of the Faculty of Medicine of Tunis (FMT) cite their affiliation to the FMT and the University of Tunis El Manar in addition to their hospital institutions and their research structure in their publications.In this study, we proposed to evaluate the FMT's membership in the publications of its teachers, to identify the different types of publications and to estimate the real number.In this bibliometric cross-sectional study, we retrieved the FMT publications indexed in medline/pubmed database (1964-June2019). We have chosen the keywords corresponding to the publications of group1 (referenced FMT) and group2 (referenced FMT or annexed hospital-university institutions). Next, we calculated the rate of group1 on group2 and sorted the different types of items in group2. Finally, We estimated, after randomization, the actual number of FMT publications for a 99% confidence interval (99% CI).For groups 1 and 2, 1477 and 5194 publications were retrieved, respectively. The FMT membership rate averaged 28% ranging from 4% (1990-2010) to 44% (2011-2019). Of the FMT publications, 30% were free of charge and 55% were original articles. After a draw for 300 group2 publications, the estimated number of total FMT publications was between 4519 and 4934 for a 99% CI.It is essential to mention its affiliation to «the Faculty of Medicine of Tunis» and to «the University of Tunis El Manar» in order to improve the visibility and ranking of our two academic institutions.

Published
2020

2. A finite element method for the inverse problem of boundary data recovery in an oxygen balance model

Author

Naïma Débit, Souad Khiari, Henda El Fekih, and Faker Ben Belgacem

Subjects
Applied Mathematics, Mathematical analysis, 02 engineering and technology, Mixed finite element method, Inverse problem, Boundary knot method, 01 natural sciences, Finite element method, 010101 applied mathematics, 0202 electrical engineering, electronic engineering, information engineering, Method of fundamental solutions, 020201 artificial intelligence & image processing, Boundary value problem, 0101 mathematics, Differential algebraic equation, Extended finite element method, Mathematics
Abstract

The inverse problem under investigation consists of the boundary data completion in a deoxygenation-reaeration model in stream-waters. The unidimensional model we deal with is based on the one introduced by Streeter and Phelps, augmented by Taylor dispersion terms. The missing boundary condition is the load or/and the flux of the biochemical oxygen demand indicator at the upstream point. The counterpart is the availability of two boundary conditions on the dissolved oxygen tracer at the same point. The major consequence of these non-standard boundary conditions is that dispersion-reaction equations on both oxygen indicators are strongly coupled and the resulting system becomes ill-posed. The main purpose here is a finite element space-discretization of the variational problem. Mixed finite elements turn out to be well fitted and yield a non-symmetric saddle point system. The obtained semi-discrete problem is a differential algebraic equation that needs specific tools for its analysis. Combining analytical calculations and theoretical justifications, we try to elucidate the main properties of this ill-posed dynamical problem and understand its mathematical structure.

Published
2015

3. Dirichlet boundary control for a parabolic equation with a final observation I: A space–time mixed formulation and penalization

Author

Faker Ben Belgacem, Henda El Fekih, and Christine Bernardi

Subjects
Well-posed problem, symbols.namesake, Adjoint equation, General Mathematics, Dirichlet boundary condition, Dirichlet's principle, Mathematical analysis, symbols, Dirichlet's energy, Boundary value problem, Mixed boundary condition, Optimal control, Mathematics
Abstract

We are interested in the optimal control problem of a parabolic equation with no state constraints, where the quadratic cost functional involves a final observation and the control variable is a Dirichlet boundary condition. Practical considerations lead us to use Dirichlet controls with no more regularity than square integrability, which arise some technical difficulties in the mathematical analysis. After setting the state equation and the related adjoint equation we fit the two coupled equations into a mixed space-time variational framework. The resulting saddle-point problem turns out to be well posed. We then use a Robin penalization on the Dirichlet control which enables us to re-transcript the mixed problem in a form better suited to numerical computations. We analyze and establish the convergence when the penalty parameter tends to zero, first without additional smoothness assumptions on the optimal control and then for smooth controls.

Published
2011

4. Spectral and High Order Methods for Partial Differential Equations - ICOSAHOM 2012 : Selected Papers From the ICOSAHOM Conference, June 25-29, 2012, Gammarth, Tunisia

Author

Mejdi Azaïez, Henda El Fekih, Jan S. Hesthaven, Mejdi Azaïez, Henda El Fekih, and Jan S. Hesthaven

Subjects
Mathematics, Spectral theory (Mathematics)--Congresses, Differential equations, Partial--Numerical solutions--Congresses
Abstract

The book contains a selection of high quality papers, chosen among the best presentations during the International Conference on Spectral and High-Order Methods (2012), and provides an overview of the depth and breath of the activities within this important research area. The carefully reviewed selection of the papers will provide the reader with a snapshot of state-of-the-art and help initiate new research directions through the extensive bibliography. ​

Published
2014

5. On Cauchy's problem: II. Completion, regularization and approximation

Author

Henda El Fekih, Mejdi Azaïez, and Faker Ben Belgacem

Subjects
Cauchy problem, Mathematical optimization, Applied Mathematics, Cauchy distribution, Inverse problem, Regularization (mathematics), Computer Science Applications, Theoretical Computer Science, Sobolev space, Tikhonov regularization, Signal Processing, Initial value problem, Minification, Mathematical Physics, Mathematics
Abstract

In Ben Belgacem and El Fekih (2005 On Cauchy's problem: I. A variational Steklov–Poincare theory Inverse Problems 21 1915–36), a new variational theory is introduced for the data completion Cauchy problem, and studied in the Sobolev scales. Reformulating it, owing to the Dirichlet-to-Neumann operator, enables us to prove several mathematical results for the obtained Steklov–Poincare problem and to establish the connection with some well-known minimization methods. In particular, when the over-specified data are incompatible and the existence fails for the Cauchy problem, it is stated that the least-squares incompatibility measure equals zero and so does the minimum value of the Kohn–Vogelius function, though all the minimizing sequences blow up. Because of the ill-posedness of the Cauchy–Steklov–Poincare problem, an efficient numerical simulation of it can scarcely be achieved without some regularization materials. When combined with carefully chosen stopping criteria, they bring stability to the computations and dampen the noise perturbations caused by possibly erroneous measurements. This paper, part II, is the numerical counterpart of I and handles some practical issues. We are mainly involved in the Tikhonov scheme and the finite-element method applied to the unstable data completion problem. We lay down a new non-distributional space, in the Steklov–Poincare framework, that allows for an elegant investigation of the reliability of both regularizations in: (i) approximating the exact solution, for compatible data and (ii) providing a consistent pseudo-solution, for incompatible data, that turns also to be a minimizing sequence of the Kohn–Vogelius gap function. Moreover, some convergence estimates with respect to the regularization parameters are stated for some worthy indicators such as the incompatibility measure and the minimum value of the Kohn–Vogelius and energy functions. Finally, we report and discuss some informative computing experiences to support the theoretical predictions of each regularization and to assess their reliability.

Published
2006

6. On Cauchy's problem: I. A variational Steklov–Poincaré theory

Author

Faker Ben Belgacem and Henda El Fekih

Subjects
Cauchy problem, Partial differential equation, Applied Mathematics, Mathematical analysis, Computer Science Applications, Theoretical Computer Science, Semi-elliptic operator, Elliptic partial differential equation, Signal Processing, Free boundary problem, Cauchy boundary condition, Boundary value problem, Laplace operator, Mathematical Physics, Mathematics
Abstract

In 1923 (Lectures on Cauchy's Problem in Linear PDEs (New York, 1953)), J Hadamard considered a particular example to illustrate the ill-posedness of the Cauchy problem for elliptic partial differential equations, which consists in recovering data on the whole boundary of the domain from partial but over-determined measures. He achieved explicit computations for the Laplace operator, due to the squared shape of the domain, to observe, in fine, that the solution does not depend continuously on the given boundary data. The primary subject of this contribution is to extend the result to general domains by proving that the Cauchy problem has a variational formulation that can be put under a (variational) pseudo-differential equation, set on the boundary where the data are missing, and defined by a compact Steklov?Poincar?-type operator. The construction of this operator is based on the Dirichlet-to-Neumann mapping, and its compactness is derived from the elliptic regularity theory. Next, using mathematical tools from the linear operator theory and the convex optimization, we provide a comprehensive analysis of the reduced problem which enables us to state that (i) the set of compatible data, for which existence and uniqueness are guaranteed, is dense in the admissible data space; (ii) when the existence fails, due to possible noisy data, the variational problem can be consistently approximated by the least-squares method, that is the incompatibility measure (the deviation indicator or the variational crime made on the Steklov?Poincar? equation) equals zero though all the minimizing sequences blow up.

Published
2005

7. Singular perturbation for the Dirichlet boundary control of elliptic problems

Author

Faker Ben Belgacem, Hejer Metoui, and Henda El Fekih

Subjects
Dirichlet problem, Statistics::Theory, Numerical Analysis, Applied Mathematics, Mathematical analysis, Mixed boundary condition, Robin boundary condition, Statistics::Computation, Statistics::Machine Learning, Computational Mathematics, symbols.namesake, Modeling and Simulation, Dirichlet's principle, Dirichlet boundary condition, symbols, Neumann boundary condition, Statistics::Methodology, Cauchy boundary condition, Boundary value problem, Analysis, Mathematics
Abstract

A current procedure that takes into account the Dirichlet boundary condition with non-smooth data is to change it into a Robin type condition by introducing a penalization term; a major effect of this procedure is an easy implementation of the boundary condition. In this work, we deal with an optimal control problem where the control variable is the Dirichlet data. We describe the Robin penalization, and we bound the gap between the penalized and the non-penalized boundary controls for the small penalization parameter. Some numerical results are reported on to highlight the reliability of such an approach.

Published
2003

8. Boundary stabilizability of the linearized viscous Saint-Venant system

Author

Henda El Fekih, Faker Ben Belgacem, Hassen Arfaoui, Jean-Pierre Raymond, Institut de Mathématiques de Toulouse UMR5219 (IMT), Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS), Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), and Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)

Subjects
Physics, 0209 industrial biotechnology, Steady state, Applied Mathematics, 010102 general mathematics, Boundary (topology), 02 engineering and technology, Heat transfer coefficient, Mechanics, 01 natural sciences, Physics::Fluid Dynamics, 020901 industrial engineering & automation, Flow (mathematics), Exponential stability, 93C20 (35Q35 76B75 93D15), Discrete Mathematics and Combinatorics, 0101 mathematics, Shallow water equations, ComputingMilieux_MISCELLANEOUS, Linear stability, Communication channel
Abstract

We consider a shallow water flow in a channel modeled by the Saint-Venant equations with a viscous term. We are interested in the stabilization of the flow at a steady state. We establish that the semi-group of the linearized system is exponentially stable. However when the convection coefficient is dominant, the natural stabilization turns out to be very slow. One way to enhance the stabilization of the system is to use boundary controls by means of a moving device located at the extremities of the channel. We determine, by an extension method due to Fursikov, boundary Dirichlet controls able to accelerate the stabilization of the flow. Numerical experiments illustrate the efficiency of the control.

Published
2011

9. Parameter choice in the Lavrentiev regularization of the data completion problem

Author

Faker Ben Belgacem, Henda El Fekih, and F Jelassi

Subjects
History, Mathematical optimization, Quadratic equation, General theory, Linear rate, A priori and a posteriori, Regularization (mathematics), Computer Science Applications, Education, Mathematics
Abstract

We use the Lavrentiev method for the regularization of the severely ill-posed data completion problem, put under a variational Steklov-Poincare form. In the choice of the regularizing parameter, we check a 'super-optimal' a priori convergence criterion. Consequently, the solutions obtained by the regularization provide a minimizing sequence of the Kohn-Vogelius function, with a 'quadratic' decaying of the minimum value of it toward zero, instead of the linear rate predicted by the general theory. We call such a result the 'super-convergence' of the approximated 'incompatibility measure' of the variational problem. Finally, we apply the a posteriori Morozov discrepancy principle to the Kohn-Vogelius functional and show how it yields a regularizing strategy. We achieve by some numerical illustrations to support our analysis.

Published
2008

10. Spectral element methods on simplicial meshes

Author

Richard Pasquetti, Francesca Rapetti, Laboratoire Jean Alexandre Dieudonné (JAD), Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS), Control, Analysis and Simulations for TOkamak Research (CASTOR), Inria Sophia Antipolis - Méditerranée (CRISAM), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Alexandre Dieudonné (JAD), Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (... - 2019) (UNS), Mejdi Azaïez, Henda El Fekih, Jan S. Hesthaven, Université Nice Sophia Antipolis (1965 - 2019) (UNS), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Alexandre Dieudonné (LJAD), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA), and Laboratoire Jean Alexandre Dieudonné (LJAD)

Subjects
Linear system, MathematicsofComputing_NUMERICALANALYSIS, 010103 numerical & computational mathematics, Solver, Cartesian product, 01 natural sciences, Quadrature (mathematics), 010101 applied mathematics, Combinatorics, Algebra, symbols.namesake, Elliptic operator, Tensor product, ComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATION, symbols, Schur complement, Gaussian quadrature, 0101 mathematics, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA], ComputingMethodologies_COMPUTERGRAPHICS, Mathematics
Abstract

International audience; We present a review in the construction of accurate and efficient multivariate polynomial approximations on elementary domains that are not Cartesian products of intervals, such as triangles and tetrahedra. After the generalities for high-order nodal interpolation of a function over an interval, we introduce collapsed coordinates and warped tensor product expansions. We then discuss about the choice of interpolation and quadrature points together with the assembling of the final system matrices in the case of elliptic operators. We also present two efficient ways of solving the associated linear system, namely a Schur complement strategy and a p-multigrid solver. Two applications to Computational Fluid Dynamics problems conclude this contribution.

Published
2014

11. High-Order Locally Implicit Time Integration Strategies in a Discontinuous Galerkin Method for Maxwell’s Equations

Author

Stéphane Descombes, Stéphane Lanteri, Ludovic Moya, Laboratoire Jean Alexandre Dieudonné (JAD), Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS), Numerical modeling and high performance computing for evolution problems in complex domains and heterogeneous media (NACHOS), Inria Sophia Antipolis - Méditerranée (CRISAM), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Alexandre Dieudonné (JAD), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (... - 2019) (UNS), Mejdi Azaïez and Henda El Fekih and Jan S. Hesthaven, Laboratoire Jean Alexandre Dieudonné (LJAD), Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Alexandre Dieudonné (LJAD), and COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (1965 - 2019) (UNS)

Subjects
010101 applied mathematics, symbols.namesake, Maxwell's equations, Discontinuous Galerkin method, symbols, Applied mathematics, Development (differential geometry), 010103 numerical & computational mathematics, 0101 mathematics, High order, [INFO.INFO-MO]Computer Science [cs]/Modeling and Simulation, 01 natural sciences, Mathematics
Abstract

International audience; This paper discusses about the development of high-order locally implicit time integration strategies in a discontinuous Galerkin method for Maxwell's equations.

Published
2013

12. Towards a High Order Fourier-SEM Solver of Fluid Models in Tokamaks

Author

Audrey Bonnement, Sebastian Minjeaud, Richard Pasquetti, Control, Analysis and Simulations for TOkamak Research (CASTOR), Inria Sophia Antipolis - Méditerranée (CRISAM), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Alexandre Dieudonné (LJAD), Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA), Laboratoire Jean Alexandre Dieudonné (LJAD), Mejdi Azaïez and Henda El Fekih and Jan S. Hesthaven, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Alexandre Dieudonné (JAD), Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS), and Laboratoire Jean Alexandre Dieudonné (JAD)

Subjects
Physics, Partial differential equation, Tokamak, Anisotropic diffusion, Spectral element method, 010103 numerical & computational mathematics, 01 natural sciences, Finite element method, 010305 fluids & plasmas, law.invention, Computational physics, Magnetic field, symbols.namesake, Fourier transform, Physics::Plasma Physics, law, 0103 physical sciences, symbols, 0101 mathematics, Diffusion (business)
Abstract

International audience; We investigate a fluid modeling approach to describe the plasma behavior in tokamaks. For the numerical approximation, we use a high order method based on Fourier expansions in the toroidal direction and the spectral element method (SEM) in the poloidal plane. We first focus on anisotropic diffusion, because in tokamaks diffusion strongly dominates along the magnetic field lines, and provide some comparisons with finite element results. Then we give preliminary results for a plasma two fluid (ions and electrons) numerical model.

Published
2013

13. A high-order discontinuous Galerkin method for viscoelastic wave propagation

Author

Fabien Peyrusse, Nathalie Glinsky, Stéphane Lanteri, Céline Gélis, Numerical modeling and high performance computing for evolution problems in complex domains and heterogeneous media (NACHOS), Inria Sophia Antipolis - Méditerranée (CRISAM), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Alexandre Dieudonné (JAD), Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS), Département Géotechnique, Eau et Risques (IFSTTAR/GER), Institut Français des Sciences et Technologies des Transports, de l'Aménagement et des Réseaux (IFSTTAR)-PRES Université Paris-Est, Institut de Radioprotection et de Sûreté Nucléaire (IRSN), Mejdi Azaïez and Henda El Fekih and Jan S. Hesthaven, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Alexandre Dieudonné (LJAD), Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (1965 - 2019) (UNS), and COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)

Subjects
Physics, 010504 meteorology & atmospheric sciences, Wave propagation, Differential equation, Numerical analysis, Mathematical analysis, Isotropy, Lagrange polynomial, 010502 geochemistry & geophysics, Mass matrix, 01 natural sciences, [INFO.INFO-MO]Computer Science [cs]/Modeling and Simulation, Mathematics::Numerical Analysis, symbols.namesake, Discontinuous Galerkin method, symbols, Time domain, 0105 earth and related environmental sciences
Abstract

We present a high-order discontinuous Galerkin method for the simulation of P-SV seismic wave propagation in heterogeneous media and two dimensions of space. The first-order velocity-stress system is obtained by assuming that the medium is linear, isotropic and viscoelastic, thus considering intrinsic attenuation. The associated stress-strain relation in the time domain being a convolution, which is numerically intractable, we consider the rheology of a generalized Maxwell body replacing the convolution by differential equations. This results in a velocity-stress system which contains additional equations for the anelastic functions including the strain history of the material. Our numerical method, suitable for complex triangular unstructured meshes, is based on a centered numerical flux and a leap-frog time-discretization. The extension to high order in space is realized by Lagrange polynomial functions, defined locally on each element. The inversion of a global mass matrix is avoided since an explicit scheme in time is used. The method is validated through numerical simulations including comparisons with a finite difference scheme.

Published
2012

14. High-Order ADI Schemes for Convection-Diffusion Equations with Mixed Derivative Terms

Author

Michel Fournié, Alain Rigal, Bertram Düring, Department of Mathematics [Sussex], University of Sussex, Institut de Mathématiques de Toulouse UMR5219 (IMT), Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS), Mejdi Azaïez, Henda El Fekih, Jan S. Hesthaven, Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), and Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)

Subjects
Mathematical analysis, Numerical Analysis (math.NA), 010103 numerical & computational mathematics, Derivative, Mixed derivative, Space (mathematics), 01 natural sciences, 010101 applied mathematics, Alternating direction implicit method, Scheme (mathematics), FOS: Mathematics, Mathematics - Numerical Analysis, 0101 mathematics, High order, Convection–diffusion equation, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA], Mathematics
Abstract

We present new high-order Alternating Direction Implicit (ADI) schemes for the numerical solution of initial-boundary value problems for convection-diffusion equations with mixed derivative terms. Our approach is based on the unconditionally stable ADI scheme proposed by Hundsdorfer. Different numerical discretizations which lead to schemes which are fourth-order accurate in space and second-order accurate in time are discussed., Comment: 10 pages. The final publication is available at Springer via http://dx.doi.org/10.1007/978-3-319-01601-6_17

Published
2012

15. Coupling of an exact transparent boundary condition with a DG method for the solution of the time-harmonic Maxwell equations

Author

Nabil Gmati, Stéphane Lanteri, J. Salhi, M. El Bouajaji, Robust control of infinite dimensional systems and applications (CORIDA), Institut Élie Cartan de Nancy (IECN), Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique de Lorraine (INPL)-Université Nancy 2-Université Henri Poincaré - Nancy 1 (UHP)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique de Lorraine (INPL)-Université Nancy 2-Université Henri Poincaré - Nancy 1 (UHP)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire de Mathématiques et Applications de Metz (LMAM), Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-Inria Nancy - Grand Est, Institut National de Recherche en Informatique et en Automatique (Inria), Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique de Lorraine (INPL)-Université Nancy 2-Université Henri Poincaré - Nancy 1 (UHP)-Institut National de Recherche en Informatique et en Automatique (Inria), Laboratoire de Modélisation Mathématique et Numérique dans les Sciences de l'Ingénieur [Tunis] (LR-LAMSIN-ENIT), Ecole Nationale d'Ingénieurs de Tunis (ENIT), Université de Tunis El Manar (UTM)-Université de Tunis El Manar (UTM), Numerical modeling and high performance computing for evolution problems in complex domains and heterogeneous media (NACHOS), Inria Sophia Antipolis - Méditerranée (CRISAM), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Alexandre Dieudonné (JAD), Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS), Mejdi Azaïez and Henda El Fekih and Jan S. Hesthaven, Institut National de Recherche en Informatique et en Automatique (Inria)-Université Henri Poincaré - Nancy 1 (UHP)-Université Nancy 2-Institut National Polytechnique de Lorraine (INPL)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche en Informatique et en Automatique (Inria)-Université Henri Poincaré - Nancy 1 (UHP)-Université Nancy 2-Institut National Polytechnique de Lorraine (INPL)-Centre National de la Recherche Scientifique (CNRS)-Laboratoire de Mathématiques et Applications de Metz (LMAM), Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-Inria Nancy - Grand Est, Institut National de Recherche en Informatique et en Automatique (Inria)-Université Henri Poincaré - Nancy 1 (UHP)-Université Nancy 2-Institut National Polytechnique de Lorraine (INPL)-Centre National de la Recherche Scientifique (CNRS), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Alexandre Dieudonné (LJAD), Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (1965 - 2019) (UNS), and COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)

Subjects
Physics, Discretization, Truncation, Wave propagation, 010103 numerical & computational mathematics, 01 natural sciences, [INFO.INFO-MO]Computer Science [cs]/Modeling and Simulation, Domain (mathematical analysis), 010101 applied mathematics, symbols.namesake, Classical mechanics, Maxwell's equations, Discontinuous Galerkin method, symbols, T-matrix method, Boundary value problem, 0101 mathematics
Abstract

The numerical simulation of electromagnetic wave propagation in open domains involving scattering objects or/and inhomogeneous regions naturally raises the question of the appropriate treatment of the artificial truncation of the infinite propagation domain. The main issue is to find a suitable way to efficiently model the far-field propagation region, by limiting the extent of the volume discretization.

Published
2012

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