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3. A weighted finite element mass redistribution method for dynamic contact problems

Author

Dabaghi, Farshid, Krejci, Pavel, Petrov, Adrien, Pousin, Jérôme, and Renard, Yves

Subjects
Mathematics - Numerical Analysis, Physics - Classical Physics
Abstract

This paper deals with a one-dimensional wave equation being subjected to a unilateral boundary condition. An approximation of this problem combining the finite element and mass redistribution methods is proposed. The mass redistribution method is based on a redistribution of the body mass such that there is no inertia at the contact node and the mass of the contact node is redistributed on the other nodes. The convergence as well as an error estimate in time are proved. The analytical solution associated with a benchmark problem is introduced and it is compared to approximate solutions for different choices of mass redistribution. However some oscillations for the energy associated with approximate solutions obtained for the second order schemes can be observed after the impact. To overcome this difficulty, an new unconditionally stable and a very lightly dissipative scheme is proposed.

Published
2016

5. A Transport for imaging process

Author

Besson, Olivier, Picq, Martine, and Pousin, Jérôme

Subjects
Mathematics - Numerical Analysis, 35F40, 35L85, 35R05
Abstract

This work originates from a heart's images tracking which is to generate an apparent continuous motion, observable through intensity variation from one starting image to an ending one both supposed segmented. Given two images $\rho_0$ and $\rho_1$, we calculate an evolution process $\rho(t,\cdot)$ which transports $\rho_0$ to $\rho_1$ by using the optical flow. In this paper we propose an algorithm based on a fixed point formulation and a space-time least squares formulation of the transport equation for computing a transport problem. Existence results are given for a transport problem with a minimum divergence for a dual norm or a weighted $H^1_0$-semi norm, for the velocity. The proposed transport is compare with the transport introduced by Dacorogna-Moser. The strategy is implemented in a 2D case and numerical results are presented with a first order Lagrange finite element, showing the efficiency of the proposed strategy., Comment: arXiv admin note: substantial text overlap with arXiv:1009.3420

Published
2012

6. Computing the time-continuous Optimal Mass Transport Problem without Lagrangian techniques

Author

Besson, Olivier, Picq, Martine, and Pousin, Jérôme

Subjects
Mathematics - Classical Analysis and ODEs, Mathematics - Analysis of PDEs, Mathematics - Differential Geometry, Mathematics - Probability
Abstract

This work originates from a heart's images tracking which is to generate an apparent continuous motion, observable through intensity variation from one starting image to an ending one both supposed segmented. Given two images p0 and p1, we calculate an evolution process p(t, \cdot) which transports p0 to p1 by using the optimal extended optical flow. In this paper we propose an algorithm based on a fixed point formulation and a time-space least squares formulation of the mass conservation equation for computing the optimal mass transport problem. The strategy is implemented in a 2D case and numerical results are presented with a first order Lagrange finite element, showing the efficiency of the proposed strategy.

Published
2010

7. Un Mod\`ele simple d'injection diphasique avec phase condensable

Author

Pousin, Jérôme, Zeltz, Eric, and Debicki, Gérard

Subjects
Mathematics - Numerical Analysis
Abstract

L'objectif de cette note est de proposer un mod\`ele math\'ematique simple permettant de comprendre l'arr\^et de la p\'en\'etration d'un flux de vapeur d'eau condensable sur un mur de b\'eton, observ\'e exp\'erimentalement (voir par exemple les diff\'erentes exp\'eriences d'injection de vapeur dans du b\'eton pr\'esent\'ees dans [11], et [7]). Un mod\`ele homog\'en\'eis\'e simple d'injection dans un milieu poreux est propos\'e, donnant une borne pour la position asymptotique en temps du front de p\'en\'etration. The aim of this paper is to propose a simple mathematical model to understand the decision of the penetration of a stream of water vapor condensing on a concrete wall, observed experimentally (see for example the situations described in [11], and [7]). A simple homogenized model for the injection in a porous medium is proposed, giving a bound for the asymptotic-time position at the front of penetration.

Published
2010

8. An Overview of Recent Results on Nitsche’s Method for Contact Problems

Author

Chouly, Franz, Fabre, Mathieu, Hild, Patrick, Mlika, Rabii, Pousin, Jérôme, Renard, Yves, Barth, Timothy J., Series Editor, Griebel, Michael, Series Editor, Keyes, David E., Series Editor, Nieminen, Risto M., Series Editor, Roose, Dirk, Series Editor, Schlick, Tamar, Series Editor, Bordas, Stéphane P. A., editor, Burman, Erik, editor, Larson, Mats G., editor, and Olshanskii, Maxim A., editor

Published
2017
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9. Integrating Fiber Orientation Constraint into a Spatio-temporal FEM Model for Heart Borders and Motion Tracking in Dynamic MRI

Author

Stoica, Răzvan, Pousin, Jérôme, Casta, Christopher, Croisille, Pierre, Zhu, Yue-Min, Clarysse, Patrick, Hutchison, David, editor, Kanade, Takeo, editor, Kittler, Josef, editor, Kleinberg, Jon M., editor, Mattern, Friedemann, editor, Mitchell, John C., editor, Naor, Moni, editor, Nierstrasz, Oscar, editor, Pandu Rangan, C., editor, Steffen, Bernhard, editor, Sudan, Madhu, editor, Terzopoulos, Demetri, editor, Tygar, Doug, editor, Vardi, Moshe Y., editor, Weikum, Gerhard, editor, Camara, Oscar, editor, Mansi, Tommaso, editor, Pop, Mihaela, editor, Rhode, Kawal, editor, Sermesant, Maxime, editor, and Young, Alistair, editor

Published
2013
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10. Driving Dynamic Cardiac Model Adaptation with MR-Tagging Displacement Information

Author

Casta, Christopher, Clarysse, Patrick, Pousin, Jérôme, Schaerer, Joël, Croisille, Pierre, Zhu, Yue-Min, Hutchison, David, Series editor, Kanade, Takeo, Series editor, Kittler, Josef, Series editor, Kleinberg, Jon M., Series editor, Mattern, Friedemann, Series editor, Mitchell, John C., Series editor, Naor, Moni, Series editor, Nierstrasz, Oscar, Series editor, Pandu Rangan, C., Series editor, Steffen, Bernhard, Series editor, Sudan, Madhu, Series editor, Terzopoulos, Demetri, Series editor, Tygar, Doug, Series editor, Vardi, Moshe Y., Series editor, Weikum, Gerhard, Series editor, Metaxas, Dimitris N., editor, and Axel, Leon, editor

Published
2011
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11. Incorporating Low-Level Constraints for the Retrieval of Personalised Heart Models from Dynamic MRI

Author

Casta, Christopher, Clarysse, Patrick, Pousin, Jérôme, Schaerer, Joël, Croisille, Pierre, Zhu, Yue-Min, Hutchison, David, editor, Kanade, Takeo, editor, Kittler, Josef, editor, Kleinberg, Jon M., editor, Mattern, Friedemann, editor, Mitchell, John C., editor, Naor, Moni, editor, Nierstrasz, Oscar, editor, Pandu Rangan, C., editor, Steffen, Bernhard, editor, Sudan, Madhu, editor, Terzopoulos, Demetri, editor, Tygar, Doug, editor, Vardi, Moshe Y., editor, Weikum, Gerhard, editor, Camara, Oscar, editor, Pop, Mihaela, editor, Rhode, Kawal, editor, Sermesant, Maxime, editor, Smith, Nic, editor, and Young, Alistair, editor

Published
2010
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12. A Hyperelastic Deformable Template for Cardiac Segmentation in MRI

Author

Rouchdy, Youssef, Pousin, Jérôme, Schaerer, Joël, Clarysse, Patrick, Hutchison, David, editor, Kanade, Takeo, editor, Kittler, Josef, editor, Kleinberg, Jon M., editor, Mattern, Friedemann, editor, Mitchell, John C., editor, Naor, Moni, editor, Nierstrasz, Oscar, editor, Rangan, C. Pandu, editor, Steffen, Bernhard, editor, Sudan, Madhu, editor, Terzopoulos, Demetri, editor, Tygar, Doug, editor, Vardi, Moshe Y., editor, Weikum, Gerhard, editor, Sachse, Frank B., editor, and Seemann, Gunnar, editor

Published
2007
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17. Residual-based a posteriori error estimation for contact problems approximated by Nitsche's method

Author

Chouly, Franz, Fabre, Mathieu, Hild, Patrick, Pousin, Jérôme, Renard, Yves, Chouly, Franz, Fabre, Mathieu, Hild, Patrick, Pousin, Jérôme, and Renard, Yves

Abstract

We introduce a residual-based a posteriori error estimator for contact problems in two- and three-dimensional linear elasticity, discretized with linear and quadratic finite elements and Nitsche's method. Efficiency and reliability of the estimator are proved under a saturation assumption. Numerical experiments illustrate the theoretical properties and the good performance of the estimator.

Published
2021

28. Solutions for Linear Conservation Laws with Velocity Fields in $$L^{\rm \infty}$$

Author

Besson, Olivier, Pousin, Jérôme, Besson, Olivier, and Pousin, Jérôme

Abstract

A Space-Time Integrated Least Squares (STILS) method is derived for solving the linear conservation law with a velocity field in $$L^{\rm \infty}$$ . An existence and uniqueness result is given for the solution of this equation. A maximum principle is established and finally a comparison with a renormalized solution is presented

Published
2018

32. Estimation et analyse du mouvement

Author

Clarysse , Patrick, Pousin , Jérôme, Imagerie et modélisation Vasculaires, Thoraciques et Cérébrales (MOTIVATE), Centre de Recherche en Acquisition et Traitement de l'Image pour la Santé (CREATIS), Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université de Lyon-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Hospices Civils de Lyon (HCL)-Université Jean Monnet [Saint-Étienne] (UJM)-Institut National de la Santé et de la Recherche Médicale (INSERM)-Centre National de la Recherche Scientifique (CNRS)-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Hospices Civils de Lyon (HCL)-Université Jean Monnet [Saint-Étienne] (UJM)-Institut National de la Santé et de la Recherche Médicale (INSERM)-Centre National de la Recherche Scientifique (CNRS), Modélisation mathématique, calcul scientifique (MMCS), Institut Camille Jordan [Villeurbanne] (ICJ), École Centrale de Lyon (ECL), Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université Jean Monnet [Saint-Étienne] (UJM)-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-École Centrale de Lyon (ECL), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS), Patrick Clarysse, Denis Friboule, 1 - Imagerie et modélisation Vasculaires, Thoraciques et Cérébrales ( MOTIVATE ), Centre de Recherche en Acquisition et Traitement de l'Image pour la Santé ( CREATIS ), Université Claude Bernard Lyon 1 ( UCBL ), Université de Lyon-Université de Lyon-Institut National des Sciences Appliquées de Lyon ( INSA Lyon ), Université de Lyon-Institut National des Sciences Appliquées ( INSA ) -Institut National des Sciences Appliquées ( INSA ) -Hospices Civils de Lyon ( HCL ) -Université Jean Monnet [Saint-Étienne] ( UJM ) -Institut National de la Santé et de la Recherche Médicale ( INSERM ) -Centre National de la Recherche Scientifique ( CNRS ) -Université Claude Bernard Lyon 1 ( UCBL ), Université de Lyon-Institut National des Sciences Appliquées ( INSA ) -Institut National des Sciences Appliquées ( INSA ) -Hospices Civils de Lyon ( HCL ) -Université Jean Monnet [Saint-Étienne] ( UJM ) -Institut National de la Santé et de la Recherche Médicale ( INSERM ) -Centre National de la Recherche Scientifique ( CNRS ), Institut Camille Jordan [Villeurbanne] ( ICJ ), Centre National de la Recherche Scientifique ( CNRS ) -Université Jean Monnet [Saint-Étienne] ( UJM ) -École Centrale de Lyon ( ECL ), Université de Lyon-Institut National des Sciences Appliquées ( INSA ) -Institut National des Sciences Appliquées ( INSA ) -Université Claude Bernard Lyon 1 ( UCBL ), Université de Lyon, and Patrick Clarysse, Denis Friboulet

Subjects
[ SPI.SIGNAL ] Engineering Sciences [physics]/Signal and Image processing, [SPI.SIGNAL]Engineering Sciences [physics]/Signal and Image processing, ComputingMilieux_MISCELLANEOUS
Abstract

International audience

Published
2015

33. Sur la méthode de redistribution de masse pondérée pour un problème élastodynamique avec des contraintes unilatérales

Author

Dabaghi, Farshid, Krejčí, Pavel, Petrov, Adrien, Pousin, Jérôme, Renard, Yves, Legrand, Mathias, Modélisation mathématique, calcul scientifique (MMCS), Institut Camille Jordan [Villeurbanne] (ICJ), École Centrale de Lyon (ECL), Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université Jean Monnet [Saint-Étienne] (UJM)-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-École Centrale de Lyon (ECL), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS), Académie des sciences de la République tchèque, 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), and CSMA

Subjects
solution numérique, [PHYS.MECA]Physics [physics]/Mechanics [physics], méthode de redistribution de masse, [PHYS.MECA] Physics [physics]/Mechanics [physics], contact
Abstract

International audience; On considère une barre élastique homogène vibrant longitudinalement dont une de ses extrémités est libre de bouger, tant qu'elle ne touche pas un obstacle rigide et l'autre extrémité est fixée. Le problème mathématique peut être formulé comme une équation des ondes monodimentionnelles soumise à une condition limite unilatérale. La méthode de redistribution de masse pondérée est introduite et sa convergence est prouvée. Ensuite, différents choix de redistribution de masse sont présentés et analysés.

Published
2015

34. Convergence of mass redistribution method for the wave equation with a unilateral constraint at the boundary

Author

Dabaghi, Farshid, Petrov, Adrien, Pousin, Jérôme, Renard, Yves, Modélisation mathématique, calcul scientifique (MMCS), Institut Camille Jordan [Villeurbanne] (ICJ), École Centrale de Lyon (ECL), Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université Jean Monnet [Saint-Étienne] (UJM)-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-École Centrale de Lyon (ECL), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-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), 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
convergence, uniqueness, mass redistribution method, Existence, variational inequality, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA], unilateral contact
Abstract

This paper focuses on a one-dimensional wave equation being subjected to a unilateral boundary condition. Under appropriate regularity assumptions on the initial data, a new proof of existence and uniqueness results is proposed. The mass redistribution method, which is based on a redistribution of the body mass such that there is no inertia at the contact node, is introduced and its convergence is proved. Finally, some numerical experiments are reported.

Published
2014

39. Principe du Maximum Discret pour une solution au sens des moindres carrés espace-temps pour l'équation de transport avec des éléments finis

Author

Benmansour, Khadidja, Piffet, Loic, Pousin, Jérôme, Institut Camille Jordan [Villeurbanne] (ICJ), École Centrale de Lyon (ECL), Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université Jean Monnet [Saint-Étienne] (UJM)-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS), Département de Mathematiques [Tlemcen], Université Aboubekr Belkaid - University of Belkaïd Abou Bekr [Tlemcen], and Benmansour, Khadidja

Subjects
Transport equation, total variation, 35F15 35J70 65M30 65M60, space-time least squares methods, [MATH.MATH-NA] Mathematics [math]/Numerical Analysis [math.NA], [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]
Abstract

International audience; In this note, we deal with a least squares formulation for the transport equation. Some numerical schemes are proposed in order that a discret maximum principle holds true. This schemes are obtained by considering optimization problems subject to constraints.

Published
2013

40. Discrete maximum principle for a space-time least squares formulation of the transport equation with finite element

Author

Benmansour, Kadidja, Bretin, Elie, Piffet, Loic, Pousin, Jérôme, Pousin, Jerome, Modélisation mathématique, calcul scientifique (MMCS), Institut Camille Jordan [Villeurbanne] (ICJ), École Centrale de Lyon (ECL), Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université Jean Monnet [Saint-Étienne] (UJM)-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-École Centrale de Lyon (ECL), and Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)

Subjects
variational formulation for the transport equation, 65J10, 65J15, 65J20, dicrete maximum principle, penalized total variation, [MATH.MATH-NA] Mathematics [math]/Numerical Analysis [math.NA], [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]
Abstract

Finite element methods are known to produce spurious oscillations when the transport equation is solved. In this paper, a variational formulation for the transport equation is proposed, and by introducing a positivity constraint combined with a penalization of the total variation of the solution, a discrete maximum principle is verified for lagrange first order finite element methods. Moreover, the oscillations are cancelled.

Published
2013

41. Residual-based a posteriori error estimation for contact problems approximated by Nitsche's method.

Author

CHOULY, FRANZ, FABRE, MATHIEU, HILD, PATRICK, POUSIN, JÉRÔME, and RENAR, YVES

Subjects
ERROR analysis in mathematics, CONTACT mechanics, FINITE element method, LAGRANGE equations, APPROXIMATION theory
Abstract

We introduce a residual-based a posteriori error estimator for contact problems in two- and threedimensional linear elasticity, discretized with linear and quadratic finite elements and Nitsche's method. Efficiency and reliability of the estimator are proved under a saturation assumption. Numerical experiments illustrate the theoretical properties and the good performance of the estimator. [ABSTRACT FROM AUTHOR]

Published
2018
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42. Equation du transport, formulation au sens des moindres carrées espace-temps et principe du maximum

Author

Pousin, Jérôme, Benmansour, Khadidja, Institut Camille Jordan [Villeurbanne] (ICJ), École Centrale de Lyon (ECL), Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université Jean Monnet [Saint-Étienne] (UJM)-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS), Département de Mathematiques [Tlemcen], Université Aboubekr Belkaid - University of Belkaïd Abou Bekr [Tlemcen], and Benmansour, Khadidja

Subjects
Principe du maximum, Moindres carrés espace-temps, Equation du Transport, [MATH.MATH-NA] Mathematics [math]/Numerical Analysis [math.NA], [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]
Abstract

International audience; We propose a formulation according to the least square space-time of the transport equation which provides a maximum principle for an approximation with a first order Finite Element space Lagrangian quadrangular

Published
2012

43. Singular perturbation with a reduced approximation order in space for the transport equation

Author

Belhout, Mohammed, Pousin, Jérôme, Renard, Yves, Institut Camille Jordan [Villeurbanne] (ICJ), École Centrale de Lyon (ECL), Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université Jean Monnet [Saint-Étienne] (UJM)-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS), and Renard, Yves

Subjects
degenerate operator, error estimates, singular mass matrix, [MATH.MATH-NA] Mathematics [math]/Numerical Analysis [math.NA], [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]
Abstract

International audience; This work is devoted to singular transport phenomena by convection with fast-low time scales, or to transport in porous media with vanishing discontinuous porosities. For P1-P0 Finite element, by using a reduction of the approximation order for the time differential operator, we propose a numerical method which does not have any oscillations in the neighborhood of the coefficient discontinuity. Error estimates of order one with respect to space are provided. Euler explicit and implicit time schemes are proposed, and by considering a toy problem, the order one of convergence with respect to time and space is checked.

Published
2012

46. Procedure for the bond graph construction of an optimal control problem

Author

Mouhib, Omar, Chereji, Bogdan, Marquis-Favre, Wilfrid, Thomasset, Daniel, Pousin, Jérôme, Picq, Martine, Ampère (AMPERE), École Centrale de Lyon (ECL), Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE), Institut Camille Jordan [Villeurbanne] (ICJ), Université de Lyon-Université Jean Monnet [Saint-Étienne] (UJM)-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Jean Monnet [Saint-Étienne] (UJM)-Centre National de la Recherche Scientifique (CNRS), and Ampère, Publications

Subjects
[SPI.AUTO] Engineering Sciences [physics]/Automatic, [SPI.NRJ]Engineering Sciences [physics]/Electric power, bond graph, port-hamiltonian system, bicausality, pontryagin Maximum Principle, [SPI.NRJ] Engineering Sciences [physics]/Electric power, Optimal control, [SPI.AUTO]Engineering Sciences [physics]/Automatic
Abstract

Disponible on-line sur http://www.articlearchives.com/international-journal-tomography-statistics/377715-1.html; International audience; This paper aims at providing a procedure and the proof of its effectiveness introducing an optimal control formulation into the bond graph language. The class of optimal control problems presented concerns linear time invariant MIMO systems where the integral performance index corresponds to minimising the input and dissipative energy. The procedure enables the formulation to be set up exclusively at a graphical (namely bond graph) level. The proof uses the Pontryagin principle applied to the port-Hamiltonian formulation of the system.

Published
2006

47. An Optimal Control Problem: Bond Graph Representation and Solver Implementation

Author

Chereji, Bogdan, Mouhib, Omar, Marquis-Favre, Wilfrid, Thomasset, Daniel, Pousin, Jérôme, Picq, Martine, Ampère (AMPERE), École Centrale de Lyon (ECL), Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE), Institut Camille Jordan [Villeurbanne] (ICJ), Université de Lyon-Université Jean Monnet [Saint-Étienne] (UJM)-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS), F. Breitenecker, I. Troch, and Ampère, Publications

Subjects
[SPI.AUTO] Engineering Sciences [physics]/Automatic, [SPI.AUTO]Engineering Sciences [physics]/Automatic
Abstract

International audience; The paper deals with an optimal control problem, namely a bond graph approach, from the problem definition up to the simulation stage. The main role of this article is to supply an alternative approach for solving optimal control problems, both at the representation level and the numerical resolution level.The work presented in this paper, although it concerns optimal control, applies this effort at different levels. The framework of this research belongs to a more general task of dimensioning mechatronic systems. The optimal control implementation constitutes one of the phases that has to be overcome, in order to advance in the direction of the virtual prototyping of these systems.The class of the problem concerns linear time invariant single input single output systems, where the performance index corresponds to dissipative energy. The control variable is taken into account as dissipative loss also, using a weighting factor.

Published
2006

48. Modélisation et analyse numérique de couches limites réactives d'air

Author

Pousin, Jérôme and Rappaz, Jacques

Abstract

The objective of this work is the numerical simulation of the reactive laminar boundary layer which occurs in a neighbourhood of a body moving in the air. We have investigated the modelling of the reactive boundary layer when, the "chemical equilibrium" hypothesis concerning the chemical reactions occuring in the air is satisfied, and when the chemical reaction rates are finite. We have made a mathematical study of the simplified problems coming from the modelling of the reactive boundary layer. We recall the method to state the conservation equations which are written for the ten functions representing the five mass fractions of the chemical species constituting the air, the mean density of the air, the temperature of the air, the mean velocity and the pressure. Then we consider the chemical reactions occuring in the air, and we propose a mode1 for the production terms of the chemical species. In the case where the "chemical equilibrium" is satisfied, we investigate the regularity of the functions representing the mass fractions of the chemical species. Finally, we state a relation which allows us to consider the free enthalpy function as a Lyapounov's function for the equations of conservation of the species when the species diffusion is neglected. The reactive boundary layer equations are semi-linear partial differential equations of parabolic type which degenerate on the part of the boundary of the domain corresponding to the moving body. When considering simplified problems derived from the reactive boundary layer equations, we investigate the type of degeneration taking place in these equations and we state convergence results and error estimates for the approximation of these problems with finite difference methods. In the case where the diffusion of the chemical species is neglected, we have investigated the asymptotic behavior of the functions representing the mass fractions of the species when approaching the body. Finally, we propose an algorithm to compute numerically the reactive boundary layer equations.

Published
2005
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