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INRIA, Evaluation of Theme Computational Models and

Simulation

Project-team POEMS

March 17-19, 2009

Project-team title : “Propagation d’Ondes :Etude Mathematique et Simulation”

Scientific leader : Patrick Joly

Research center : Rocquencourt

Common project-team with : CNRS and ENSTA

1 Personnel

Personnel (September 2004)

Misc. INRIA CNRS ENSTA Total

DR (1) / Professors 1 2 1 4

CR (2) / Assistant Professors 4 2 2 8

Permanent Engineer (3) 1 1

Temporary Engineer (4)

PhD Students 19 19

Post-Doc 1 1

Total 20 5 5 3 33

External Collaborators 3 3

Visitors (> 1 month)

(1) “Senior Research Scientist (Directeur de Recherche)”(2) “Junior Research Scientist (Charge de Recherche)”(3) “Civil servant (CNRS, INRIA, ...)”(4) “Associated with a contract (Ingenieur Expert or Ingenieur Associe)”

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Personnel (March 17-19, 2009)1

Misc. INRIA CNRS ENSTA Total

DR / Professors 1 2 1 4

CR / Assistant Professors 3 2 2 7

Permanent Engineer 1 1

Temporary Engineer

PhD Students 13 13

Post-Doc(s) 1 1

Total 14 4 5 3 26

External Collaborators 3 3

Visitors (> 1 month) 2 1 3

Changes in staff

DR / Professors Misc. INRIA CNRS University TotalCR / Assistant Professors

Arrivals 1 1

Leaving 1 1 2

Comments :

- Houssem Haddar left October 1, 2007, and became the head of Project-Team DEFIat INRIA Saclay;

- Jeronimo Rodriguez (CR, CNRS) arrived March 1, 2006 and left December 31, 2008for joining the University of Santiago de Compostela;

- Jing Rebecca Li is about to leave during the first semester 2009 for joining INRIASaclay.

Current composition of the project-team (March 17-19, 2009):

Permanent INRIA researchers

• Patrick Joly, DR0

• Eliane Becache, CR1

• Gary Cohen, CR1

• Jing Rebecca Li, CR1

Permanent CNRS researchers

• Anne-Sophie Bonnet-Ben Dhia, DR2

• Marc Lenoir, DR2

• Christophe Hazard, CR1

• Jean-Francois Mercier, CR1

Permanent ENSTA researchers

1Visitors: Liliana Borcea, Paul Martin, Ricardo Weder.

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• Patrick Ciarlet, Professor

• Laurent Bourgeois, Assistant Professor

• Eric Luneville, Assistant Professor

Exterior collaborators

• Francis Collino, Independant researcher

• Jerome Le Rousseau, Professor (Univ. of Orleans)

• Christine Poirier, Assistant Professor (Univ. of Versailles)

Engineer

• Colin Chambeyron, CNRS

PhD students

We indicate in parenthesis the name of the advisor (and co-advisor if any).

• Vahan Baronian (A.-S. Bonnet-Ben Dhia, A. Lhemery, E. Luneville)

• Morgane Bergot (G. Cohen)

• Juliette Chabassier (P. Joly)

• Julien Coatleven (P. Joly)

• Jeremi Darde (L. Bourgeois, F. Jouve)

• Berangere Delourme (P. Joly)

• Sonia Fliss (P. Joly)

• Benjamin Goursaud (A.-S. Bonnet-Ben Dhia, C. Hazard)

• Sebastien Imperiale (G. Cohen)

• Lauris Joubert (A.-S. Bonnet-Ben Dhia, P. Joly)

• Matthieu Leautaud (J. Le Rousseau)

• Adrien Semin (P. Joly)

• Alexandre Sinding (G. Cohen)

Post-Doc

• Kersten Schmidt

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Current position of former project-team members (including PhD stu-dents during the period September 2004 to March 17-19, 2009):

Permanent researchers

• Houssem Haddar, DR2 (INRIA Saclay Ile de France)

• Jeronimo Rodriguez, Teacher-Researcher (Univ. of Santiago de Compostela, Spain)

Former PhD students

• Chokri Ben Amar, Assistant (ENI Tunis, Tunisia)

• Kamel Berriri, Assistant (ENI Sousse, Tunisia)

• Nicolas Castel, High School Professor

• Xavier Claeys, Post-Doc (ETH Zurich, Switzerland)

• Fabrice Delbary, Post-Doc (Univ. of Gottingen, Germany)

• Edouard Demaldent, Post-Doc (INRIA Rocquencourt)

• Julien Diaz, CR2 (INRIA Bordeaux Sud-Ouest)

• Eve-Marie Duclairoir, Engineer (Dassault Systemes)

• Marc Durufle, Assistant Professor (Univ. of Bordeaux I)

• Abdelaaziz Ezziani, Assistant Professor (Univ. of Pau et Pays de l’Adour)

• Pascal Grob, Engineer (Canada)

• Erell Jamelot, Research Engineer (CEA)

• Samir Kaddouri, CPGE Professor (Versailles)

• Sri Poernomo Sari, Assistant Professor (Univ. of Jakarta, Indonesia)

• Sebastien Tordeux, Assistant Professor (INSA Toulouse)

• Carlo Maria Zwolf, Engineer (Societe Generale)

Former Post-Docs students

• Grace Hechme, Research Engineer (EDF)

• Guillaume Legendre, Assistant Professor (Univ. of Paris IX)

• Mourad Ismail, Assistant Professor (Univ. of Grenoble I)

• Christoph Kirsch, Post-Doc (Univ. of Magdeburg, Germany)

• Francois Loret, Scientific Consulting (Glaizer Group)

• Andres Prieto, Teacher-Researcher (Univ. of Santiago de Compostela, Spain)

• David Sanchez, Assistant Professor (INSA Toulouse)

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Last INRIA enlistments

No INRIA enlistment was made during the period September 2004 to March 17-19, 2009.

2 Work progress

2.1 Context and overall goal of the project

2.1.1 Overall objectives

The propagation of waves is one of the most common physical phenomena one can meetin nature. From the human scale (sounds, vibrations, water waves, telecommunications,radar), to the scale of the universe (electromagnetic waves, gravity waves), to the scaleof the atom (spontaneous or stimulated emission, interferences between particles), theemission and the reception of waves are our privileged way to understand the world thatsurrounds us.

The study and the simulation of wave propagation phenomena constitute a very broadand active field of research in the various domains of physics and engineering science.

The variety and the complexity of the underlying problems, their scientific and indus-trial interest, the existence of a common mathematical structure to these problems fromdifferent areas justify together a research project in Scientific Computing entirely devotedto this theme.

The general activity of the project is oriented toward the conception, the analysis, thenumerical approximation, and the control of mathematical models for the description ofwave propagation in mechanics, physics, and engineering sciences.

Beyond the general objective of contributing to the progress of the scientific knowledge,three goals can be ascribed to the project:

• the development of an expertise relative to various types of waves (acoustic, elastic,electromagnetic, gravity waves, ...) and in particular for their numerical simulation,

• the treatment of complex problems whose simulation is close enough to real lifesituations,

• the development of original mathematical and numerical techniques,

• the development of computational codes, in particular in collaboration with externalpartners (scientists from other disciplines, industry, state companies...)

2.1.2 Scientific foundations

Warning to the reader. This section is directly extracted from our annual activitiesreport. It is written at a very elementary level and certainly of no interest to a specialistin wave propagation.

Our activity relies on the existence of mathematical models established by physicists tomodel the propagation of waves in various situations. The basic ingredient is a partialdifferential equation (or a system of partial differential equations) of the hyperbolic type

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that are often (but not always) linear for most of the applications we are interested in.The prototype equation is the wave equation:

∂2u

∂t2− c2∆u = 0,

which can be directly applied to acoustic waves but which also constitutes a simplifiedscalar model for other types of waves (this is why the development of new numerical meth-ods often begins by their application to the wave equation). Of course, taking into accountmore realistic physics will enrich and complexify the basic models (presence of sources,boundary conditions, coupling of models, integro-differential or non linear terms,...)

It is classical to distinguish between two types of problems associated with these models:the time domain problems and the frequency domain (or time harmonic) problems. Inthe first case, the time is one of the variables of which the unknown solution depends andone has to face an evolution problem. In the second case (which rigorously makes senseonly for linear problems), the dependence with respect to time is imposed a priori (via thesource term for instance): the solution is supposed to be harmonic in time, proportionalto eiωt, where ω > 0 denotes the pulsation (also commonly, but improperly, called thefrequency). Therefore, the time dependence occurs only through this pulsation which isgiven a priori and plays the role of a parameter: the unknown is only a function of spacevariables. For instance, the wave equation leads to the Helmholtz wave equation (alsocalled the reduced wave equation) :

−c2∆u − ω2u = 0.

These two types of problems, although deduced from the same physical modelization, havevery different mathematical properties and require the development of adapted numericalmethods.

However, there is generally one common feature between the two problems: the existenceof a dimension characteristic of the physical phenomenon: the wavelength. Intuitively,this dimension is the length along which the searched solution varies substantially. In thecase of the propagation of a wave in an heterogeneous medium, it is necessary to speakof several wavelengthes (the wavelength can vary from one medium to another). Thisquantity has a fundamental influence on the behaviour of the solution and its knowledgewill have a great influence on the choice of a numerical method.

Nowadays, the numerical techniques for solving the basic academic and industrial prob-lems are well mastered. A lot of companies have at their disposal computational codeswhose limits (in particular in terms of accuracy or robustness) are well known. However,the resolution of complex wave propagation problems close to real applications still poses(essentially open) problems which constitute a real challenge for applied mathematicians.A large part of research in mathematics applied to wave propagation problems is orientedtowards the following goals:

• the conception of new numerical methods, more and more accurate and high per-forming.

• the treatment of more and more complex problems (non local models, non linearmodels, coupled systems, ...)

• the study of specific phenomena or features such as guided waves, resonances,...

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• the development of approximate models in various situations,

• imaging techniques and inverse problems related to wave propagation.

These areas constitute the main fields of interest for the Project-Team POEMS.

2.1.3 Application domains

As already indicated above, we are concerned with all application domains where linearwave problems arise: acoustics and elastodynamics (including fluid-structure interactions),electromagnetism and optics, and gravity water waves. We give in the sequel some detailson each domain, pointing out our main motivations and collaborations.

Acoustics. As the acoustic propagation in a fluid at rest can be described by a scalarequation, it is generally considered by applied mathematicians as a simple preliminary stepfor more complicated (vectorial) models. However, several difficult questions concerningcoupling problems have occupied our attention recently.

Aeroacoustics, or more precisely, acoustic propagation in a moving compressible fluid,is for our team a recent and very challenging topic, which gives rise to a lot of openquestions, from the modelling until the numerical approximation of existing models. Ourworks in this area are partially supported by EADS (and Airbus). The final objective isto reduce the noise radiated by Airbus planes.

Vibroacoustics, which concerns the interaction between sound propagation ans vibrationsof thin structures, also raises up a lot of relevant research subjects. Our collaborationwith EADS on this subject, with application to the comfort of the cockpits of airplanes,allowed us to develop a new research direction about time domain integral equations.

A particularly attractive application concerns the simulation of musical instruments, whoseobjectives are both a better understanding of the behaviour of existing instruments andan aid for the manufactoring of new instruments. After the timpani and the guitar, we arebeginning in collaboration with A. Chaigne of ENSTA a study devoted to the modellingand the simulation of the piano.

Electromagnetism. This is a particularly important domain, first because of the ma-jor technological applications but also because the treatment of Maxwell’s equations posesnew and challenging mathematical questions.

Applied mathematics for electromagnetism during the last ten years have mainly con-cerned stealth technology, electromagnetic compatibility, and design of optoelectronicmicro-components.

Stealth technology relies in particular on the conception and simulation of new absorbingmaterials (anisotropic, chiral, non-linear...). The simulation of antennas raises delicatequestions related to the complexity of the geometry (in particular the presence of edgesand corners). Finally micro and nano optics have seen recently fantastic technologicaldevelopments, and there is a real need for tools for the numerical simulation in these areas.

Our team has taken a large part in this research in the past few years. In the begin-ning, our activity was essentially concerned with radar stealth (supported by the French

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Army and Aeronautic Companies). Now, it is evolving in new directions thanks to newexternal (academic and industrial) contacts:

• We have been developing since 2001 a collaboration with ONERA on EM modellingby higher order methods (theses of M. Durufle and E. Demaldent, current thesis ofM. Bergot).

• As partners of ONERA, we have been selected by the CEG (a research organismof the French Army) to contribute to the development of a general computationalcode in electromagnetism. The emphasis is on the hybridization of methods and thepossibility of incorporating specific models for slits, screens, wires,...

• Optics is becoming a major application topic. In the past our contribution to thissubject was quite important but remained at a rather academic level. Our collab-oration about the simulation of micro and nano opto-components with the Institutd’Electronique Fondamentale (Orsay) which has been funded by the ANR has mo-tivated an intense activity during the evaluation period.

• Our expertise in numerical methods for Maxwell’s equations could play a main rolefor the challenging simulation of Vlasov-Maxwell equations, arising in the contextof controlled thermonuclear fusion. This is the object of the thesis of A. Sinding(funded by the DGA - French army) and of a collaboration with the project-teamCALVI.

Elastodynamics. Wave propagation in solids is with no doubt, among the three fun-damental domains that are acoustics, electromagnetism and elastodynamics, the one thatposes the most significant difficulties from mathematical and numerical points of view.Our activity on this topic, which unfortunately has been forced to slow down in the mid-dle of the 90’s due to the disengagement of French oil companies in matter of research,has seen a most welcomed rebound through new academic and industrial contacts.

The two major application areas of elastodynamics are geophysics and non destructivetesting. A recent interest has also been brought to fluid-stucture interaction problems.

• In geophysics, one is interested in the propagation of elastic waves under ground.Such waves appear as natural phenomena in earthquakes but they are also used asa tool for the investigation of the subsoil, mainly by the petroleum industry for oilprospecting (seismic methods). This constitutes an important field of applicationfor numerical methods. We are currently defining the framework of a collaborationwith TOTAL company.

• Another important application of elastic waves is non-destructive testing: the prin-ciple is typically to use ultra-sounds to detect the presence of a defect (a crack forinstance) inside a metallic piece. This topic has been the object of an importantcooperation with EDF (French Company of Electricity) in view on the applicationto the control of nuclear reactors. This led us to become an active member of theGDR 2501 (a french-UK network on Ultrasonic Non-Destructive Testing) where wemet people of the LIST (Laboratoire d’Integration des Systemes et des Technologies)at the CEA (French Nuclear Agency). We develop currently several active collab-orations with this team (ANR project MOHYCAN, theses of Vahan Baronian andSebastien Imperiale).

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2.2 Objectives for the evaluation period

On the occasion of the previous evaluation of the project-team POEMS (whose name wasONDES at the time) in 2004, in addition to the continuation of current topics inside ourteam, we announced six more specific objectives. The following paragraphs in italic are aa cut and paste from our report for the previous evaluation.

1. modelling in micro and nano-optics :

This will constitute a new orientation for the Project. A collaboration with the Insti-tut d’Electronique Fondamentale (Orsay) should start in the near future. The objective isto develop new methods for simulating photonic microstructures with high refractive indexcontrasts.

The simulation of the transition between an optical fiber and an integrated microguideraises in particular a lot of very difficult questions, which we will try to handle thanks toour experience on non uniform waveguides and PMLs.

Band gap components, with perodic microstructure, also lead to very interesting math-ematical questions. We plan to increase our activity on this subject, with a particularinterest to the modal analysis of miscrostruturated optical fibers and to the derivation ofDtN maps in infinite or semi-infinite periodic media.

2. Numerical modelling in aeroacoustics and vibroacoustics.

These reseach subjects are at the heart of our collaboration with EADS and have beeninitiated during the last four years. A lot of academic and practical questions remain tobe solved.

Our research about the simulation of acoustic waves in flows, with linearized Euler systemor Galbrun’s equations, will continue in particular in the direction of the treatment of gen-eral non uniform flows.

Our research on vibroacoustics is the central motivation of the development of coupledfinite element-retarded potentials methods. It will also be the opportunity to investigatevarious mechanical models for thin structures (Kirchhof-Love, Mindlin Reissner, dynamicshell equations).

3. Hybridization of numerical techniques :

This topic, that we have already encountered through our works on domain decomposi-tion and mesh refinement should be reinforced through our collaborations with EADS (inaeroacoustics), ONERA and CEG (electromagnetism). Let us cite for instance:

• Coupling finite differences, finite element methods and discontinuous Galerkin meth-ods through non conforming grids.

• Coupling volumic methods with approximate models (impedance conditions, wiresand slot models,...) - see also the item below.

• Coupling, in time domain, volumic methods (finite elements, finite differences) withsurfacic methods (integral equations) or exact transparent conditions.

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• Hybridization of standard numerical methods with high frequency techniques (in col-laboration with J. D. Benamou)

4. Asymptotic methods and approximate models :

Our activity in this domain will increase during the next four years, in particular bynew future cooperations:

• the INRIA-NSF project ”Collaborative Effort on Approximate Boundary ConditionsFor Computational Wave Problems”,

• the collaboration with CEG and ONERA on Computational Electromagnetics,

• the continuation (still not decided) of the ARC HEADEXP.

The particular subjects that we shall work on are:

• Generalized impedance boundary conditions for thin layers or boundary layers ap-proximations. An effort should be paid to the case of singular boundaries and timedomain problems.

• Time domain effective transmission conditions for internal thin layer problems.

• Approximate models for thin slots problems. This concerns the extension of the PhDthesis of S. Tordeux to 3D problems, Maxwell’s equations and time domain.

• Wire models. Our wish is to revisit the question of thin wire models through the socalled matched asymptotic expansions technique.

• Effective models for scattering by rough (periodic and not periodic) surfaces andinterfaces.

5. Perfectly matched layers :

This domain has seen a lot of progress (as least for us) during the past four years. Howeverthere are still open challenging questions to be solved:

• The stability of numerical schemes inside PML’s. This question poses real difficul-ties, in particular with higher order methods.

• The construction of stable PML’s for anisotropic wave propagation models such asanisotropic elasticity or Galbrun’s equations.

• The analysis of time harmonic PML’s in waveguides (in particular elastic waveg-uides).

6. Inverse problems :

Up to now, our efforts on inverse problems have been focused on more or less academicsproblems. Indeed, our works concerned essentially inverse scattering problems in free space,using a large amount of data and a deterministic setting. Our main objective now is tomove towards real life applications, as was intiated with the study of burried objects de-tection. To progress in the resolution of complex problems, we intent to couple differentapproaches as explained in the section ”Main contributions”. Interesting and challengingquestions concern for instance

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• The inverse scattering problems in waveguides, where few data are available (becauseevanescent modes do not contribute to the far field).

• Data completion.

• Including statistical approaches for more realistic inverse problems simulations.

We estimate that we have reached most of our objectives. In the next four subsections2.3 to 2.6, we have chosen to present in more detail our activity related to the first fourobjectives. In the subsection 2.7, we shall briefly describe our other activites, the onesthat concern objectives 5 and 6, and the other subjects we have treated.

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2.3 Objective 1 : Modelling in micro and nano optics

2.3.1 Personnel

Anne-Sophie Bonnet-Ben Dhia, Patrick Ciarlet, Julien Coatleven, Sonia Fliss, BenjaminGoursaud, Christophe Hazard, Patrick Joly, Andres Prieto, Carlo-Maria Zwolf

2.3.2 Project-team positioning

During the evaluation period, we have worked on three specific new subjects:

• The simulation of tapers in integrated optics,

• The propagation of waves in photonic crystals,

• The modelling of metamaterials.

To attack the first subject, POEMS can rely on a well-established expertise on theoreti-cal and computational aspects of open waveguides (for instance A.S. Bonnet and P. Jolywrote a chapter on this subject in a SIAM book on mathematics for optics - optical fibersare particular open waveguides), of resonances (which are for diffraction problems analo-gous to leaky modes in open waveguides) and of Perfectly Matched Layers for handlingunbounded media. The method we are developing aims at combining these three featuresin a same subject. Let us mention in particular that there are currently several teamswhich study the possibility of using PMLs for computing resonances: Thorsten Hohage inGottingen, S. Kim and J. E. Pasciak in Texas University and that is a natural topic forour group to investigate similar questions in the context of open waveguides.

The second subject was completely new for us. The mathematical theory of partial dif-ferential equations with periodic coefficients is now rather well developed, in particular inthe context of wave propagation. The development of reliable numerical methods in thisframework is much less advanced than the mathematical theory but it has recently becomea very popular topic in both applied and theoretical communities. Our achievements havealready received a lot of attention from both communities. P. Joly has been invited toseveral important conferences, workshops or advanced schools to present our works in thisdomain. We also have been invited to contribute to a collective book Wave Propagationin Periodic Media Analysis, Numerical Techniques and practical Applications in the SeriesProgress in Computational Physics.

The third subject can be seen as a continuation of the previous one since metamaterials areoften considered as homogenized periodic materials. They generate currently an intenseactivity in physics, because of their exceptional properties (let us mention in particular, inFrance, the Institut Fresnel, UMR 6133, in Marseille). However, there are very few teamswhich are concerned with the mathematical and numerical aspects of metamaterials mod-elling (most of existing mathematical works being focused on homogenization aspects).What we did for the last four years has already known a certain impact as indicates thenumerous sollicitations that A. S. Bonnet-Ben Dhia and P. Ciarlet received to give talksin workshops on this subject. Note that we made a first incursion in this subject 6 yearsago with the PhD thesis of K. Ramdani.

2.3.3 Scientific achievements

The numerical simulation of tapers in integrated optics. A main challenge inintegrated optics is the realization of components achieving a low loss coupling between

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a microwaveguide and an optical fiber. An efficient structure has been realized by theInstitut d’Electronique Fondamentale: due to a progressive reduction of the dimensions ofthe core of the microguide along the propagation axis, the fundamental mode becomes lessand less confined, and is at the output well adapted to the optical fiber. The numericalevaluation of scattering losses in this taper is difficult and costly, because of the differentscales of the problem. We developed for a 2D scalar model an original approach com-bining Perfectly Matched Layers to bound the domain in the transverse directions and amultimodal technique. This leads to consider the so-called leaky modes, whose numericalcomputation is known to be very difficult, due to their exponentially growing behaviourat infinity. Our main contributions have been to explain this difficulty by applying thenotion of pseudospectrum to the related non-selfadjoint spectral problem and to suggesta solution in terms of “non-convex PMLs” (we mean that the physical computational do-main surrounded by the PMLs is no longer convex as it is usually) which can be set veryclose to the core waveguide [140].

The propagation of waves in photonic crystals. We have worked on inventing effi-cient numerical methods for computing the propagation of waves inside media that differfrom periodic media only in bounded regions (a defect, small with respect to the totalsize of the propagation domain). Let us remark that the application to electromagneticwaves in photonic crystals is not the only possible application of our works (cf. the nondestructive testing of composite materials that we consider in collaboration with EADS).For these problems, a major difficulty is the reduction of the pure numerical computationsto bounded domains surrounding the defect. It is typically a situation for which PMLtechniques, in their classical conception, cannot work since “outgoing” waves will inter-act with the exterior medium. To reach this goal, the key point is to take advantage ofthe periodic structure of the exterior problem to construct artificial (but exact) boundaryconditions. That is why we investigated the generalization of the Dirichlet to Neumann(DtN) approach, well developed in homogeneous media, to periodic media. We have pro-posed a solution for constructing the DtN operator for the 2D scalar Helmholtz equationwhen the “interior domain” coincides with a rectangular union of periodicity cells. ThisDtN operator acts on functions of a scalar variable x (typically the abscissa along theboundary Γ of the interior domain). We factorize this DtN operator as a product of twooperators. The first operator is constructed with a method which combines the use of an-alytical tools such as the Floquet-Bloch transform and the numerical solution of local cellproblems [104]. The computation of the second operator requires the numerical solutionof non-standard integral equations in the (x, k) plane, where k denotes the dual variablein the Floquet-Bloch transform [42]. This method is well established, rigorously justifiedand successfully tested in the case of absorbing media.

The numerical modelling of metamaterials. It is commonly admitted that metama-terials can be modelized at the frequencies of interest by usual Maxwell equations wherethe dielectric permittivity ε and the magnetic permeability µ are chosen to be negativereal valued functions. In practice, metamaterials are used with standard dielectric mate-rials, so that simulations have to deal with a sign shift of ε and µ across some interfaceΓ. Due to this sign shift, the time harmonic equations do not fit into a classical mathe-matical framework. We developed several approaches [160], [139], [17] which ensure thewell-posedness of the problem and the convergence of appropriate finite element schemes.All results require sufficiently large contrasts of ε and µ across Γ, and in 3D the regularityof the interface.

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2.3.4 Collaborations

1. Collaboration with the Institut d’Electronique Fondamentale (IEF) (Paris 11 uni-versity / CNRS, UMR 8622), Groupe MIcro et NAno dispositifs PHOToniquessur silicium (MINAPHOT), Departement Composants pour la Microelectroniqueet l’Optoelectronique (CMO), in the ANR project SIM NANO PHOT.

2. Partnership with EADS IW on ultrasonic waves in composite materials.

3. Informal discussion with the Institut Fresnel.

2.3.5 External support

1. ANR project SIM NANO PHOT

2. Contract EADS-2

3. PhD Scholarship for Sonia Fliss (CIFRE/EADS)

4. PhD Scholarship for Benjamin Goursaud (Ecole Polytechnique)

2.3.6 Self assessment

The simulation of optical tapers has motivated an interesting work concerning PMLs andleaky modes. Some unexpected results have been obtained on “non-convex” PMLs (in thesense of section 2.4.3) for instance. But at this point, we are not convinced that usingleaky modes in multimodal techniques is a good idea, due to the very strong difficultiesrelated to the numerical manipulation of exponentially growing solutions.

Concerning periodic media, even though a major step has been made with the PhD thesisof S. Fliss, we think that the story is only starting. From the theoretical point of view,many open questions have to be addressed to complete, if possible, the justification of ourapproach. Concerning the improvement of the existing method, we are currently workingto a numerical limiting absorption procedure for treating non absorbing media and to theproblem of multiple scatterers. Finally, we wish to develop more realistic applications in3D electromagnetism. Julien Coatleven just began his PhD thesis on a subject which isin the natural continuation of the thesis of S. Fliss.

Concerning metamaterials, we have at this point a good understanding of the mathemati-cal properties of available models. Some questions remain open in 3D, when the interfacebetween the dielectric and the metamaterial has geometrical singularities. Besides let usrecall that models of metamaterials are derived from a homogenization process: experi-ments show that they do not allow to recover correctly interface phenomena which occuron the boundary of the metamaterial. Our objective is to try to develop new interfacemodels in partnership with physicists (Institut Fresnel for instance).

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2.4 Objective 2 : Numerical modelling in aeroacoustics

2.4.1 Personnel

Kamel Berriri, Anne-Sophie Bonnet-Ben Dhia, Eve-Marie Duclairoir, Pascal Grob, PatrickJoly, Lauris Joubert, Eric Luneville, Jean-Francois Mercier, Jeronimo Rodriguez


This is a difficult topic because it is at the interface between two scientific areas, wavepropagation and fluid mechanics, and accumulates some of the difficulties of each subject.New mathematical difficulties, compared to more traditional models in acoustics, elastic-ity or electromagnetism, are encountered. In particular, due to the presence of convectionterms in the equations, some basic properties of the model are changed: the underlyingspace differential operators are non selfadjoint (even non normal) and, as a consequence,the conservation of energy is no longer valid and the model authorizes the development ofso-called hydrodynamic instabilities. Most of the existing research in this domain has beenaccomplished by people originating from the Computational Fluid Dynamics communitywho began to look at linear wave propagation problems. Conversely, it might be interestedto have the point of view of researchers from the traditional Computational Wave Propa-gation community making an incursion into the world of fluid dynamics. As a matter offact, the simulation of acoustic propagation in a moving fluid is a topic which has beenaddressed recently by the community of applied mathematicians studying waves. As itraises various unusual mathematical questions (in particular concerning artificial bound-aries), it has even become a major research area or at least a challenging test case forseveral teams in the world (C.D. Munz in Stuttgart, F.K. Hu in Norfolk, T. Hagstrom inNew Mexico...). Note that most of the existing results concern the solution of LinearizedEuler Equations in the time domain, and our approach which consists in solving Galbrun’smodel in the time harmonic case is non conventional.


Time-harmonic aeroacoustics. As already mentioned, the originality of our approachcomes from the choice of a non-conventional model (Galbrun’s equation) which is well-suited for a variational approach (compared to Euler’s equations). The unknown u isthe perturbation of the Lagrangian displacement and it is expressed as a function of theEulerian variables. A main advantage is that physical boundary conditions are very easyto handle in Galbrun’s framework while the counterpart is “quite difficult” with Eulerequations. The main point is that a direct discretization by Lagrange Finite Elementsdoes not work, due to a lack of H1 coerciveness. The solution which we developed consistsin adding to the original equation a term which does not change the value of the solutionand which restores coerciveness. This term is related to hydrodynamic phenomena andrequires the evaluation of curl u, which does not vanish except in a uniform flow (dueto the coupling between hydrodynamic and acoustic phenomena). The method has beenvalidated during the PhD of E. M. Duclairoir [5, 61, 162] in the simple case of a parallelnon-vanishing shear flow, using an analytical expression of the hydrodynamic term. Thisrequires the evaluation of an oscillating integral, coupling all degrees of freedom locatedon the same streamline. This difficulty can be avoided for slow flows by replacing thisnon-local term by its Low-Mach (local) approximation; this amounts to neglecting theconvection of vortices. This Low-Mach approach has been validated in 2D, in the caseof regular rigid boundaries, with an analytic or potential flow [19]. To get rid of theLow Mach hypothesis, we are currently developing a discontinuous Galerkin method to

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simulate accurately the convection of vortices, which will be eventually coupled to thefinite element solution of the augmented Galbrun equation.

For several applications (in particular noise reduction in aeronautics), one has to take intoaccount boundary conditions of the form div u = Fun (un denotes the normal componentof the displacement u) which modelize absorbing walls or “liners”. Up to now, we haveconsidered this question only in the case of a uniform flow in 2D. On one hand, we havedeveloped and validated transparent boundary conditions based on modal DtN maps inan infinite lined waveguide (PhD of S. Poernomo Sari, in collaboration with E. Redon inDijon). On the other hand, we have studied and compared different models for a linerdiscontinuity (when F is a Heaviside like function).

Time-domain aeroacoustics. On this topic, we can identify three distinct subjects wehave worked on:

• Numerical methods for linearized Euler equations,

• Numerical modelling via Galbrun’s equations,

• Asymptotic models in aeroacoustics.

The nature of our work on the first subject goes further the application to aeroacousticsand justifies that we incorporate its presentation in the section devotes to hybrid numeri-cal methods (see section 2.5).

The second subject constitutes the time-domain counterpart of our work on time-harmonicaeroacoustics and corresponded to the PhD thesis of K. Berriri [7]. Most of the resultswe obtained about concerned the case of a uniform reference flow. The extension of theapproach to general flows faces difficulties, in particular concerning the stability of themethod. Our work gave us the opportunity to clarify the relations between Galbrun equa-tions and linearized Euler equations, but at this stage of our research, we are not convincedthat the use of Galbrun’s equations are, in the time domain, a fruitful alternative to lin-earized Euler equations as far as numerical methods are concerned.

The last and more recent subject is in some sense the more challenging and exciting one.As already mentioned above, it is important to simulate the interactions of acoustic waveswith boundaries (walls, wings,...) that may be, at least partially, treated acoustically (byadding a thin coating called acoustic liner). Moreover, the presence of walls and bound-aries influences the structure of the reference flow: in particular, boundary layers of verysmall width are present close to the boundaries. For an efficient modelling of acousticwaves in the presence of boundary layers if the mean flow, one would like to use bound-ary conditions that would represent the conjugated effect of the boundary layer and theacoustic treatment. This problem has obviously been the subject of a lot of research andvarious lining conditions have been proposed by engineers, to begin with the well-knownMyers condition. However, as has been recently pointed out, all these conditions lead toill-posed initial boundary value problems. Thus, the question of a satisfactory treatmentof boundaries in aeroacoustics remains essentially open. As a first step, we investigate thepropagation of acoustic waves in a duct in the presence of a laminated flow when the widthof the duct is small with respect to the wavelength. In such a situation, one expects thatthe propagation of waves can be accurately described with a 1D simplified model. This isobvious in the absence of flow, but much more delicate in the presence of a flow. Underthe assumption that the Mach profile of the flow is obtained by a scaling of the Mach

16

profile of a reference flow, it is possible to derive a quasi-1D limit model which appearsto be of integro-differential type : it is local in the longitudinal direction and non-localin the transverse direction (in scaled coordinates). The study of the well-posedness of thelimit problem is a delicate issue. This is due to the non-normality of the generator A

of the underlying semi-group. The results highly depend on the Mach profile (see [274]).Moreover, when the limit problem is strongly ill-posed, we deduce from this analysis newresults on hydrodynamic instabilities in compressible fluids.

Finally, in the case where the limit problem is well-posed, it is not easy to justify rig-orously the approximate model and the analysis also points out the difficulties for theconstruction of a stable discretization scheme (standard approximation techniques fail).A fundamental question is the derivation of a reliable numerical procedure for the com-putation of the solution of the limit problem. It appears that a possible approach wouldconsist of combining the use of a Laplace transform in time with the use of complex planetechniques.

Vibroacoustics. We have worked in both time-domain and frequency domain vibroa-coustics. Because of its nature, our work in time domain (corresponding to the PhD thesisof P. Grob [9]) is reported in section 2.5, first paragraph.

In the frequency domain, we have also considered a model problem of vibro-aero-acoustics:an elastic plate is placed in an infinite 2D duct which contains a compressible moving fluid.In the case of a rigid plate in a fluid at rest, it is well-known that there are a finite numberof resonance frequencies which correspond to acoustic modes trapped around the plate.The objective of our study was to investigate the influence of a uniform flow and of theelasticity of the plate. Due to the fluid-structure coupling, a quadratic eigenvalue problemis involved, in which the resonance frequencies k solve the fixed-point equations λ(k) = k2

where the λ(k) are the eigenvalues of a self-adjoint operator A + kB. The eigenvalueslocated below the essential spectrum are studied by using the Min-Max principle. Thenthe fixed-point equations are studied.

First we have proved that a linear eigenvalue problem can be recovered if the plate isrigid or if the fluid is at rest and we have established sufficient conditions that ensure theexistence of resonances [63]. Then we focused on the general problem for which elastic-ity and flow are jointly present and derived a lower bound for the number of resonances.The expression of this bound, based on the solution of two linear eigenvalue problems,points out that the coupling between elasticity and flow generally reduces the number ofresonances [18]. In both cases the theoretical results are validated numerically.


1. EADS and AIRBUS

2. CERFACS (joint publication and communications)

3. Universite de Bourgogne (joint communications)

17


1. Contract EADS-1

2. PhD scholarship EADS-CNRS for Eve-Marie Duclairoir

3. PhD Scholarship for Lauris Joubert (Ecole Polytechnique)

4. PhD Scholarship from Tunisia for Kamel Berriri

5. Contract DGA-2


Concerning time-harmonic aeroacoustics, the results obtained with the Galbrun approachare very promising. In collaboration with CERFACS, we are close to propose the firstexisting software for the solution of realistic problems that arise in industry (3D, complexgeometries, rotational flow). The main question that we have to address now concerns theboundaries which were supposed up to now regular and rigid. Singular boundaries andliners could be taken into account by writing a more general version of the augmentedGalbrun equation, using a weight function in the additional term (the so-called “weightedregularization” proposed by Costabel and Dauge for Maxwell equations).

Concerning time domain aeroacoustics, we do not intend a priori to pursue our researchon numerical methods of Galbrun’s equations and our efforts will be put on DiscontinousGalerkin methods for linearized Euler equations (see section 2.5). Our work on approx-imate models in time domain aeroacoustics is only at its beginning. We think that it isa very challenging and exciting subject, interesting from the theoretical point of view,fundamental for the applications.

Concerning the problem of vibro-aero-acoustics, we are currently extending our results(established for a uniform flow) to the case of a potential flow. A challenging objectiveconcerns the study of the instabilities (non real resonance frequencies) which are observedexperimentally.

Concerning the lined waveguide, we will continue our collaboration on DtN maps with E.Redon and we aim at extending our approach to the 3D case and to non uniform flows.

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2.5 Objective 3 : Hybridization of numerical techniques

2.5.1 Personnel

Vahan Baronian, Anne-Sophie Bonnet-Ben Dhia, Pascal Grob, Patrick Joly, Eric Luneville,Jean-Francois Mercier, Jeronimo Rodriguez


The hybridization of numerical methods, in the most general sense, is a transverse andvery popular topic in numerical analysis and scientific computing, particularly for its ap-plication to wave propagation which often involve large-scale and multi-physics problems.The French school occupies a rather privileged place in this domain with the developmentof the variational approaches (for domain decomposition in particular, mortar elements,...). The project team POEMS has itself acquired a strong reputation in particular thanksto recognized achievements for domain decomposition methods for time-harmonic waves,fictitious domain methods for time-domain waves, local time stepping methods or multi-modal approaches.


Coupling between volumic methods and time-domain integral equations. Thisis for us a completely new thematic which has been developed in collaboration with EADS.We were first interested into an application in vibro-acoustics which was the subject ofthe PhD thesis of P. Grob [9]. We considered the acoustic radiation of the vibrations of athin mechanical structure (typically a plate). We developed an original method based onthe coupling between spectral finite elements for the mechanical part of the problem andretarded potentials for the acoustic part [75].

This first work was the starting point for a more ambitious project that we developedin collaboration with T. Abboud (IMACS) and I. Terrasse (EADS) in the frameworkof the contract ADNUMO with AIRBUS. Our objective is to use time-domain integralequations (developed in particular at IMACS and EADS) as a tool for constructing trans-parent boundary conditions for wave problems in unbounded media. The application wehave in mind foremost is aeroacoustics, namely the computation of sound propagationaround an airplane. More precisely, we wanted to couple (possibly high order) discontin-uous Galerkin methods for the numerical approximation of the interior equations with aspace-time Galerkin approximation of the integral equations that represent the transpar-ent boundary conditions. This task is a priori difficult due to the very different nature ofthe two discretization procedures. In particular, the stability of the coupling scheme isa key issue. We have found a solution to this problem by imposing during the construc-tion of the method that the solution of the coupled problem satisfies a discrete energyidentity that implies the stability of the method under the usual CFL condition for theinterior problem. Moreover, as the discontinuous Galerkin method requires smaller timesteps than the discretization of time-domain integral equations, we have included thepossibility of using different time steps: the time step for the integral equation is sup-posed to be a multiple of the time step for the interior equation. This has been solvedby adapting the ideas we developed in the past for space-time mesh refinement methods.The well-posedness and the stability of the resulting method has been successfully ana-lyzed. The method has been first developed for the acoustic wave equation (written as afirst order system) then extended to general symmetric hyperbolic systems (in the senseof Friedrichs) with zero order perturbation : this includes in particular linearized Euler

19

equations, namely the model we wish to treat within the ADNUMO project. The cou-pling algorithm has been implemented for the wave equation, using the library Sledge++(http://www. caam.rice.edu/ timwar/NUDG/Software/Sledge++.html) for the discon-tinuous Galerkin part and the code Sonate (IMACS) for the integral equation part. Thefirst results on academic problems are quite encouraging.

Mesh refinement and local time-stepping for DG methods. This thematic hasbeen developed via the post-Doc of A. Ezziani, again in collaboration with Airbus. Thegeneral framework of this collaboration is the hybridization of numerical domains for thetime-domain solution of Linearized Euler equations in aeroacoustics. This application wasone of the motivations for looking at Discontinuous Galerkin methods. The other motiva-tion is that such methods allow non-conforming meshes in a simpler way than with finiteelements, avoiding, for instance, the treatment of Lagrange multipliers.

We have been interested in non conforming space-time mesh refinement methods for wavepropagation in aeroacoustics, in the spirit of previous work in electromagnetism and elas-todynamics. We have developed a method which is applicable to zero order perturbationsof symmetric hyperbolic systems in the sense of Friedrichs ( Linearized Euler equationsare of this type). The method is based on the one hand on the use of a conservativehigher order discontinuous Galerkin approximation for space discretization and a finitedifference scheme in time, on the other hand on appropriate discrete transmission condi-tions between the grids. We use a discrete energy techniques to drive the construction ofthe matching procedure between the grids and guarantee the stability. Moreover, undersuitable geometrical conditions on the grids, this method is quasi explicit [27].

Mesh hybridization for higher order methods. We have developed in past years anintense research activity on efficient higher order spectral Galerkin approximation methodsfor time dependent and time-harmonic wave equations on hexahedral mexhes. However,the resolution of realistic industrial problems often requires tetrahedral meshes, at leastlocally. It is then natural to mix these two elements in the same computation and thisraises the question of building connecting elements, which can be made with the help ofpyramids and wedges. Wedge elements are classically obtained by the tensorial productof a triangular element and 1D element. The main new difficulty lies in the constructionof high-order pyramidal finite element spaces that should be easily connected to hexahe-dral or tetrahedral elements, which imposes some properties of the traces of the shapefunctions on quadrangular and triangular faces. This is the subject of the thesis of M.Bergot which began recently in collaboration with M. Durufle. Following pioneering worksby Bedrosian, we can construct rational polynomial shape functions at any order. Thefirst theoretical (stability, error estimates, numerical dispersion) and numerical results arequite promising.

Coupling finite elements and modal decomposition in elastic waveguides. Thepotentiality of guided ultrasonic waves in Non Destructive Testing is currently investi-gated. Indeed, compared to conventional techniques, guided waves could allow a rapidinspection of large areas and of non accessible parts of particular structures like plates orpipes. Our work, which has been the subject of the PhD of Vahan Baronian, in partnershipwith the CEA-LIST, concerns the numerical finite element computation, in the frequencydomain, of the diffracted wave produced by a defect (crack, inclusion, perturbation ofthe boundaries etc..) located in an infinite elastic waveguide. The objective is to usemodal representations to build transparent conditions on the artificial boundaries of the

20

computational domain. This cannot be achieved in a classical way, due to non standardproperties of elastic modes. In particular, the derivation of a “Dirichlet-to-Neumann”operator (relating the normal stress to the displacement) is not tractable. However, abiorthogonality relation allows to build an operator, relating hybrids displacement/stressvectors. An original mixed formulation has been derived and implemented, whose un-knowns are the displacement field in the bounded domain and the normal component ofthe normal stresses on the artificial boundaries [16]. The method applies to 2D and 3Dheterogeneous isotropic waveguides. We will consider now the possibility of an extensionto anisotropic waveguides.

Hybridization of standard numerical methods with high frequency techniques.This topic is inscribed in the MOHYCAN project funded by the ANR (RNTL) and isa work in collaboration with the laboratories LIST-CEA and SINETICS EDF-Clamart.The MOHYCAN project aims at extending the features of ultrasonic non destructive test-ing simulation tools to deal with industrial, potentially complex configurations. In suchsimulations we are interested in computing the signal on a transducer when the mediumis excited by a punctual source on the surface. On many applications, the computationaldomain is a simple medium (typically piecewise homogeneous with straight interfaces)that is perturbed by small geometrical details (for example cracks). The main goal of theproject is to couple a finite element method solving the full elastodynamic equations in theneighborhood of the complex geometry (ATHENA code, developed by EDF) with a semi-analytical resolution in the regions with simple configurations (where further assumptionsallowing to simplify the elastodynamic equations can be made yielding to an importantreduction of the computational cost). We have proposed a technique that computes thesignal on the transducer in two steps:

• a first contribution coming from the incident field (that does not consider the smalldefaults) that is computed by the semi-analytical method,

• a second contribution that takes into account the field coming from the scattering bythe small obstacles. To do so, we use a finite element method to compute the fieldson a small neighborhood of the complex region and then we use the Auld reciprocityprinciple to propagate the information till the transducer.

The proposed method assumes that the scattered field is out-going with respect to the finiteelement method computational domain, this means that the coupling is weak (multipleinteractions are not considered). The future work will be on the direction of conceiving astronger coupling.


1. EADS and AIRBUS

2. CEA LIST, EDF, ONERA


1. Contracts ADNUMO and EADS-2

2. PhD scholarship CEA-CNRS for Vahan Baronian

3. PhD scholarship Cifre-EADS for Pascal Grob

21


Concerning the coupling between volumic methods and time-domain integral equations,we are quite happy with the results we have obtained : we believe that we have constructedthe first coupling method whose stability can be proven. The future of this research islinked to the future of our collaboration with AIRBUS. The recent echoes we get make usconfident that there will be a contract ADNUMO2 as the continuation of ADUMO. Thismeans that we should enter a more operational phase with, in particular, the developmentof a computational code for linearized Euler equations. Concerning more theoretical as-pects, we intend to look at other Galerkin approaches than the centered fluxes approach(which is probably not the best suited for treating convection terms) and to study othertime discretization schemes (possibly higher order - a topic that we are developing inde-pendently, see section 2.7). This should constitute the subject of our future collaborationwith J. Rodrıguez (University of Santiago de Compostela).

The work on pyramidal finite elements is only at its beginning. It is one of the subjectsof our future collaboration with M. Durufle (University of Bordeaux).

The future of our work on coupling ray tracing techniques with finite element approachesis closely linked to the future of the ANR Project MOHYCAN. We are thinking to a strongcoupling method for which we would like to exploit, in the framework of a collaborationwith F. Collino, the ideas of microlocal analysis of finite element computation results.

Concerning the coupling of finite elements and modal decomposition in elastic waveguides,the strong point of this activity is that we have provided to CEA an efficient method whichthey needed for the simulation of ultrasonic non-destructive testing by guided waves. Theweak point is that the robustness of the method which has been experimentally assessedis not mathematically proved. The difficulty comes from the lack of mathematical resultsconcerning elastic modes (for instance, completeness is not clear, even in the simplest2D Lamb case). Despite this, we aim to continue and develop numerical tools for theanisotropic plates which are used in aeronautics (this study will be done in partnershipwith CEA-List and EADS).

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2.6 Objective 4 :Asymptotic methods and approximate models

2.6.1 Personnel

Xavier Claeys, Patrick Ciarlet, Berangere Delourme, Marc Durufle, Samir Kaddouri,Patrick Joly, Houssem Haddar, Adrien Semin.


Taking into account small perturbations or small scales in a given problem by direct nu-merical methods is often difficult (the method must be quite accurate) and costly. Thetypical example in wave propagation is the presence inside the computational domain ofgeometrical details whose dimensions are small with respect to the wavelength which apriori requires the use of very thin meshes.

The development of approximate (or effective) models, which should be at the same timecheaper from the computational point of view and rich enough to take into account ac-curately the effect of the perturbation (or the small scale), offers a very interesting, ifnot absolutely necessary, alternative. This is also a very exciting challenge for an appliedmathematician since it combines a step of modelling (a given problem is immersed into afamily of problems depending on a small parameter ε, typically of geometrical nature, andthe derivation of the approximate models is based on appropriate ansatz or heuristics forthe asymptotic behaviour of the solution when ε → 0), a step of mathematical analysis(justification of the model via stability results, convergence proofs and error estimates)and finally a step of numerical analysis ( development of well suited numerical methodsfor the approximate problem) and validation.

We were about 8 years ago when we began with this thematic with the thesis of S. Tordeux,with whom we did an important contribution [105], [106], [47] for the modelling of junc-tions such as the one between a half-space and a thin slot. In the domain of (possiblymulti-scale) asymptotic analysis of PDEs, which was for long dominated by the Englishschool (in the tradition of British applied mathematics, oriented to (semi-)analytic solutionof physical problems) and the Russian school (which was more devoted to the develop-ment of a rigorous theory for academic problems), the French mathematical school hasbeen quite active, with the specificity of combining a rigorous mathematical approach toproduce approximate models well adapted to numerical approximation of non academicproblems. Our work during the past five years is in this spirit and we have developed arecognized expertise on this type of question in the domain of wave propagation.


Generalized impedance boundary conditions. We have made important contri-butions to the development (theory and numerics) of generalized impedance boundaryconditions (GIBC’s - a notion which is also used in the engineering literature - see thebook by Senior-Volakis) for acoustic and electromagnetic scattering. Following previousworks on thin coatings, we have proposed and analyzed (with optimal error estimates)GIBC’s for taking into account highly conducting scatterers (where thin boundary layersdevelop) in the time harmonic case [127], [43]. Moreover, we have developed, in the codeMONTJOIE, an efficient and accurate variational procedure [239] to deal with such con-ditions. The derivation of GIBC’s relies on an appropriate (local) scaling in the directionnormal to the boundary. The difficulty lies more in the use of tools from differential ge-ometry and in the derivation of stability results and error estimates. With the PhD thesis

23

of B. Delourme, in the framework of a contract with the CEA (LETI), we are workingon the construction of GITC’s (Generalized impedance transmission conditions) for thetransmission of waves across thin layers of width ε. We consider a situation of a “roughinterface” where the physical characteristics of this layer vary periodically in the tangentdirections with a period proportional to the same small parameter ε than the layer width.In such a case, scaling techniques are no longer sufficient and it is necessary to combine anhomogenization ansatz with matched asymptotics (see also the next paragraphs). More-over, the construction of stable transmission conditions from the asymptotic analysis facesnew difficulties that we were able to solve in a non classical way (see RA2007 and RA2008for more details).

Junctions of thin structures. This thematic is the continuation of the work with S.Tordeux on 1D-2D junction models. During the Post-Doc of D. Sanchez, we have in-vestigated the extension of the work in [106] to the case of 3D-2D junction models forMaxwell’s equations. However, the rigorous justification of our model still faces unsolveddifficulties in the case of non absorbing media (reason why we still have not publishedon the subject). With the PhD thesis of A. Semin, we work on 1D - 1D junction mod-els for wave propagation in networks of thin slots. The traditional 1D model consists inusing Kirchhoff conditions (by analogy with electric networks) that can be proven to bethe correct limit model. Using matched asymptotics, we were able to derive improvedKirchhoff conditions that in particular take into account the geometry of the network,contrary to usual Kirchhoff conditions which only see the topology of the network. Suchconditions can be proven to be more accurate : in particular they take into account firstorder physical phenomena that are absent in the limit model [273].

Wave diffraction by thin wires. The general problematic is the diffraction of waves byvery elongated objects in 3D (typically perfectly conducting objects in electromagnetism).In such a case, ε is the dimension of the scatterer in two transverse directions, so that,when ε goes to 0, the scatterer collapses into a segment or a portion of a curve. The majortypical application in electromagnetism is the modelling of thin antennas. The asymptoticanalysis of the associated exterior problem is quite delicate since the limit exterior problemdoes not really make sense (the notion of trace on a line of a 3D function will have nomeaning in a traditional functional framework). The recent PhD thesis of X. Claeys [2]allowed us to make a big step in the understanding of this question. Using a particularcoordinate setting and an adapted version of matched asymptotics, we are able to describethe complete expansion of the solution of the 3D scalar wave equations as a function ofε [279]. The rigorous justification of this expansion is a delicate problem that has beencompletely solved in the scalar case and is still open in the vectorial case, except in the(simpler) case of absorbing media. Moreover, such an analysis leads to the first rigorousjustification of the Pocklington integral equation used by engineers as an approximatemodel and opens the door to the construction of more accurate models [24].

Enriched Galerkin methods. We have also investigated the construction of efficientnumerical procedures using the results of an asymptotic analysis. The main objective toavoid the numerical locking, which occurs when the accuracy of the numerical solution isreasonable only when h (the mesh size) or ∆t (for time dependent problems) is of the orderof ε. For the thin wire problem, we have proposed to couple a fictitious domain approachwith an enriched Galerkin method : one of the main reasons for which a standard numer-ical method fails to give an accurate approximation with ε independent meshes is the factthat the solution that one wants to compute has a quasi-singular behaviour in the sense

24

that it varies strongly at the scale ε. In a standard Galerkin approach, such a behaviourcannot be accurately represented with classical shape functions except when h is of theorder of ε. A natural idea to circumvent this difficulty is to enrich the approximationspace with additional shape functions that would help to reproduce this quasi-singularbehaviour. Of course, the asymptotic analysis of the continuous problem will be the guidefor the design of these additional shape functions, which requires an ¨off-line¨ calculationon normalized geometries. Applying this approach to wire diffraction problems, we areable to justify, improve and generalize the well-known Holland’s model currently used byengineers [25].

Quasi-singularities in Maxwell’s equations. ¿From a theoretical point of view, it iswell-known that the electromagnetic fields can be unbounded near sharp reentrant corners.From a numerical point of view, this singular behaviour needs to be handled with care, withthe help of methods such as the Singular Complement Method or the Weighted Regular-ization Method (those two methods fit into the framework of Continuous Galerkin FEM).However, due to the manufacturing processes, ’real life’ devices exhibit imperfections, inthe sense that the actual corners are not exactly sharp. The resulting electromagneticfields are then bounded, but the bounds depend very strongly on the size of the imper-fections. Those imperfections can be modelled by ’rounded’ corners of small curvature ǫ,with varying shapes (for instance, it can be parabolic). Then, one has to build originalnumerical methods, that allow one to compute the fields in a robust manner. By robust-ness, it is understood that one needs a method that is independent of ǫ. Among others,the shape of the computational domain should be ǫ-independent, to avoid costly meshgenerations. Such an approach leads to the design of the Quasi-Singular ComplementMethod, which we use to model the corona discharge, around a ’rounded’ corner [6, 70].This method relies on multiscaled asymptotic expansions. More precisely, our goal is todetermine the value of the charge density at the exact tip of this corner. To that aim,the electrostatic potential is computed numerically, and an explicit relationship describingthe value of the charge density (with respect to ǫ) is established. The 2D cartesian andaxisymmetric cases have been solved. The same analysis is currently carried out in 2D1/2 prismatic and axisymmetric geometries. The resulting method has been implementednumerically, and tested on a number of test-cases. Among others, it has been comparedto an integral method, which is much more costly to implement. Results are comparable.

Theory of matched asymptotic expansions for wave propagation problems.With the PhD thesis of S. Tordeux and X. Claeys, we have made a big step in the un-derstanding and rigorous justification of the technique of matched asymptotics for timeharmonic . In his thesis [2], X. Claeys has proposed a general framework (a user’s guide)for analyzing this technique to a large class of problems (including the particular caseof thin wires). His theory uses sophisticated mathematical tools (analytic operator the-ory, Mellin transform, weighted Sobolev spaces....) and allows to obtain existence anduniqueness results for the asymptotic expansions as well as error estimates for truncatedexpansions. Finally, during the first part of the thesis of A. Semin [273] (on the junctionof thin slots), we have been able to extend such an analysis to the time dependent case.


A research contract with CEA-LETI.

25


1. PhD scolarship DGA/CNRS for Xavier Claeys.

2. PhD scolarship from University Paris XI for Adrien Semin.

3. PhD scolarship from CEA for Berangere Delourme.


We can claim that during the last four years, we made a lot of progress in the understand-ing and exploitation for numerical purposes of asymptotic methods for partial differentialequations, a domain to which we already have made substantial and fundamental contri-butions that have already received a real interest. On the other hand, there are still manyunsolved questions and we realize that it is a very useful tool for the practical solution ofreal life problems. That is why we shall certainly continue this thematic for the next fouryears. The ongoing theses of B. Delourme and A. Semin enter this thematic.

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2.7 Summary of other researches

Objective 5 : Perfectly matched layers. With respect to the announced objectives,we did not make a lot of progress on the important question of anisotropic waves orstability of higher order schemes. However, we continued our constant efforts about thetreatment of unbounded media. As this is a transverse topic to many applications, it ispresent in most of work and in particular inside the four objectives presented in subsections2.3 to 2.6. Moreover, one can identify one specific subject which was the object of thecollaboration between Eliane Becache and Andres Prieto.

• Exact PMLs for time dependent problems. For the time-harmonic Helmholtzequation, the idea of using a singular layer parameter in order to get exact boundedPMLs has been proposed in a recent paper of Bermudez, Hervella, Prieto and Ro-driguez. During the post-doc made by Andres Prieto in our lab, we have investi-gated the question of the extension of this work to time domain problems. On thenumerical point of view, the results are very satisfactory. There is a significant gaincompared to more classical damping functions, even if it is not so spectacular than inthe frequency domain. Another advantage of this method is that it avoids the deli-cate choice of the damping function parameters. Concerning the theoretical analysisof this model, we have shown the existence and uniqueness of the solution as wellas the exact character of the bounded layers. The main difficulty is related to thefunctional framework, which involves the use of weighted spaces. In this analysis, weconsidered the model in cylindrical coordinates and obtained some estimates of thesolution in the time domain. We then explored other methods to obtain analogousresults, with the aim of (i) improving the estimates in the time domain (in particulartrying to loose one order less of regularity in time), (ii) extending the results to anyother coordinates system. This last work is still in progress.

Objective 5 : Inverse problems. One of the reasons for which we have chosen not todetail our activity in this domain is the fact that Houssem Haddar, who was the leaderof this thematic inside our group and developed in particular a intense activity about thelinear sampling method and its variants, left POEMS in September 2007 to create his ownresearch team, DEFI, at INRIA Saclay. Nevertheless the activity is continuing, partly incollaboration with DEFI, spurred on by Laurent Bourgeois. We refer the reader to theactivity reports RA2005 to RA2007 for more details about Houssem’s activity on inverseproblems. Let us describe briefly our achievements directly related to our objectives of2004:

• Imaging of buried objects. We considered the application of sampling methodsto the problem of buried objects imaging from multi-static electromagnetic data at afixed frequency. This problem simulates experiments of mine detection or infrastruc-ture imaging using ground penetrating radar (GPR) devices. One major numericaldifficulty in solving this problem using the classical linear sampling method is thecomputation the Green tensor of the background (multi-layered) medium. A refor-mulation of this method using the reciprocity gap concept enabled us to proposea new algorithm that only require the (much cheaper) computation of the Greentensor of the probed region. The analysis of the new algorithm and the discussionon its effectiveness with respect to classical approaches have been the object of twopublications: [123] for the scalar problem and [89] for the electromagnetic one.

• Inverse scattering in waveguides. We addressed the question of how we canapply sampling methods to waveguides. The fact that the domain is bounded fol-lowing one or two directions introduces some evanescent modes in the description

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of the forward scattering problem, which leads to a loss of information contained inthe far field. Since the data used in the inverse problem consist of the far field, theill-posedness of the inversion process is increased compared to the classical free spaceconfiguration. More specifically, we analyzed, both from a theoretical and numericalpoint of view, two particular cases. First, the case of the 3D shallow ocean wasaddressed by using a sampling method based on the convex scattering support, andis the object of [65]. Secondly, the case of a 3D cylinder was addressed by using theclassical Linear Sampling Method, and is the object of [145].

• Method of quasi-reversibility. We revisited several aspects of the method ofquasi-reversibility, which was introduced forty years ago in order to solve data com-pletion problems for elliptic PDE’s. This method consists of transforming a second-order ill-posed problem into a family (depending on a small parameter ǫ) of fourth-order well-posed problems. One issue concerns the choice of ǫ. An efficient techniquebased on duality in optimization was suggested in [87] and applied in [164] in orderto make this choice following the classical discrepancy principle. Next, we also ad-dressed the question of the convergence rate of the method when ǫ tends to 0, whichis strongly related to the classical question of stability for ill-posed elliptic PDE’s.Some results were given in [87] and [64], but these results were improved in [271]and [272], where the object is to analyze how stability is influenced by the regularityof the domain of interest. Precisely, we focus on C1,1 domains in [271], while [272]concerns C0,1 domains. From a numerical point of view, we analyzed several finiteelement methods to solve these fourth-order problems. A mixed formulation basedon classical Lagrange finite elements was introduced in [220], while non conform-ing finite elements were used in [164] (Morley’s element) and in [272] (Fraeijs deVeubeke’s first element).

• Coupling the method of quasi-reversibility and a level set method. Weimplemented a new method coupling the method of quasi-reversibility and a levelset approach in order to solve obstacle type problems by using partial Cauchy dataon the boundary of the domain of interest. Contrary to the situation describedin the previous paragraph, the subdomain in which the solution solves a PDE is anadditional unknown of the problem. Our method does not include some optimizationprocess, which makes it original. This work is part of the PhD of Jeremi Darde(advised by Laurent Bourgeois and Francois Jouve, form Paris 7 University). Thetheoretical and numerical results obtained up to now seem very promising.

We did not work on statistical approaches to inverse problems.

Other research subjects

• We have continued our long term research on higher order methods for the discretiza-tion of wave equations. Following the PhD thesis of S. Pernet [15], defended at thebeginning of the evaluation period, that dated our first incursion in the topic of Dis-continuous Galerkin (DG) methods, one of our major achievements in the domainof higher order methods has been the PhD thesis of Marc Durufle on higher orderspectral (continuous and discontinuous) Galerkin methods (especially with hexaedricmeshes) for frequency domain wave problems (see [8], [73]). The achievement of thisthesis has coıncided with the development of the computational code MONTJOIE(see also section 3.2) which incorporates most of our research in terms of numericalmethods for the last past ten years and that we consider as a major realization forthe past four years. Let us mention also that half of the PhD thesis of P. Grob has

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been devoted to higher order methods on hexahedral meshes and allowed us to makeprogress in the theory [26] of these methods. Finally, with the PhD thesis of A.Sinding, we got interested to the discretization of Maxwell’s equations in view of thesolution Vlasov-Maxwell equations: the objective is to build spectral-like Galerkinmethod that would permit at the same time to recover a continuous electric fieldand the continuity of charge. The idea is to mix ideas from mixed finite elementsand DG methods.

• A new topic has been developed during the last four years. It concerns higher ordertime discretization of second order hyperbolic equations. We have concentrated our-selves to explicit energy preserving schemes. Starting from study the even order (2m)schemes obtained by the modified equation method, we propose a notion of optimalnumerical scheme based of the maximisation of the CFL limit whose constructionwas based on a non standard optimization problem. At this stage of the work, wehave achieved, in collaboration with Jean-Charles Gilbert from project-team ES-TIME, a fairly complete analysis of the optimization, derived efficient numericalalgorithms for the actual computation of these schemes [28], obtained promising nu-merical results on academic test cases, completed by an asymptotic (with respect tothe order) complexity analysis of the schemes.

• Approximation of the wave equation with fractional order dissipative terms. Such amodel describes acoustic waves traveling in a duct with viscothermal losses at thelateral walls is a wave equation with spatially-varying coefficients, which involvesfractional-order integrals and derivatives. The typical application is the numericalmodelling of wind musical instruments. The main goal of our investigations is topropose an efficient numerical discretization of the coupled model, that avoids forinstance the storage of the solution during past steps which would be penalizing forlong time simulations. Our approach is based on so-called diffusive representationsof the fractional integral where, roughly speaking, the fractional-order time kernel inthe integral is represented by its Laplace transform (see RA2007 for more details).

• Let us mention a “come-back” (this was a traditional subject for our team during the90’s) to numerical modelling of seismic waves via the PhD thesis of A. Ezziani [240]in which two “complex” modelization problems were considered: the propagation ofwaves in general viscoelastic media [100]. For more details, we refer the reader tothe activity reports RA2004 and RA2005.

• We also have chosen to omit in our detailed presentation some more individual works(we mean that, for the moment, that they do not enter a collective strategy or do notnecessarily concern wave propagation) such as (the following list is not exhaustive)the work of P. Ciarlet in linear elasticity, the works of J. Rodrıguez on reduced basismethods for time harmonic wave propagation problems [21], [176], the work of C.Hazard on the singularity expansion method [76], [78] or the work by J. R. Li on thenumerical approximation of diffusion equations [183].

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3 Knowledge dissemination

3.1 Publications

The following table has been built from our publication data base

http://uma.ensta.fr/poems/pagesdebase/pages/publications.phpwhich has also served for establishing the bibliography at the end of this report (see section6). We are not sure that these data are complete (the correct formulation would be : weare almost sure that our data are not complete ...) and we are confident in the followingfigures up to a 10 per cent error.

Two of these figures deserved to be commented. The figure of Conferences in 2005 isabnormally high : one partial explanation is the occurrence of the Waves Conference inBrown in 2005, the other explanation is that a lot of (very good) PhD theses have beendefended in 2004-2005 which explains a (local in time) increase of oral presentations. Thenumber of published articles in 2008 is abnormally low. One of the explanations is thedeparture of Houssem Haddar in 2007. The other is a question of conjuncture and delaysof the publication in some journals (note that 17 articles are already accepted in 2009).

2005 2006 2007 2008 to appear

PhD Thesis 3 3 3 2

H.D.R (*) 1

Journal 21 27 30 15 17

Conference proceedings (**) 67 17 31 23

Book chapter 1 6

(*) HDR Habilitation a diriger des Recherches(**) Conference with a program committee

The SIAM journals on Numerical Analysis and Applied Mathematics and NumerischeMathematik, are privileged journals to publish our works in applied mathematics or nu-merical analysis. The Journal of Computational Physics, the SIAM journal of ScientificComputing or Communications in Computational Physics are also natural places for re-porting on our activity in scientific computation. As an important place of our activityis given to mathematical modelling, journals like Mathematical Models and Methods inApplied Sciences (M3AS) or Mathematical modelling and Numerical Analysis (M2AN) arealso important. Concerning our works on inverse problems, the journal Inverse Problemsis obviously our reference journal. Otherwise, we try to diversify the rest of our math-ematical papers in various journal of applied mathematics ( Num. Methods for PDE’s,Math. Meth. Appl. Sciences, J. Comp. Appl. Math., IMA J. on Appl. Math) and also,because of the interdisciplinary and applied nature of some of our work, in more appliedor specialized journals (CMAME, Journal of Comp. Acoustics or some IEEE journals).

Concerning conferences, the situation is more complicated to describe. The conferenceWAVES (International Conference on Mathematical and Numerical Aspects of Wave Prop-agation Phenomena) is of course a major conference in our field. We have been partici-pating in the past in general conferences in Applied Mathematics such as ENUMATH andECCOMAS, or in more specialized ones such as ICOSAHOM (International Conference on

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Spectral and Higher Order Methods), DDM (International Conference on Domain Decom-position Methods) or MAFELAP (on Finite Elements). We are also invited to participateto more specific workshops such as the workshops organized at Oberwolfach or Marseille(CIRM). We also have a real presence in applied conferences, particularly in acoustics andelectromagnetism (see again section 6).

3.2 Software

We are led to develop two types of software. The first category is prototype softwares:various softwares are developed in the framework of specific research contracts (and some-times sold to the contractor) or during PhD theses. They may be also contributions toalready existing softwares developed by other institutions such as CEA, ONERA or EDF.The second category is advanced software which are intended to be developed, enrichedand maintained over longer periods. Such softwares are devoted to help us for our re-search and/or promote our research. We have chosen to present here only our advancedsoftwares.

MELINA

This software has been developed under the leadership of D. Martin for several yearsin order to offer to the researchers a very efficient tool (in Fortran 77 and objectoriented) for easily implementing finite element based original numerical methodsfor solving partial differential equations. It has specific and original potential in thedomain of time harmonic wave problems (integral representations, spectral DtN con-ditions,...). Nowadays, it is fully functional in various application areas (acousticsand aeroacoustics, elastodynamics, electromagnetism, water waves). It is an opensource software with on line documentation available at

http://perso.univ-rennes1.fr/daniel.martin/melina/

The software is regularly used in about 10 research laboratories (in France andabroad) and number of research papers have published results obtained with MELINA(see the Web site). Moreover, every 2 years, a meeting is organized which combinesa workshop which teaches new users with presentations by existing users.

During the last four years, apart from various local improvements of the code, newfunctionalities have been developed:

• Higher order finite elements (up to 10th order),

• Higher order quadrature formulae,

• DtN boundary conditions in 3D.

A new C++ version of the software is under development. We will take advantageof this evolution for extending the class of finite elements (mixed elements, tensorvalued elements, ...).

MONTJOIE

This is a software for the efficient and accurate wave propagation numerical mod-elling in both time dependent or time harmonic regimes in various domains of appli-cation: acoustics, aeroacoustics, elastodynamics and electromagnetism . It is basedessentially on the use of quadrilateral/hexaedric conforming meshes and continuous

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or discontinuous Galerkin approximations, The use of tensor product basis func-tions coupled to judicious numerical quadrature techniques leads to important gainsin both computing time and memory storage. Various techniques for treating un-bounded domains have been incorporated : DtN maps, local absorbing conditions,integral representations and PML’s.

We have written an interface for the use of other libraries : SELDON, a C++ lin-ear algebra library (interfaced with BLAS and LAPACK) used for iterative linearsolvers, MUMPS and UMFPACK for direct linear solvers, ARPACK for eigenvaluecomputations. The mesh generation is not part of the code. It can be done withModulef, Gmsh, Ghs3D or Cubit.

This code has been developed by Marc Durufle during his PhD thesis. Some othercontributors have brought more specific enrichments to the code.

3.3 Valorization and technology transfert

We refer the reader to our list of research contracts.

3.4 Teaching

All members of Project-Team POEMS, permanent or not, are very much involved in teach-ing. The location of a part of the team in the Ecole Nationale de Techniques Avancees(ENSTA) has naturally let us to invest particularly this school, but we also teach in sev-eral other institutions in the Paris area : Ecole Polytechnique, Ecole Centrale de Paris,Ecole des Mines de Paris, ENS of Cachan, Universite Paris IX (Dauphine) and Paris VI(Jussieu), UVSQ (Universite de Versailles-Saint Quentin).

We detail below for each permanent member the institutions where he/she had teach-ing activities during the last four years:

Eliane Becache

ENSTA (graduate courses)

Master Modelisation et Simulation of INSTN

Anne-Sophie Bonnet-Ben Dhia



Ecole Centrale de Paris (Master of Mechanics)

Laurent Bourgeois


Colin Chambeyron

Universite Paris IX (undergraduate courses)

Patrick Ciarlet

Ecole Polytechnique (graduate courses)



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Gary Cohen

Universite Paris IX (Master of Applied Mathematics)

Christophe Hazard


Patrick Joly


Universite Paris VI (Master of Applied Mathematics)

Marc Lenoir


ENS Cachan (Preparation to agregation)


Jing Rebecca Li


Ecole des Mines de Paris (graduate courses)

Eric Luneville



Jean-Francois Mercier



Jeronimo Rodriguez


3.5 Visibility

The project participates actively in the organization and is composing a large part of thescientific committee of the International Conferences on Mathematical and Numer-ical Aspects of Wave Propagation (created in 1991 by G. Cohen and P. Joly). Themost recent conference was WAVES2007 in Reading (UK) in July 2007. The nextone will take place at the University of Pau (France) in June 2009.

The project organizes a monthly seminar. The seminar takes place alternatively at INRIAand ENSTA (changing each three months) and is composed of two talks each time.

The project organizes regularly a series of INRIA workshops (high level courses for re-searchers and engineers) on wave propagation (Ecole des Ondes). These workshopsare part of the CEA-EDF-INRIA summer school. The most recent workshops wason Discontinuous Galerkin methods for wave equations, in November 2006.

A.S. Bonnet-Ben Dhia and P. Joly are members of the Executive Committee of the GDR2501 “Etude de la propagation ultrasonore en milieux non homogenes en vue ducontrole non destructif”.

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A.S. Bonnet-Ben Dhia is a member of the Comite d’Orientation Strategique of the GDR2493 “Bruit des transport”.

A.S. Bonnet-Ben Dhia is the head of the team Electromagnetism and Acoustics at CER-FACS.

P. Ciarlet is an editor of DEA (Differential Equations and Applications)

P. Joly is a member of the Scientific Committee of the Seminar in Applied Mathematicsof College de France (P. L. Lions).

P. Joly is member of the Editorial Board of the Journal M2AN (Modelisation Mathematiqueet Analyse Numerique).

P. Joly is member of the Editorial Board of the Book series “Scientific Computation” ofSpringer. (Modelisation Mathematique et Analyse Numerique).

P. Joly is a member of the scientific committee of CEA-DAM.

P. Joly is an expert for the MRIS (Mission pour l’Innovation et la Recherche Scientifique)of DGA (Direction Generale de l’Armement)

P. Joly is a regular lecturer at College Polytechnique (Advanced courses for engineerswho are working in industry).

4 External Funding

To be honest, we, and in particular the project leader, are not very interested in thequestions of money and do not follow carefully the financial aspects of our contracts. Thefigures that we put in the table have been reconstituted from data from our administra-tion. A 20 per cent error is possible.

(k euros) year1 year2 year3 year4

National initiatives

ANR SIMNANOPHOT 17 17 17 7

ANR MOHYCAN 23 18 18

Industrial contracts

EDF 53

EADS-1 10

EADS-2 9 9 9

EADS-3 10 10 10

AIRBUS 13 13 13

ONERA 30 40

CE GRAMAT 32 32 22 22

DGA-1 40 40 40 40

DGA-2 7.2

Total 192 184 124 116.2

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We found too difficult and tedious to indicate, year by year, the amount of money wegot from exterior institutions for PhD or Post Doc Scolarships. We first give below thelist of the students whose presence has an overlaping with the evaluation period and haveobtained an external (at least partially) funding for their PhD. For each of them, weindicate the organism that provided the scholarship.

Vahan Baronian, Scolarship from CNRS-CEA (Tunisia)Chokri Ben Amar, Scolarship from ENIT (Tunisia)Morgane Bergot, Scolarship from DGA-INRIAKamel Berriri, Scolarship from ENIT (Tunisia)Juliette Chabassier, Scolarship from Ecole PolytechniqueXavier Claeys, Scolarship from CNRS-DGAJulien Coatleven, Scolarship from Ecole PolytechniqueJeremi Darde, Scolarship from Paris VI UniversityFabrice Delbary, Scolarship from Paris IX UniversityBerangere Delourme, Scolarship from CEA (LETI)Edouard Demaldent, Scolarship from ONERAJulien Diaz, Scolarship from Versailles UniversityEve-Marie Duclairoir, Scolarship from CNRS-EADSMarc Durufle, Scolarship from Paris IX UniversityAbdelaaziz Ezziani, Scolarship from Paris IX UniversitySonia Fliss , Scolarship from CIFRE-EADSBenjamin Goursaud, Scolarship from Ecole PolytechniquePascal Grob, Scolarship from CIFRE-EADSSebastien Imperiale, Scolarship from CEA (LIST)Erell Jamelot, Scolarship from Ecole PolytechniqueLauris Joubert, Scolarship from Ecole PolytechniqueSamir Kaddouri, Scolarship from Paris XI UniversityMatthieu Leautaud, Scolarship from Paris VI UniversityAdrien Semin, Scolarship from Paris XI UniversityAlexandre Sinding, Scolarship from DGASebastien Tordeux, Scolarship from Versailles UniversityCarlo Maria Zwolf, Scolarship from Versailles University

Finally, let us mention external Post-Doc scholarships that have benefited some Post-Docsof our team:

Marc Durufle, Post-Doc Scolarships from ANR SIMNANOPHOT and DGAChristoph Kirsch, Post-Doc Scolarship from Swiss National FoundationAndres Prieto, Post-Doc Scolarships from ANR SIMNANOPHOT and Spain

National initiatives

ANR Project SimNanoPhot: Simulation de micro- et nano-structures photoniques a fortcontraste d’indice (2006 - 2008): project of the ANR (Programme blanc) in collab-oration with IEF (Institut d’Electronique Fondamentale) of the University of Orsay.It concerns the modelization of micro and nano-structures in optics.

ANR (RNTL) project MOHYCAN: MOdelisation HYbride et Couplage semi-ANalytiquepour la simulation du CND (2007-2009). Topic: coupling of the finite element codeATHENA with the semi-analytic code CIVA for application to non-destructive test-ing. Collaborators: CEA-LIST (main contact), EDF and CEDRAT.

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Groupement de Recherches 2501 Etude de la propagation ultrasonore en milieux nonhomogenes en vue du controle non destructif : french-UK network which regroupsacademic and industrial research laboratories in Acoustics and Applied Mathematicsworking on ultrasonic nondestructive testing.

Industrial contracts

Contract ONERA (2005) Participants: Gary Cohen, Marc Durufle.

This contract is about the numerical simulation o1064 f time harmonic wave propaga-tion using higher order discretization methods (mixed finite elements, DiscontinuousGalerkin). 100 kE in 3 years.

Contract EDF (2005) Participants: Julien Diaz, Patrick Joly.

The object of this collaboration is the modelization of the structural noise for crackdetection in welds by ultrasonic waves.

Contract EADS-1 (2005-2006) Participants: Gary Cohen, Pascal Grob, Patrick Joly.

This contract is about the numerical simulation of time dependent vibro-acousticsphenomena using coupled methods (3D / 2D finite elements, retarded potentials /2D finite elements).

Contract EADS-2 (2005-2007) Participants: Sonia Fliss, Patrick Joly.

This contract is about the numerical simulation of elastic wave propagation in com-posite materials (periodic structures with a defect) in the time harmonic regime.

Contract EADS-3 (2005-2007) Participants: Anne-Sophie Bonnet-Ben Dhia, Eve-MarieDuclairoir, Jean-Francois Mercier.

This contract is about the numerical simulation of frequency domain aeroacousticsusing Galbrun’s equations and regularized finite element techniques.

Contract Airbus (2006-2008) Participants: Abdelaaziz Ezziani, Patrick Joly, JeronimoRodrıguez.This contract is about the hybridation of time domain numerical techniques in aeroa-coustics (Linearized Euler equations).

Contract CE Gramat (FEMGD) (2005-2008) Participants: Morgane Bergot, Gary Cohen,Marc Durufle, Patrick Joly.

This contract is about hybrid methods for the time domain solution of Maxwell’sequations.

Contract DGA-1 (2005-2008) Participants: Laurent Bourgeois, Patrick Ciarlet, ChristopheHazard, Grace Hechme, Erell Jamelot, Francois Loret, Eric Luneville.

This contract concerned has the Singular Expansion method for time dependentproblems, the resolution of transient Maxwell’s equations in singular domains andthe identification of buried objects using the linear sampling method.

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Contract DGA-2 (2005) Participants: Anne-Sophie Bonnet-Ben Dhia, Jean-FrancoisMercier.

This contract concerns Galbrun’s acoustics in non uniform flows.

Contract CEA (CASSIS) (2008-) Participants: Gary Cohen, Edouard Demaldent.

This new contract is about the modelling of wave propagation in a layered anisotropicelastic medium for NDT. Funded by the EADS Fundation. 134.5 kE in 3 years.

Contract ONERA-CE Gramat (NADEGE) (2008-) Participants: Gary Cohen, AlexandreSinding.

This new contract is about resolution of Vlasov-Maxwell equations by coupling high-order FEM and PIC methods. 80 kE in 3 years.

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5 Objectives for the next four years

There are several ways to present our objectives, in terms of mathematical problems andtechniques or in terms of application. We found easier to adopt the second point of view.We also have chosen to make the distinction between new research subjects and newobjectives inside continuing research subjects.

New research directions.

• Wave propagation in fractal networks. This is a subject we are initiating incollaboration with B. Maury (University of Orsay) in the framework of the PhDthesis of A. Semin. We are interested in studying the wave propagation on aninfinite tree (we consider a tree as a network with the additional notion of successivegenerations, as a genealogical tree with many generations, seen as an infinite tree: this problem has been motivated by the application to the human lung ( that wedevelop in collaboration with Bertrand Maury from Orsay University) that can beseen, modulo reasonable approximations, as such a tree. In order to solve the problemnumerically, a natural idea would be to replace each sub-tree after the generation n

by a DtN like transparent condition, the first generations being treated by a purelynumerical approach. For this, we can assume that the sub-trees are self-similar(or geometric) p-adic trees (namely each branch is divided into p branches withthe geometrical property that the length of a branch is a fixed sub-multiple (withrate α < 1) of the lengths of the branches of the previous generation).

• The numerical simulation of a piano concert. It is a come back to an attractivetopic : the numerical simulation, using realistic physical models, of musical instru-ments. This topic will be developed within the PhD thesis of Juliette Chabassier incollaboration with A. Chaigne from ENSTA, who is a specialist of musical acoustics,with whom we already collaborated on the simulation of the timpani and of theguitar. The modelization of the piano is a very attractive application field for us, inparticular because it is multiphysics (fluid-structure equations, coupling phenomenaliving in different space dimensions), and in a natural field for applying (or develop-ing new) hybrid numerical methods. It will also give us the opportunity to developa new (for us) subject, namely the numerical approximation of non linear waveequations. For a realistic sound synthesis, it appears that the nonlinear couplingbetween transversal and longitudinal vibrations of piano strings has to be taken intoaccount, as does the “geometrically exact” model described by Morse and Ingard.The corresponding model fits into the class of systems of non linear wave equationsin Hamiltonian form which are energy preserving. Our objective will be to extendto such models our traditional variational methods for linear models and to buildenergy preserving schemes after time discretization.

• Hybrid numerical modelling for 3D seismic wave propagation. Our ob-jective is to initiate a collaboration with TOTAL in this thematic. The generalobjective is to simulate seismic wave propagation in a physical medium who is madeof a smoothly variable medium locally perturbed with strong heterogeneities. Theidea would be to build a method in the frequency domain that would couple the useof paraxial approximations in the smooth regions with the full vectorial Helmholtzequation around the heterogeneity. This implies in particular to address the follow-ing challenges

– build highly accurate paraxial approximations of time harmonic elastic wave

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equations in dimension 3,

– construct accurate and efficient numerical schemes for the approximation ofthese equations,

– define a robust strategy for the coupling by domain decomposition of the twotechniques.

At longer term, another idea would be to use paraxial approximations for precondi-tionning the full vectorial Helmholtz equation.

New objectives on old topics.

• Mathematical and numerical modelling in aeroacoustics. This topic concerns(at least) three subjects: the mathematical modelling of time harmonic aeroacousticsusing Galbrun’s equations and augmented regularized finite element methods, thenumerical modelling of time domain aeroacoustics using linearized Euler equations,discontinuous Galerkin methods and retarded potentials, the construction of effectiveboundary conditions for modelling acoustic liners in the presence of flows. The firsttwo subjects are entering a more operational phase and will be developed in theframework of two industrial / academic collaborations, EADS and CERFACS forthe first subject, AIRBUS and the University of Santiago de Compostela for thesecond subject (see also sections 2.4 and 2.5). The third subject is more academicand prospective but not deconnected of course from the two previous ones since it hasa real possible impact on the applications. Clearly, it has a non empty intersectionwith our other works involving asymptotic ansalysis (see the third point below).This subject is difficult, thus more risky but also very exciting.

• Mathematical and numerical modelling in optics. Our works on optical ta-pers, or more generally, on non-uniform optical waveguides will be continued, fromboth the theoretical and the numerical point of view. We will consider as far as pos-sible in parallel the 2D scalar model (planar taper) end the 3D vectorial case. Thetheoretical objective is to exhibit radiation condition ensuring existence and unique-ness for the time-harmonic diffraction by a bounded junction between two opticalwaveguides. The numerical objective is the development and implementation of afinite element method restricted to the bounded region containing the junction.

Concerning metamaterials, we are interested on one hand, in the continuity of ourprevious works, to develop finite element methods for the existing rough models ofinterface between a metamaterial and a dielectric. Let us recall that some mathe-matical questions are still unsolved in the case of s singular interface. We aim on theother hand to develop more accurate models by homogenization techniques. Thisshould be done in partnership with specialists of homogenization and physicists toassess the models.

Finally we shall probably amplify our research in the domain of periodic media.We wish to pursue our research on DtN approaches by investigating the theoreti-cal aspects of the method, its extension and improvement to non absorbing media,multiple scattering and 3D electromagnetism. We also intend to treat line defectsused photonic crystals, such defects are created to construct an (open) waveguide toconcentrate light. We wish to adapting the DtN approach to transform the associ-ated eigenvalue problem in unbounded media into a nonlinear eigenvalue problem inbounded media, as we did in the past for optical fibers or integrated optics waveg-uides.

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• Development of approximate models via asymptotic analysis. This is adomain where we are convinced that a sophisticated mathematical analysis can offera substantial added value to the efficiency of numerical methods and correspondingcomputational codes, as it is the case for instance for higher order numerical methods.We hope to pursue the work of X. Claeys on wire diffraction and more specifically toextend the fictitious domain / enriched Galerkin approach to 3D electromagnetism.We also intend to adapt this kind of approach to the treatment of rounded corners.A new research direction for asymptotic methods has been recently initiated withthe PhD Thesis of B. Delourme. It concerns effective transmission conditions forthin rough interface transmission problems. With the Post Doc of K. Schmidt, weare going to investigate an analogous but different problem : the goal is to studythe effect of perforated (with periodically spaced holes) walls on the propagation,reflection and transmission of acoustic waves. The novelty is that, at certain asymp-totic regimes, it appears important to take into account the effect of the viscosityof the fluid, at least in the neighborhood of the holes, to represent the attenuationphenomena that are observed in experiments.

• Numerical modelling for non destructive testing. This thematic is of moreapplied nature that our other subjects. It constitutes the heart of our collaborationwith CEA-LIST that we should amplify in the future, to begin with the ContractCASSIS whose objective is to develop a code including and adapting our most re-search achievements on numerical methods for the purpose of the simulation of nondestructive testing experiments. This subject should give the opportunity to amplifyour research on PMLs and non reflecting boundary conditions for anisotropic elasticwaves (which is also the object of a new collaboration with D. Givoli in Tel Havivand T. Hagstrom in New Mexico). Finally, with the PhD of S. Imperiale, we areinitiating a new research devoted to the modelization of piezo-electric sensors whichare thin structures constructed by assembling a great number of periodically spacedpiezoelectric devices.

Of course, we shall continue on more traditional (for us) topics to begin with higherorder methods. In particular, we shall pursue our effort in the construction of pyramidalelements and hybrid meshes, on non classical approaches to higher order time steppingmethods or to the adaptation of spectral element methods to Vlasov-Maxwell’s equations.

The hybridization and coupling of numerical methods and the treatment of unboundedmedia will remain two major transversal topics.

Concerning inverse problems, we aim at extending our imaging techniques to realisticsituations in the field of mechanical engineering : for example, the Linear Sampling Methodwill be adapted to elastic waveguides and an interesting application of the technique,combining quasi-reversibility and level set methods, could be the imaging of plastic zonesin an elastic body.

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6 Bibliography of the project-team

Remark : We have included the PhD theses of S. Pernet and S. Tordeux because theyhave been defended after the last evaluation.

References

6.1 Doctoral dissertations and “Habilitation” theses

[1] Poernomo Sari Sri, Propagation acoustique dans des conduits a parois traitees enpresence d’ecoulement : modelisation par la methode des elements finis, Universitede Bourgogne, (2008)

[2] Claeys Xavier, Analyse asymptotique et numerique de la diffraction d’ondes par desfils minces, (2008)

[3] Zwolf Carlo Maria, Methodes variationnelles pour la modelisation des problemes detransmission d’onde electromagnetique entre dielectrique et meta-materiau, (2008)

[4] Ben Amar Chokri, Etude theorique et numerique de processus de retournement tem-porel, Soutenue a Tunis le 23 juin, These en cotutelle ENIT / Ecole Polytechnique,(2007)

[5] Duclairoir Eve-Marie, Rayonnement acoustique dans un ecoulement cisaille : Unemethode d’elements finis pour la simulation du regime harmonique, Ecole Polytech-nique, (2007)

[6] Kaddouri Samir, Resolution du probleme du potentiel electrostatique dans des do-maines prismatiques et axisymetriques singuliers. Etude asymptotique dans des do-maines quasi-singuliers, These de l’Ecole Polytechnique, (2007)

[7] Berriri Kamel, Approche analytique et numerique pour l’aeroacoustique en regimetransitoire par le modele de Galbrun, Universite Paris-Dauphine, (2006)

[8] Durufle Marc, Integration numerique et elements finis d’ordre eleve appliques auxequations de Maxwell en regime harmonique, Universite Paris-Dauphine, (2006)

[9] Grob Pascal, Methodes numeriques de couplage pour la vibroacoustique instation-naire : Elements finis spectraux d’ordre eleve et potentiels retardes, Universite Paris-Dauphine, (2006)

[10] Haddar Houssem, Imagerie et Modeles Asymptotiques en Electromagnetisme, Habili-tation Universite Paris-Dauphine, (2006)

[11] Diaz Julien, Approches analytiques et numeriques de problemes de transmission enpropagation d’ondes en regime transitoire. Application au couplage fluide-structure etaux methodes de couches parfaitement adaptees, Universite Paris 6, (2005)

[12] Ezziani Abdelaaziz, Modelisation mathematique et numerique de la propagationd’ondes dans les milieux viscoelastiques et poroelastiques, Universite Paris IX, (2005)

[13] Jamelot Erell, Resolution des equations de Maxwell avec des elements finis deGalerkin continus, Ecole Polytechnique, (2005)

41

[14] Tordeux Sebastien, Methodes Asymptotiques pour la Propagation des Ondes dans lesMilieux comportant des Fentes, Universite de Versailles Saint-Quentin-en-Yvelines,(2004)

[15] Pernet Sebastien, Etude de methodes d’ordre eleve pour resoudre les equations deMaxwell dans le domaine temporel. Application a la detection et a la compatibiliteelectromagnetiqu, Universite Paris IX, (2004)

6.2 Articles in referred journals and book chapters

To appear

[16] Baronian Vahan, Bonnet-BenDhia Anne-Sophie and Luneville Eric, Transparentboundary conditions for the harmonic diffraction problem in an elastic waveguide,J. Comput. Appl. Math, (to appear)

[17] Bonnet-BenDhia Anne-Sophie, Ciarlet Patrick and Zwolf Carlo Maria, Time har-monic wave diffraction problems in materials with sign-shifting coefficients, J. Com-put. Appl. Math, (to appear)

[18] Bonnet-BenDhia Anne-Sophie and Mercier Jean-Francois, Resonances of an elasticplate coupled with a compressible confined flow, Quarterly Journal of Mechanics andApplied Mathematics, (to appear)

[19] Bonnet-BenDhia Anne-Sophie, Mercier Jean-Francois, Millot Florence and PernetSebastien, A low Mach model for time harmonic acoustics in arbitrary flows, J. Com-put. Appl. Math., (to appear)

[20] Castel Nicolas, Cohen Gary and Durufle Marc, Discontinuous Galerkin method forhexahedral elements and aeroacoustic, Journal of Computational Acoustics, (to ap-pear)

[21] Chen Yanlai, Hesthaven Jan S., Maday Yvon and Rodrıguez Jeronimo, A MonotonicEvaluation of Lower Bounds for Inf-Sup Stability Constants in the Frame of ReducedBasis Approximations, C. R. Acad. Sci. Paris, Ser. I, (to appear)

[22] Ciarlet Patrick and Ciarlet Philippe, Direct computation of stresses in planar lin-earized elasticity, Math. Models Meth. App. Sci., (to appear)

[23] Ciarlet Patrick and Labrunie simon, Numerical analysis of the generalized Maxwellequations (with an elliptic correction) for charged particle simulations, Math. ModelsMeth. App. Sci., (to appear)

[24] Claeys Xavier, On the theoretical justification of Pocklington’s equation, Math. ModelsMethods Appl. Sci., (to appear)

[25] Claeys Xavier and Collino Francis, Augmented Galerkin Schemes for the NumericalSolution of Scattering by Small Obstacles, Numerische Mathematik, (to appear)

[26] Durufle Marc, Grob Pascal and Joly Patrick, Influence of the Gauss and Gauss-Lobatto quadrature rules on the accuracy of a quadrilateral finite element method inthe time domain, Numerical Methods for Partial Differential Equations, (to appear)

42

[27] Ezziani Abdelaaziz and Joly Patrick, Space-time mesh refinement for discontunuousGalerkin methods for symmetric hyperbolic systems, J. Comput. Appl. Math., (toappear)

[28] Gilbert Jean-Charles and Joly Patrick, Higher order time stepping for second orderhyperbolic problems and optimal CFL conditions, Springer, ”Numerical Analysis andScientific Computing for PDEs and their Challenging Applications”, (to appear)

[29] Haddar Houssem , Li Jing-Rebecca and Matignon Denis, Efficient solution of a waveequation with fractional order dissipative terms, J. Comput. Appl. Math., (to appear)

[30] Joly Patrick and Rodrıguez Jeronimo, Optimized higher order time discretization ofsecond order hyperbolic problems: Construction and numerical study, J. Comput.Appl. Math., (to appear)

[31] Lenoir Marc, Theorie spectrale et applications - Generalites et operateurs compacts,Encyclopedie des techniques de l’ingenieur, vol. AF-567, (to appear)

[32] Le Rousseau Jerome, Fourier-integral-operator product representation of solutions tofirst-order symmetrizable hyperbolic systems, J. Analyse Math., pp 1–55, (to appear)

2008

[33] Assous Franck, Ciarlet Patrick and Garcia Emmanuelle, A characterization of singularelectromagnetic fields by an inductive approach, Numerical Analysis and modelling,vol. 5, pp 491–515, (2008)

[34] Benner Peter, Li Jing-Rebecca and Penzl Thilo, Numerical solution of large-scaleLyapunov equations, Riccati equations, and linear-quadratic optimal control problems,Numerical Linear Algebra with Applications, vol. 15, pp 755–777, (2008)

[35] Bonnet-BenDhia Anne-Sophie, Ciarlet Patrick and Zwolf Carlo Maria, A new com-pactness result for electromagnetic waves. Application to the transmission problembetween dielectrics and metamaterials, Math. Models Meth. App. Sci., vol. 18, pp1605–1631, (2008)

[36] Bourgeois Laurent and Luneville Eric, The Linear Sampling Method in a waveguide:a modal formulation, Inverse Problems, vol. 24, pp 015018, (2008)

[37] Becache Eliane, Rodrıguez Jeronimo and Tsogka Chrysoula, Convergence results ofthe fictitious domain method for a mixed formulation of the wave equation with a Neu-mann boundary condition, Mathematical Modelling and Numerical Analysis, (2008)

[38] Ciarlet Patrick and Ciarlet Philippe, A new approach for approximating linear elas-ticity problems, C. R. Acad. Sci. Paris, Ser. I, vol. 346, pp 351–356, (2008)

[39] Ciarlet Patrick and Hechme Grace, Computing electromagnetic eigenmodes with con-tinuous Galerkin approximations, Comput. Methods Appl. Mech. Engrg., vol. 198,pp 358–365, (2008)

[40] Demaldent Edouard, Levadoux David and Cohen Gary, Spectral Elements for theIntegral Equations of Time-Harmonic Maxwell Problems, IEEE Transactions on An-tennas and Propagation, vol. 56, pp 3001–3010, (2008)

43

[41] Derveaux Gregoire, Joly Patrick and Rodrıguez Jeronimo, Space time mesh refine-ment methods. “Effective computational methods for wave propagation”, Chapman &Hall/CRC, Numer. Insights, vol. 5, pp 385–424, (2008)

[42] Fliss Sonia and Joly Patrick, Exact boundary conditions for time-harmonic wavepropagation in locally perturbed periodic media, Applied Numerical Mathematics,doi:10.1016/j.apnum.2008.12.013, (2008)

[43] Haddar Houssem, Joly Patrick and N’Guyen Hoai Minh, Construction and analy-sis of approximate models for electromagnetic scattering from imperfectly conductingscatterers, Math. Models Methods Appl. Sci., vol. 18, 10, pp 1787–1827, (2008)

[44] Hazard Christophe and Luneville Eric, An improved multimodal approach for nonuniform acoustic waveguides, IMA Journal of Applied Math., vol. 73 (4), pp 668–690,(2008)

[45] Hechme Grace, Nechepurenko Yuri and Sadkane Miloud, Efficient methods for com-puting spectral projectors for linearized hydrodynamic equations, SIAM J. Sci. Com-put., vol. 31, pp 667–686, (2008)

[46] Joly Patrick and Semin Adrien, Construction and analysis of improved Kirchoff con-ditions for acoustic wave propagation in a junction of thin slots, ESAIM Proceeding,vol. 25, pp 44–67, (2008)

[47] Joly Patrick and Tordeux Sebastien, Matching of asymptotic expansions for wavepropagation in media with thin slots II. The error estimates, M2AN, Math. Model.Numer. Anal, vol. 42, pp 193–221, (2008)

[48] Joly Patrick, Finite element methods with continuous displacement.“Effective com-putational methods for wave propagation”, Chapman & Hall/CRC, Numer. Insights,vol. 5, pp 247–266, (2008)

[49] Joly Patrick, The mathematical model for elastic wave propagation. “Effective com-putational methods for wave propagation”, Chapman & Hall/CRC, Numer. Insights,vol. 5, pp 247–266, (2008)

[50] Joly Patrick and Tsogka Chrysoula, Numerical methods for treating unbounded me-dia. “Effective computational methods for wave propagation”, Chapman & Hall/CRC,Numer. Insights, vol. 5, pp 425–472, (2008)

[51] Joly Patrick and Tsogka Chrysoula, Fictitious domains methods for wave diffraction.“Effective computational methods for wave propagation”, Chapman & Hall/CRC, Nu-mer. Insights, vol. 5, pp 359–384, (2008)

[52] Joly Patrick and Tsogka Chrysoula, Finite element methods with discontinuous dis-placement. “Effective computational methods for wave propagation”, Chapman &Hall/CRC, Numer. Insights, vol. 5, pp 331–357, (2008)

[53] Rodrıguez Jeronimo, A Spurious-Free Space-Time Mesh Refinement for Elastody-namics, International Journal for Multiscale Computational Engineering, vol. 6, pp263–279, (2008)

2007

44

[54] Amrouche Cherif, Ciarlet Patrick and Ciarlet Philippe, Vector and scalar potentials,Poincare’s theorem and Korn’s inequality, C. R. Acad. Sci. Paris, Ser. I, vol. 345, pp603–608, (2007)

[55] Barthelme Regine, Ciarlet Patrick and Sonnendrucker Eric, Generalized formula-tions of Maxwell’s equations for numerical Vlasov-Maxwell simulations, Math. ModelsMeth. App. Sci., vol. 17, pp 657–680, (2007)

[56] Ben Amar Chokri, Gmati Nabil, Hazard Christophe and Ramdani Karim, Numeri-cal simulation of time-harmonic reversal mirrors for acoustic waves, SIAM J. Appl.Math., vol. 67, pp 777–791, (2007)

[57] Benabdallah Assia, Dermenjian Yves and Le Rousseau Jerome, On the controllabilityof linear parabolic equations with an arbitrary control location for stratified media, C.R. Acad. Sci. Paris, Ser. I, vol. 344, pp 189–207, (2007)

[58] Benabdallah Assia, Dermenjian Yves and Le Rousseau Jerome, Carleman estimatesfor the one-dimensional heat equation with a discontinuous coefficient and applicationsto controllability and an inverse problem, J. Math. Anal. Appl., vol. 336 (2), pp 865–887, (2007)

[59] Benabdallah Assia, Gaitan Patricia and Le Rousseau Jerome, Stability of discontin-uous diffusion coefficients and initial conditions in an inverse problem for the heatequation, SIAM J. Control Optim., vol. 45 (5), pp 1849–1881, (2007)

[60] Bonnet-BenDhia Anne-Sophie, Ciarlet Patrick and Zwolf Carlo Maria, Two-field andthree-field formulations for wave transmission between media with opposite sign di-electric constants, Journal of Computational and Applied Mathematics, vol. 204, pp408–417, (2007)

[61] Bonnet-BenDhia Anne-Sophie, Duclairoir Eve-Marie, Legendre Guillaume andMercier Jean-Francois, Time-harmonic acoustic propagation in the presence of a shearflow, J. Comput. Appl. Math, vol. 204(2), pp 428–439, (2007)

[62] Bonnet-BenDhia Anne-Sophie, Duclairoir Eve-Marie and Mercier Jean-Francois,Acoustic propagation in a flow: numerical simulation of the time-harmonic regime,ESAIM Proceedings, Volume 22, (2007)

[63] Bonnet-BenDhia Anne-Sophie and Mercier Jean-Francois, Resonances of an elasticplate in a compressible confined fluid, Quarterly Journal of Mechanics and AppliedMathematics, vol. 60(4), pp 397–421, (2007)

[64] Bourgeois Laurent, A stability estimate for ill-posed elliptic Cauchy problems in adomain with corners, C. R. Acad. Sci. Paris, Ser. I, vol. 345, pp 385–390, (2007)

[65] Bourgeois Laurent, Chambeyron Colin and Kusiak Steven, Locating an obstacle in a3D finite depth ocean using the convex scattering support, Journal of Computationaland Applied Mathematics, vol. 204, pp 387–399, (2007)

[66] Becache Eliane, Rodrıguez Jeronimo and Tsogka Chrysoula, A fictitious domainmethod with mixed finite elements for elastodynamics, SIAM J. Sci. Comput., vol.29, pp 1244–1267, (2007)

[67] Cakoni Fioralba and Haddar Houssem, Identification of partially coated anisotropicburied objects using electromagnetic Cauchy data, J. Int. Eq. Appl., (2007)

45

[68] Ciarlet Patrick, Ciarlet Philippe G., Geymonat Giuseppe and Krasucki Francoise,Characterization of the kernel of the operator CURL CURL, C. R. Acad. Sci. Paris,Ser. I, vol. 344, pp 305–308, (2007)

[69] Ciarlet Patrick and Jamelot Erell, Continuous Galerkin methods for solving the time-dependent Maxwell equations in 3D geometries, J. Comput. Phys., vol. 226, pp 1122–1135, (2007)

[70] Ciarlet Patrick and Kaddouri Samir, Multiscaled asymptotic expansions for the elec-tric potential: surface charge densities and electric fields at rounded corners, Math.Models Meth. App. Sci., vol. 17, pp 845–876, (2007)

[71] Ciarlet Patrick and Legendre Guillaume, Well-posedness of the Drude-Born-Fedorovmodel for chiral media, Math. Models Meth. App. Sci., vol. 17(3), pp 461–484, (2007)

[72] Claeys Xavier and Haddar Houssem, Scattering From infinite rough tubular surfaces,Math. Meth. Appl. Sci., vol. 30, pp 389–414, (2007)

[73] Cohen Gary and Durufle Marc, Non spurious spectral-like element methods forMaxwell’s equations, Journal of Computational Mathematics, vol. 25, pp 282–304,(2007)

[74] Cohen Gary and Grob Pascal, Higher Order Spectral Finite Elements for Reissner-Mindlin Equations in the Time Domain, SIAM J. Sci. Comput., vol. 29 (3), pp 986–1005, (2007)

[75] Grob Pascal and Joly Patrick, Conservative coupling between finite elements andretarded potentials. Application to vibroacoustics, SIAM Journal on Scientific Com-puting, vol. 29, 3, pp 1127–1159, (2007)

[76] Hazard Christophe and Loret Francois, The Singularity Expansion Method applied tothe transient motions of a floating elastic plate, Mathematical Modelling and Numer-ical Analysis, vol. 41, pp 925–943, (2007)

[77] Hazard Christophe and Loret Francois, Generalized eigenfunction expansions for con-servative scattering problems with an application to water waves, Proceedings of theRoyal Society of Edinburg, vol. 137A, pp 995–1035, (2007)

[78] Hazard Christophe and Meylan Mike, Spectral theory for a two-dimensional elasticthin plate floating on water of finite depth, SIAM J. Appl. Math., vol. 68(3), pp629–647, (2007)

[79] Hechme Grace, Convergence analysis of the Jacobi-Davidson method applied to ageneralized eigenproblem, C. R. Acad. Sci. Paris, Ser. I, vol. 345, pp 293–296, (2007)

[80] Joly Patrick, Numerical Methods for Elastic Wave Propagation, SpringerWien NewYork, Waves in nonlinear Pre-Stressed Materials, Michel Destrade, Giuseppe Sacco-mandi Editors, pp 181–281, (2007)

[81] Le Rousseau Jerome, On the convergence of some products of Fourier integral opera-tors and applications, Asymptotic Analysis, vol. 51, pp 189–207, (2007)

[82] Le Rousseau Jerome, Carleman estimates and controllability results for the one-dimensional heat equations with BV coefficients, J. Differential Equations, vol. 233,pp 417–447, (2007)

46

[83] Li Jing-Rebecca and Greengard Leslie, On the numerical solution of the heatequation I: fast solvers in free space, Journal of Computational Physics, vol. 226, pp1891–1901, (2007)

2006

[84] Assous Franck, Ciarlet Patrick, Garcia Emmanuelle and Segre Jacques, Time-dependent Maxwell’s equations with charges in singular geometries, Comput. MethodsAppl. Mech. Engrg., vol. 196, pp 665–681, (2006)

[85] Benabdallah Assia, Dermenjian Yves and Le Rousseau Jerome, Carleman estimatesfor the one-dimensional heat equation with a discontinuous coefficient and applica-tions, Comptes Rendus Mecanique, vol. 334, pp 582–586, (2006)

[86] Bonnet-BenDhia Anne-Sophie, Berriri Kamel et Joly Patrick, Regularisation del’equation de Galbrun pour l’aeroacoustique en regime transitoire, numero specialTAM TAM’05, ARIMA, vol. 5, pp 65–79, (2006)

[87] Bourgeois Laurent, Convergence rates for the quasi-reversibility method to solve theCauchy problem for Laplace’s equation, Inverse Problems, vol. 22, pp 413–430, (2006)

[88] Becache Eliane, Bonnet-BenDhia Anne-Sophie and Legendre Guillaume, Perfectlymatched layers for time-harmonic acoustics in the presence of a uniform flow, SIAMJournal on Numerical Analysis, vol. 44, pp 1191–1217, (2006)

[89] Cakoni Fioralba, Fares M’Barek and Haddar Houssem, Analysis of two linear sam-pling methods applied to electromagnetic imaging of buried objects, Inverse problems,vol. 22, pp 845–867, (2006)

[90] Chaigne Antoine, Derveaux Gregoire and Joly Patrick, Ameliorer la guitare acous-tique, Dossiers Pour la Science, vol. 52, pp 74–75, (2006)

[91] Chaigne Antoine, Joly Patrick and Rhaouti Leila, Le son des timbales, Dossiers Pourla Science, vol. 52, pp 66–72, (2006)

[92] Ciarlet Patrick, Jung Beate, Kaddouri Samir, Labrunie Simon and Zou Jun, TheFourier Singular Complement Method for the Poisson problem. Part II: axisymmetricdomains, Numerische Mathematik, vol. 102, pp 583–610, (2006)

[93] Ciarlet Patrick et Kaddouri Samir, Justification de la loi de Peek en electrostatique,C. R. Acad. Sci. Paris, Ser. I, vol. 343, pp 671–674, (2006)

[94] Clausel Marianne, Durufle Marc, Joly Patrick and Tordeux Sebastien, A mathematicalanalysis of the resonance of the finite thin slots, Applied Numerical Mathematics, vol.56, 10-11, pp 1432–1449, (2006)

[95] Cohen Gary, Ferrieres Xavier and Pernet Sebastien, Discontinuous Galerkin methodsfor Maxwell’s equations in the time domain, CRAS Physique, vol. 7, pp 494–500,(2006)

[96] Cohen Gary, Ferrieres Xavier and Pernet Sebastien, A spatial high-order hexahedraldiscontinuous Galerkin method to solve Maxwell’s equations in time domain, J. Com-put. Phys., vol. 217, pp 340–363, (2006)

47

[97] Collino Francis, Fouquet Thierry and Joly Patrick, Conservative space-time meshrefinement methods for the FDTD solution of Maxwell’s equations, Journal Compu-tational Physics, vol. 211, no. 1, pp 9–35, (2006)

[98] Diaz Julien and Joly Patrick, A time domain analysis of PML models in acoustics,Computer Methods in Applied Mechanics and Engineering, vol. 195, 29-32, pp 3820–3853, (2006)

[99] Durufle Marc, Haddar Houssem and Joly Patrick, High order generalized impedanceboundary conditions in electromagnetic scattering problems, C.R. Physique, vol. 7 (5),pp 533–542, (2006)

[100] Ezziani Abdelaaziz, Ondes dans les milieux poroelastiques-Analyse du modele deBiot, ARIMA, (2006)

[101] Haddar Houssem and Kress Rainer, Conformal mapping and an inverse impedanceboundary value problem, J. Inv. Ill-Posed Problems, vol. 14, pp 1–20, (2006)

[102] Haddar Houssem, Kusiak Steven and Sylvester John, The Convex Back-ScatteringSupport, SIAM J. Appl. Math., vol. 66(2), pp 591–615, (2006)

[103] Hechme Grace and Nechepurenko Yuri., Computing reducing subspaces of a largelinear matrix pencil, Russ. J. Numer. Anal. Math. Model., vol. 21 (3), pp 185–198,(2006)

[104] Joly Patrick, Li Jing-Rebecca and Fliss Sonia, Exact boundary conditions for peri-odic waveguides containing a local perturbation, Communications in ComputationalPhysics, vol. 1, 6, pp 945–973, (2006)

[105] Joly Patrick and Tordeux Sebastien, Asymptotic analysis of an approximate modelfor time harmonic waves in media with thin slots, M2AN Math. Model. Numer. Anal,vol. 40 (1), pp 63–97, (2006)

[106] Joly Patrick and Tordeux Sebastien, Matching of asymptotic expansions for wavepropagation in media with thin slots I: The asymptotic expansion, Multiscale mod-elling and Simulation: A SIAM Interdisciplinary Journal, vol. 5 (1), pp 304–336,(2006)

[107] Le Rousseau Jerome, Fourier-integral-operator approximation of solutions to first-order hyperbolic pseudodifferential equations I: convergence in Sobolev Spaces, Comm.Partial Differential Equations, vol. 31, pp 867–906, (2006)

[108] Le Rousseau Jerome and Hormann Gunther, Fourier-integral-operator approxima-tion of solutions to first-order hyperbolic pseudodifferential equations II: microlocalanalysis, J. Math. Pures Appl., vol. 86, pp 403–426, (2006)

[109] Lenoir Marc, Influence coefficients for variational integral equations, C. R. Acad.Sci., vol. 343, pp 561–564, (2006)

[110] Li Jing-Rebecca, Low order approximation of the spherical nonreflecting boundarykernel for the wave equation, Linear Algebra and its Applications, vol. 415, pp455–468, (2006)

2005

48

[111] Assous Franck, Ciarlet Patrick and Garcia Emmanuelle, Singular electromagneticfields: inductive approach, C. R. Acad. Sci. Paris, Ser. I, vol. 341, pp 605–610, (2005)

[112] Ben Abda Amel, Delbary Fabrice and Haddar Houssem, On the use of thereciprocity-gap functional in inverse scattering from planar cracks, Math. ModelsMethods Appl. Sci., vol. 15 (10), pp 1553–1574, (2005)

[113] Bonnet-BenDhia Anne-Sophie, Drissi Dorra et Gmati Nabil, Mathematical analysisof the acoustic diffraction by a muffler containing perforated ducts, Math. ModelsMethods Appl. Sci., vol. 15, n◦ 7, pp 1059–1090, (2005)

[114] Bourgeois Laurent, A mixed formulation of quasi-reversibility to solve the Cauchyproblem for Laplace’s equation, Inverse Problems, vol. 21, pp 1087–1104, (2005)

[115] Becache Eliane, Chaigne Antoine, Derveaux Gregoire and Joly Patrick, Numericalsimulation of a guitar, Comput. and Structures, vol. 83, no 2-3, pp 107–126, (2005)

[116] Becache Eliane, Derveaux Gregoire and Joly Patrick, An efficient numerical methodfor the resolution of the Kirchhoff-Love dynamic plate equation, Numer. MethodsPartial Differential Equations, vol. 21, issue 2, pp 323–348, (2005)

[117] Becache Eliane, Joly Patrick and Rodrıguez Jeronimo, Space-time mesh refinementfor elastodynamics. Numerical results, Comput. Methods Appl. Mech. Engrg., vol.194, pp 355–366, (2005)

[118] Becache Eliane and Kiselev Aleksei, Non-stationary elastic wavefields from anapodized normal transducer. Near-field asymptotics and numerics, Acta Acusticaunited with Acustica, vol. 91, no. 5, pp 822–830, (2005)

[119] Ciarlet Patrick, Augmented formulations for solving Maxwell equations, ComputerMethods in Applied Mechanics and Engineering, vol. 194, pp 559–586, (2005)

[120] Ciarlet Patrick and Ciarlet Philippe G., Another approach to linearized elasticityand a new proof of Korn’s inequality, Mathematical Models and Methods in AppliedSciences, vol. 15, pp 259–271, (2005)

[121] Ciarlet Patrick, Jung Beate, Kaddouri Samir, Labrunie Simon and Zou Jun, TheFourier Singular Complement Method for the Poisson problem. Part I: prismatic do-mains, Numerische Mathematik, vol. 101, pp 423–450, (2005)

[122] Cohen Gary and Fauqueux Sandrine, Mixed spectral finite elements for the linearelasticity system in unbounded domains, SIAM J. Sci. Comput., vol. 26 (3), pp 864–884, (2005)

[123] Colton David and Haddar Houssem, An Application of the Reciprocity Gap Func-tional to Electromagnetic Inverse Scattering Theory, Inverse Problems, vol. 21 (1),pp 383–398, (2005)

[124] Diaz Julien and Joly Patrick, Robust high order non-conforming finite element for-mulation for time domain fluid-structure interaction, J. Comput. Acoust., vol. 13, no.3, pp 403–431, (2005)

[125] Diaz Julien and Joly Patrick, An analysis of higher order boundary conditions forthe wave equation, SIAM J. Appl. Math., vol. 65, no. 5, pp 1547–1575, (2005)

49

[126] Gugercin Serkan and Li Jing-Rebecca, Smith-Type methods for balanced truncationof large sparse systems, Lecture Notes in Computational Science and Engineering,vol. 45, (2005)

[127] Haddar Houssem, Joly Patrick and Nguyen Hoai-Minh, Generalized impedanceboundary conditions for scattering by strongly absorbing obstacles: the scalar case,Math. Models Methods Appl. Sci., vol. 15, no. 8, pp 1273–1300, (2005)

[128] Haddar Houssem and Kress Rainer, Conformal mappings and inverse boundary valueproblems, Inverse Problems, vol. 21, pp 935–953, (2005)

[129] Hechme Grace, Nechepurenko Yuri and Sadkane Miloud., On numerical spectralanalysis of the hydrodynamic equations, Russ. J. Numer. Anal. Math. Model., vol. 20(2), pp 115–129, (2005)

[130] Job Stephane, Luneville Eric and Mercier Jean-Francois, Diffraction of an acousticwave by a plate in a uniform flow : a numerical approach, Journal of ComputationalAcoustics, vol. 13, (2005)

[131] Joly Patrick and Rodrıguez Jeronimo, An Error Analysis of Conservative Space-Time Mesh Refinement Methods for the 1D Wave Equation, SIAM J. Numer. Anal.,vol. 43, pp 825–859, (2005)

[132] Pernet Sebastien, Ferrieres Xavier and Cohen Gary, High Spatial Order Finite Ele-ment Method to Solve Maxwell’s Equations in Time Domain, IEEE Trans on Anten-nas and Propagation, vol. 53 (9), (2005)

6.3 Publications in Conferences and Workshops

2008

[133] Assous Franck and Ciarlet Patrick, A multiscale approach for solving Maxwell’sequations in waveguides with conical inclusions, Springer, ICCS’08, Lecture Notes inComputer Science, vol. 5102, pp 331–340, (2008)

[134] Baronian Vahan, Bonnet-BenDhia Anne-Sophie, Luneville Eric and Lhemery Alain,Numerical simulation of non destructive testing experiments in an elastic waveguide,Ultrasonic Wave Propagation in Non Homogeneous Media, Springer, (2008)

[135] Baronian Vahan, Bonnet-BenDhia Anne-Sophie and Luneville Eric, Coupling ofmodal method and finite element method for the diffraction elastic guided waves, GDR”Etude de la propagation ultrasonore en vue du controle non destructif”, Brunel,(2008)

[136] Baronian Vahan, Bonnet-BenDhia Anne-Sophie, Luneville Eric and ChambeyronColin, Scattering by a defect in an elastic waveguide : Coupling of finite elements andmodal representations, Acoustics’08 - Paris, (2008)

[137] Baronian Vahan, Bonnet-BenDhia Anne-Sophie, Luneville Eric and Lhemery Alain,Numerical simulation of non destructive testing experiments in an elastic waveguide,GDR ”Etude de la propagation ultrasonore en vue du controle non destructif”, Anglet,(2008)

50

[138] Baronian Vahan, Lhemery Alain and Bonnet-BenDhia Anne-Sophie, Simulationof non destructive inspections and acoustic emission measurements involving guidedwaves, Anglo-French Physical Acoustics Conference (AFPAC) - Arcachon (France),(2008)

[139] Bonnet-BenDhia Anne-Sophie, Ciarlet Patrick et Zwolf Carlo Maria, Etude de for-mulations elements finis en presence d’une interface entre un dielectrique et unmetamateriau, NUMELEC, (2008)

[140] Bonnet-BenDhia Anne-Sophie, Goursaud Benjamin, Hazard Christophe and PrietoAndres, Finite element computation of leaky modes in stratified waveguides, 5emesjournees du GDR ”Etude de la propagation ultrasonore en vue du controle non de-structif”, Anglet, june, (2008)

[141] Bonnet-BenDhia Anne-Sophie, Mercier Jean-Francois, Millot Florence and PernetSebastien, A finite element method for time harmonic acoustics in arbitrary flows,Acoustics’08, (2008)

[142] Bourgeois Laurent, Stabilite conditionnelle pour les problemes elliptiques mal poses: influence de la regularite du bord, Premier congres de la SM2A, Rabat (Maroc),6-8/02/2008, (2008)

[143] Bourgeois Laurent and Luneville Eric, The method of quasi-reversibility to solvethe Cauchy problems for elliptic partial differential equations, Special Issue : SixthInternational Congress on Industrial Applied Mathematics (ICIAM07), Wiley, vol. 7,pp 104201–104202, (2008)

[144] Bourgeois Laurent and Luneville Eric, The linear sampling method in a waveguide: a formulation based on modes, Special Issue : Sixth International Conference onInverse Problems in Engineering: Theory and Practice (6ICIPE), IOP, Journal ofPhysics: Conference Series, vol. 135, pp 012023, (2008)

[145] Bourgeois Laurent and Luneville Eric, The linear sampling method in a waveguide: a formulation based on modes, Conference ICIPE 2008, VVF Dourdan, Dourdan(France), 15-19/6/2008, (2008)

[146] Becache Eliane, Some contributions to Perfectly Matched Layers, WCCM8 / EC-COMAS 2008, June 30 –July 5, 2008, Venice, Italy, (2008)

[147] Durufle Marc, Elements finis d’ordre eleve, CANUM 2008, (2008)

[148] Fliss Sonia, Wave propagation in locally perturbed periodic media, Conference ”EDPet applications 2008”, Hammamet (Tunisie), (2008)

[149] Joly Patrick, Couplage entre potentiels retardes et methodes de Galerkin dis-continues. Applications en acoustique, Inauguration de la Chaire ModelisationMathematique et Simulation Numerique, Ecole Polytechnique, Octobre 2008, (2008)

[150] Joly Patrick, Numerical Methods for Wave Prtopagation in locally perturbed Peri-odic Media, Mathematical Topics in Electromagnetic Fields and Wave Propagation,Karsruhe (Allemagne), (2008)

[151] Joly Patrick, Higher order explicit time stepping and optimal CFL condition for sec-ond order hyperbolic problems second order hyperbolic problems, Numerical Methodsfor Evolution Equations, Heraklion (Crete) Evolution Equations, Heraklion (Crete),(2008)

51

[152] Joly Patrick, Rodrıguez Jeronimo and Verhille Emmanuel, Coupling DiscontinuousGalerkin Methods and Retarded Potentials for Time Dependent Wave PropagationProblems, 5th European Congress in Computational Methods in Applied Sciencesand Engineering, (2008)

[153] Li Jing-Rebecca, A fast time stepping method for evaluating fractional integrals,Fractional Differentiation and its Applications, (2008)

[154] Rodrıguez Jeronimo, La methode de domaines fictifs pour la diffraction d’ondes avecde conditions aux limites de Neumann, Journee Thematique ”Frontieres immergeeset applications”, LATP, Marseille, (2008)

[155] Semin Adrien, Propagation of acoustic waves in junction of thin slots, CEMRACS2008, (2008)

2007

[156] Baronian Vahan, Bonnet-BenDhia Anne-Sophie and Luneville Eric, Coupling ofmodal decomposition and finite element method for the diffraction of Lamb wavesin elastic waveguide, Anglo-French Physical Acoustics Conference (AFPAC) - Frejus(France), (2007)

[157] Baronian Vahan, Bonnet-BenDhia Anne-Sophie and Luneville Eric, Transparentboundary conditions for the harmonic diffraction problem in an elastic waveguide,8th International Conference on Mathematical and Numerical Aspects of Waves(WAVES’07), Reading, (2007)

[158] Ben Amar Chokri, Gmati Nabil, Hazard Christophe and Ramdani Karim, Numericalstudy of time reversal in a 2D waveguide, 8th International Conference on Mathemat-ical and Numerical Aspects of Waves (WAVES’07), Reading, (2007)

[159] Bonnet-BenDhia Anne-Sophie, Le traitement des frontieres artificielles en simula-tion des ondes : le cas des guides d’ondes en regime periodique etabli, Convergencesmathematiques franco-maghrebines, Nice, (2007)

[160] Bonnet-BenDhia Anne-Sophie, Ciarlet Patrick and Zwolf Carlo-Maria, Time-harmonic wave transmission problems with sign-shifting material coefficients, 8thInternational Conference on Mathematical and Numerical Aspects of Waves(WAVES’07), Reading, (2007)

[161] Bonnet-BenDhia Anne-Sophie, Dakhia Ghania, Hazard Christophe et ChorfiLahcene, Diffraction par un defaut dans un guide ouvert, TAMTAM (Tendances dansles Applications Mathematiques en Tunisie, Algerie, Maroc), Alger, (2007)

[162] Bonnet-BenDhia Anne-Sophie, Duclairoir Eve-Marie and Mercier Jean-Francois,Finite element simulation of time-harmonic aeroacoustics in a shear flow, 13thAIAA/CEAS Aeroacoustics Conference, Proceeding of the 13th AIAA/CEAS Aeroa-coustics Conference, (2007)

[163] Bonnet-BenDhia Anne-Sophie, Mercier Jean-Francois, Millot Florence and PernetSebastien, A low Mach model for time harmonic acoustics in arbitrary flows, 8th Inter-national Conference on Mathematical and Numerical Aspects of Waves (WAVES’07),Reading, (2007)

52

[164] Bourgeois Laurent and Luneville Eric, The method of quasi-reversibility to solve theCauchy problem for elliptic PDE, Conference ICIAM 2007, ETH, Zurich (Suisse),16-20/7/2007, (2007)

[165] Becache Eliane, Joly Patrick et Rodrıguez Jeronimo, Presentation et analyse desmethodes de raffinement de maillage espace-temps conservatives pour des problemesde propagation d’ondes, 8eme Colloque en Calcul des Structures. Giens, France, (2007)

[166] Claeys Xavier, Theoretical justification of Pocklington’s equation for diffraction bythin wires, Workshop Methodes Asymptotiques en electromagnetisme, 20eme An-niversaire du CERFACS, Toulouse, (2007)

[167] Claeys Xavier, Theoretical justification of Pocklington’s equation for diffractionbythin wires, WAVES, Reading Angleterre, (2007)

[168] Claeys Xavier and Collino Francis, A generalized Holland model for wave diffractionby thin wires, International Conference on Electromagnetics in Advanced Applica-tions, ICEAA, Turin Italie, pp 269–272, (2007)

[169] Claeys Xavier, Collino Francis and Durufle Marc, A generalized Holland model forwave diffraction by thin wires, Conference on Computational Electromagnetism andAcoustics, Oberwolfach Allemagne, (2007)

[170] Claeys Xavier, Collino Francis and Durufle Marc, A generalized Holland model forwave diffraction by thin wires, Cinquiemes journees singulieres, Luminy France, (2007)

[171] Claeys Xavier, Collino Francis and Durufle Marc, A generalized Holland model forwave diffraction by thin wires, WONAPDE, Concpcion Chili, (2007)

[172] Fliss Sonia, Joly Patrick and Li Jing-Rebecca, Exact boundary conditions for locallyperturbed 2d-periodic plane, Mathematical and numerical aspects of wave propagation,Reading, (2007)

[173] Fliss Sonia, Joly Patrick and Li Jing-Rebecca, Computation of harmonic wave propa-gation in infinite periodic media, Report No.5/2007 of Mathematisches Forschungsin-stitut Oberwolfach ”Computational Electromagnetism and Acoustics, Oberwolfach.,(2007)

[174] Gilbert J.C., Joly Patrick and Rodrıguez Jeronimo, Higher order time stepping forsecond order hyperbolic problems and optimal CFL conditions, The 8th InternationalConference on Mathematical and Numerical Aspects of Waves, (2007)

[175] Haddar Houssem , Li Jing-Rebecca and Matignon Denis, Efficient solution of a waveequation with fractional order dissipative terms, Waves, (2007)

[176] Hesthaven Jan S., Maday Yvon and Rodrıguez Jeronimo, Reduced basis outputbounds for harmonic wave propagation problems, The 8th International Conferenceon Mathematical and Numerical Aspects of Waves, (2007)

[177] Hesthaven Jan Sickmann, Maday Yvon and Rodrıguez Jeronimo, Certified DG-FEM Reduced Basis Methods and Output Bounds for the Harmonic Maxwell’s Equa-tions, International Workshop on High-Order Finite Element Methods (HOFEM).Herrsching, Germany, (2007)

53

[178] Joly Patrick, Analyse de la stabilite d’un modele pour la propagation d’ondes dans untuyau de faible epaisseur parcouru par un fluide en ecoulement, TAMTAM’07, Tipaza(Algerie), (2007)

[179] Joly Patrick, Higher order time stepping with optimal CFL conditions for secondorder hyperbolic problems, WONAPDE. Concepcion, Chili, (2007)

[180] Joly Patrick, Modeles approches pour la propagation d’ondes dans un reseau de fentesminces, Workshop Methodes Asymptotiques en electromagnetisme, 20eme Anniver-saire du CERFACS, Toulouse, (2007)

[181] Joly Patrick, Transparent boundary conditions, wave propagation and periodic media,ENUMATH07, Graz, Autriche, (2007)

[182] Joly Patrick et Semin Adrien, Etude de la propagation d’ondes dans des jonctionsde fentes minces, Seminaire ACSIOM, Montpellier II, (2007)

[183] Li Jing-Rebecca and Greengard Leslie, Fast recursive marching (FRM) method: afast solver for the heat equation, Mathematics Department Seminar, Courant Insti-tute, Columbia University, University of Michigan, Dartmouth College, (2007)

[184] Li Jing-Rebecca and Greengard Leslie, Fast and accurate computation of layer heatpotentials, 6th International Congress on Industrial and Applied Mathematics, (2007)

[185] Li Jing-Rebecca and Greengard Leslie, Fast solver for the heat equation in unboundeddomains, 6th International Congress on Industrial and Applied Mathematics, (2007)

[186] Luneville Eric and Mercier Jean-Francois, Finite element simulation of time-harmonic aeroacoustics with a generalized impedance boundary condition, 13thAIAA/CEAS Aeroacoustics Conference, Proceeding of the 13th AIAA/CEASAeroacoustics Conference, (2007)

2006

[187] Assous Franck and Ciarlet Patrick, Vlasov-Maxwell simulations in singular geome-tries, Springer, ICCS’06, Lecture Notes in Computer Science, vol. 3994, pp 623–630,(2006)

[188] Berriri Kamel, Bonnet-BenDhia Anne-Sophie et Joly Patrick, Approche analytiqueet numerique pour l’aeroacoustique dans un ecoulement discontinu, 2eme Journees surles Equations Differentielles et leurs Applications. Annaba, (2006)

[189] Berriri Kamel, Bonnet-BenDhia Anne-Sophie and Joly Patrick, Application ofthe Cagniard-de Hoop method to aeroacoustics, MATHmONDES 2, 2nd BRITISH-FRENCH WAVES MEETING, Manchester, (2006)

[190] Bonnet-BenDhia Anne-Sophie, Propagation du son dans un ecoulement : simulationnumerique du regime periodique etabli, 38e Congres National d’Analyse Numerique,Guidel, (2006)

[191] Bonnet-BenDhia Anne-Sophie, Acoustic scattering in presence of a mean flow, Work-shop on Advances in Computational Scattering, BIRS, Banff, (2006)

[192] Bourgeois Laurent, Chambeyron Colin and Kusiak Steven, Locating an obstacle ina 3D finite depth ocean using the convex scattering support, Conference PICOF 2006,Universite de Nice, Nice (France), 5-7/4/2006, (2006)

54

[193] Claeys Xavier, Modele mathematique pour les fils minces, AIMS Systemes Dy-namiques, Equations Differentielles et Applications, Poitiers France, (2006)

[194] Garcia Emmanuelle and Herlem Y., Evaluation de l’efficacite de blindage en champmagnetique apporte par le ferraillage d’un batiment lors d’un impact foudre, CEM06,pp 265–267, (2006)

[195] Garcia Emmanuelle and Vezinet Rene, CPML for a time-biased PIC code in cylin-drical coordinates, Wiley-VCH Verlag GmbH, ICNAMM 2006, pp 388–392, (2006)

[196] Hazard Christophe, Computing resonances for large time simulation of scatteringphenomena, MAFELAP 2006, (2006)

[197] Hazard Christophe and Luneville Eric, An enhanced multimodal method for nonuniform waveguides, Mathmondes 2 (journees franco-britaniques), (2006)

[198] Joly Patrick, Variational methods for time dependent non destructive testing exper-iments, Conference AFPAC’06, Wye, United Kingdom, (2006)

[199] Joly Patrick, Analyse asymptotique de modeles de propagation d’ondes dans desmilieux comportant des fentes minces, Seminaire du College de France, Paris, (2006)

[200] Joly Patrick, Approximate models for linear aeroacoustics in nearly discontinuousflows, Third Workshop on Numerical Methods for Evolution Problems, Heraklion(Crete), (2006)

[201] Luneville Eric, Exact Transparent Condition for Time-Harmonic Maxwell Equationsin a Waveguide, Advances in Scattering Theory, Banff, Canada, (2006)

[202] Luneville Eric and Mercier Jean-Francois, Simulation numerique par elements finisd’une multi-diffusion acoustique, 8eme Congres de la Societe Francaise d’Acoustique,(2006)

[203] Luneville Eric et Mercier Jean-Francois, Simulation numerique de la propagationd’onde en presence d’un ecoulement uniforme et d’une paroi traitee, 8eme Congresde la Societe Francaise d’Acoustique, (2006)

2005

[204] Ben Abda A, Delbary Fabrice and Haddar Houssem, On the use of the ReciprocityGap functional in inverse scattering from planar impedent cracks, Waves 2005, Prov-idence, USA, (2005)

[205] Ben Amar Chokri, Gmati Nabil, Hazard Christophe and Ramdani Karim, Mathe-matical and numerical study of a time reversal mirror, Seventh International Con-ference on Mathematical and Numerical Aspects of Wave Propagation, Providence,USA, (2005)

[206] Ben Amar Chokri, Gmati Nabil, Hazard Christophe et Ramdani Karim, Retourne-ment temporel dans un guide d’ondes, etude theorique et numerique, Premier CongresInternational de Conception et Modelisation des Systemes Mecaniques, Hammamet,Tunisie, (2005)

[207] Ben Amar Chokri, Gmati Nabil, Hazard Christophe and Ramdani Karim,Modelisation mathematique d’un miroir a retournement temporel, TAMTAM’05 (Ten-dances dans les Applications Mathematiques - Tunisie, Algerie, Maroc), Tunis, (2005)

55

[208] Berriri Kamel et Bonnet-BenDhia Anne-Sophie, Modele approche pour la simulationde l’instabilite de Kelvin-Helmhotz dans un ecoulement discontinu, Jounees d’Etudessur la Propagation Acoustique en Ecoulement, Angers, (2005)

[209] Berriri Kamel, Bonnet-BenDhia Anne-Sophie et Joly Patrick, Regularisation pourl’aeroacoustique en regime transitoire, 2eme colloque sur les Tendances et Applica-tions Mathematiques en Tunisie, Algerie, Maroc, Tunis, (2005)

[210] Berriri Kamel, Bonnet-BenDhia Anne-Sophie and Joly Patrick, Numerical analysisof time-dependent Galbrun equation in an infinite duct, 7th International Conferenceon Mathematical and Numerical Aspects of Waves (WAVES’05), Providence, (2005)

[211] Bonnet-BenDhia Anne-Sophie, Une methode hybride PML/EFL pour la diffractiondans un guide d’ondes, Journees Melina, Le Croisic, (2005)

[212] Bonnet-BenDhia Anne-Sophie, Couches Absorbantes Parfaitement Adaptees pour laSimulation Numerique des Ondes de Lamb, Journees d’Acoustique Physique Sous-marine et Ultra-Sonore, Aix-en-Provence, (2005)

[213] Bonnet-BenDhia Anne-Sophie, PML pour l’aeroacoustique en regime periodiqueetabli, Laboratoire de Mecanique et Acoustique, CNRS, Marseille, (2005)

[214] Bonnet-BenDhia Anne-Sophie, PML pour l’aeroacoustique en regime periodiqueetabli, Laboratoire de Mathematiques Appliquees, Pau, (2005)

[215] Bonnet-BenDhia Anne-Sophie, Ciarlet Patrick and Zwolf Carlo-Maria, A varia-tional approach for wave transmission between media with opposite sign dielectricconstant, 7th International Conference on Mathematical and Numerical Aspects ofWaves (WAVES’05), Providence, (2005)

[216] Bonnet-BenDhia Anne-Sophie, Ciarlet Patrick and Zwolf Carlo Maria, A varia-tional approach for wave transmission between media with opposite sign dielectricconstants, 7th International Conference on Mathematical and Numerical Aspects ofWaves (WAVES’05), (2005)

[217] Bonnet-BenDhia Anne-Sophie, Duclairoir Eve-Marie et Mercier Jean-Francois, Sim-ulation numerique du rayonnement d’ondes acoustiques dans un ecoulement cisailleen regime periodique etabli, Journees d’Etudes sur la Propagation Acoustique enEcoulement, Angers, (2005)

[218] Bonnet-BenDhia Anne-Sophie, Duclairoir Eve-Marie and Mercier Jean-Francois,Numerical simulation of acoustic propagation in a shear flow in the frequency do-main, 7th International Conference on Mathematical and Numerical Aspects of Waves(WAVES’05), Providence, (2005)

[219] Bonnet-BenDhia Anne-Sophie and Mercier Jean-Francois, Influence of the couplingof an elastic plate with a confined flow on resonances, 7th International Conferenceon Mathematical and Numerical Aspects of Waves (WAVES’05), Providence, (2005)

[220] Bourgeois Laurent, Localisation d’un obstacle dans un ocean 3D de profondeur finie,Journees Melina, Le Croisic, (2005)

[221] Bourgeois Laurent, Une formulation mixte de la methode de quasi-reversibilite pourles EDP elliptiques, 8emes Journees d’Analyse Numerique et Optimisation, ENIM,Rabat (Maroc), 14-16/12/2005, (2005)

56

[222] Bourgeois Laurent, Chambeyron Colin and Kusiak Steven, Locating an obstacle ina 3D waveguide using the scattering support theory, Conference Waves 2005, BrownUniversity, Providence (USA), 20-24/6/2005, (2005)

[223] Becache Eliane, Bonnet-BenDhia Anne-Sophie and Legendre Guillaume, PerfectlyMatched Layers for time-harmonic acoustics in the presence of a uniform flow,7th International Conference on Mathematical and Numerical Aspects of Waves(WAVES’05), Providence, (2005)

[224] Becache Eliane, Joly Patrick and Rodrıguez Jeronimo, Analysis of a space-time meshrefinement method for wave propagation problems, The Sixth European Conference onNumerical Mathematics and Advanced Applications (ENUMATH’05). Universidad deSantiago de Compostela, Spain, (2005)

[225] Becache Eliane, Joly Patrick and Rodrıguez Jeronimo, A Lagrange multiplier freespace-time mesh refinement method for wave propagation problems, 7th InternationalConference on Mathematical and Numerical Aspects of Waves (WAVES’05). BrownUniversity (USA), (2005)

[226] Cakoni Fioralba and Haddar Houssem, A new Linear Sampling Method for the Elec-tromagnetic Imaging of Buried Objects, Mathematical Method in Scattering Theoryand Biomedical Engineering, pp 19–30, (2005)

[227] Cakoni Fioralba, Fares M’Barek and Haddar Houssem, Imaging buried objects fromelectromagnetic measurements, Waves’05, Brown, USA, (2005)

[228] Cakoni Fioralba and Haddar Houssem, A new Linear Sampling Method for the Elec-tromagnetic Imaging of Buried Objects, Sventh International Workshop in ScatteringTheory and Biomedical Engineering, Mathematical Method in Scattering Theory andBiomedical Engineering, pp 19–30, (2005)

[229] Castel Nicolas, Une methode de Galerkin discontinue appliquee a l’equation de Gal-brun, Jounees d’Etudes sur la propagation acoustique en ecoulement, Angers, (2005)

[230] Castel Nicolas, Discontinuous Galerkin Qr. Applications in aeroacoustics, CEM-RACS, CIRM, Marseille, (2005)

[231] Castel Nicolas and Cohen Gary, A Discontinuous Galerkin Method with Qr spec-tral elements for aeroacoustics, 7th International Conference on Mathematical andNumerical Aspects of Waves (WAVES’05), Brow University(USA), 2005, (2005)

[232] Chambeyron Colin, Nouveaux Solveurs pour Melina++, Journees Melina, Le Croisic,(2005)

[233] Ciarlet Patrick and Jamelot Erell, Continuous Galerkin methods for solving Maxwellequations in 3D geometries, Springer, Numerical mathematics and advanced applica-tions (ENUMATH 2005), Santiago de Compostela, Espagne, pp 547–554, (2005)

[234] Cohen Gary and Grob Pascal, Mixed Higher Order Spectral Elements for Vibroa-coustics in Time Domain, Waves2005, Brown University, Providence(USA), (2005)

[235] Delbary Fabrice, Reconstruction of the impedance of a crack from acoustical mea-surements, Waves2005, Brown University, Providence(USA), (2005)

[236] Delbary Fabrice, Reconstruction de l’impedance d’une fissure a partir de mesuresacoustiques, Conference TAMTAM’05, Tunis, (2005)

57

[237] Durufle Marc, Elements finis d’ordre eleve pour l’equation de Helmholtz, JourneesMelina. Le Croisic, (2005)

[238] Durufle Marc and Cohen Gary, Comparison of Higher-Order Finite Element Methodsfor the 2-D Maxwell’s Equations in Frequency Domain, Waves2005, Brown University,Providence(USA), (2005)

[239] Durufle Marc, Haddar Houssem et Joly Patrick, Asymptotic models for Electromag-netic Scattering from Strongly Absorbing Obstacles, Waves2005, Brown University,Providence(USA), (2005)

[240] Ezziani Abdelaaziz, Modelisation mathematique et numerique de la propagation d’ondes dans les milieux viscoelastiques et poroelastiques, Seminaire de l’IFP, Rueil-Malmaison, France, (2005)

[241] Ezziani Abdelaaziz, Ondes dans les milieux poroelastiques, elements finis d’ordreeleves, TAMTAM’05, Tunis, Tunisia, (2005)

[242] Ezziani Abdelaaziz, A mixed finite element method and an explicit scheme for wavepropagation in viscoelastic time domain, Jano8, Rabat, Morocco, (2005)

[243] Grob Pascal, Coupling finite elements and integral equations in time domain vibroa-coustics, Waves2005, Brown University, Providence(USA), (2005)

[244] Grob Pascal, Elements finis mixtes spectraux d’ordres eleves pour la vibroacoustiqueinstationnaire, Journees Melina. Le Croisic, (2005)

[245] Grob Pascal, Regularisation de l’equation de Galbrun pour l’aeroacoustique enregime transitoire, Conference TAMTAM, Tunis, (2005)

[246] Haddar Houssem, Asymptotic Models in Electromagnetism : Example of GeneralizedImpedance Boundary Conditions For Strongly Absorbing Media, JSO ”ModelisationEM”, ONERA, Toulouse, (2005)

[247] Haddar Houssem, Imaging buried objects from electromagnetic measurements,Waves05, Brown University , Providence, USA, (2005)

[248] Haddar Houssem, Electrostatic Imaging Based on Conformal Mapping, ConferenceGAMM’05, Luxembourg, (2005)

[249] Haddar Houssem, Generalized impedance boundary conditions for strongly absorbingscatterers: various approximations and error analysis, Seminar at the University ofGottingen, Germany, (2005)

[250] Hazard Christophe et Loret Francois, Decomposition en modes resonnants pourle probleme de tenue a la mer, application numerique, 10emes Journees del’Hydrodynamique, Poitiers, (2005)

[251] Hazard Christophe and Loret Francois, The Singularity Expansion Method appliedto a transient fluid-structure interaction problem, Seventh International Conferenceon Mathematical and Numerical Aspects of Wave Propagation, Providence, USA,(2005)

[252] Hazard Christophe and Loret Francois, Decomposition en modes resonnantspour le probleme de tenue a la mer, application numerique, 10emes Journees del’Hydrodynamique, Poitiers, (2005)

58

[253] Hechme Grace, Computing eigenvalues of the discretized Navier-Stokes model by thegeneralized Jacobi-Davidson method, Springer, Proceedings of the Third InternationalConference, NAA 2004, Rousse, Bulgaria, Revised Selected Papers, vol. 3401, (2005)

[254] Jamelot Erell, Nodal finite element methods for solving Maxwell equations, ENU-MATH’05, Santiago de Compostela (Espagne), (2005)

[255] Joly Patrick, Propagation of electromagnetic waves in a locally perurbes periodicwaveguide, Workshop TiSCoPDE05, Weierstrass Institute, Berlin, (2005)

[256] Joly Patrick, Exact bounbery conditions for locally perturbed periodic waveguides,Waves Meeting, University of Reading, Angleterre, (2005)

[257] Joly Patrick, Modeles approch’es pour la propagation du son dabs des ’ecoulementsdiscontinus, Journees Scientifiques du GDR Ondes, Besancon, (2005)

[258] Joly Patrick, Propagation of Waves in Locally Perturber Periodic Media, WorkshopWIP2005, CIRM, Marseille, (2005)

[259] Joly Patrick, Propagation of Waves in a Locally Perturbed Periodic Media, WorkshopWIP2005, (2005)

[260] Joly Patrick, Modeles approches pour la modelisation de la propagation du son dansdes ecoulements discontinus, ournees Scientifiques du GDR Ondes, Besancon, (2005)

[261] Joly Patrick, Propagation of Electromagnetic Waves in a Locally Perturbed PeriodicWaveguide, Workshop TiSCoPDE05, (2005)

[262] Joly Patrick, Exact boundary conditions for locally perturbed periodic waveguides,Waves Meeting, University of Reading (England), (2005)

[263] Joly Patrick, Numerical methods for elastic wave propagation, conferences at theSummer School of GDR ONDES, Sup Elec, Gif-sur-Yvette, (2005)

[264] Joly Patrick, Exact boundary conditions for locally perturbed periodic waveguides,Enumath2005, Santiago de Compostela (Spain), (2005)

[265] Joly Patrick, Coupling retarded potentials and finite elements for time domain vi-broacoustics, Enumath2005, Santiago de Compostela (Spain), (2005)

[266] Joly Patrick, Mathematical analysis of time domain PML’s, Waves2005, Brown Uni-versity, Providence(USA), (2005)

[267] Joly Patrick, Li Jing-Rebecca and Fliss Sonia, Exact boundary conditions for periodicwaveguides with a local perturbation, (2005)

[268] Joly Patrick and Tordeux Sebastien, Matching of asymptotic expansions for the wavepropagation in media with thin slot, WAVES 2005, Brown University, Providence,(2005)

[269] Luneville Eric and Mercier Jean-Francois, Generalized impedance boundary condi-tions in acoustics with flow, Waves 2005, Providence, USA, (2005)

[270] Tordeux Sebastien, Matching of asymptotic expansions for the wave propagation inmedia with thin slot, TiSCoPDE workshop (New Trends in Simulation and Controlof PDEs), Berlin, Allemagne, (2005)

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6.4 Internal Reports

2008

[271] Bourgeois Laurent, Conditional stability for ill-posed elliptic Cauchy problems : thecase of C1,1 domains (part I), Rapport de recherche INRIA, (2008)

[272] Bourgeois Laurent and Darde Jeremi, Conditional stability for ill-posed ellipticCauchy problems : the case of Lipschitz domains (part II), Rapport de rechercheINRIA, (2008)

[273] Joly Patrick and Semin Adrien, Propagation of an acoustic wave in a junction oftwo thin slots, INRIA Research Report, INRIA Research Report, vol. RR-6708, ppR1–R61, (2008)

2007

[274] Bonnet-BenDhia Anne-Sophie, Durufle Marc, Joly Patrick and Patrick, Constructionet analyse mathematique d’un modele approche pour la propagation d’ondes acous-tiques dans un tuyau mince parcouru par un fluide en ecoulement, INRIA ResearchReport, INRIA Research Report, vol. RR-6363, pp R1–R47, (2007)

[275] Claeys Xavier, Asymptotic analysis for the solution to the Helmholtz problem in theexterior of a finite thin straight wire, (2007)

[276] Claeys Xavier and Collino Francis, Augmented Galerkin schemes for the numericalsolution of scattering by small obstacles, (2007)

[277] Haddar Houssem and Joly Patrick, Construction and analysis of approximatemodels for electromagnetic scattering from imperfectly conducting scatterers, INRIA,5839, (2007)

2006

[278] Becache Eliane, Rodrıguez Jeronimo and Tsogka Chrysoula, On the convergence ofthe fictitious domain method for wave propagation problems, Technical Report 5802INRIA, pp 37, (2006)

[279] Claeys Xavier, Haddar Houssem et Joly Patrick, Etude d’un probleme modele pourla diffraction par des fils minces par developpements asymptotiques raccordes Cas 2D,(2006)

[280] Tordeux Sebastien, Un probleme de Laplace non standard en milieu non borne,INRIA, (2006)

2005

[281] Ciarlet Patrick, Jung Beate, Kaddouri Samir, Labrunie Simon and Zou Jun, TheFourier Singular Complement Method for the Poisson problem. Part III: implementa-tion issues, Rapport de Recherche SFB393/05-12, Technische Universitat Chemnitz,(2005)

[282] Joly Patrick, Lenoir Marc and Tordeux Sebastien, Modeles asymptotiques pour lapropagation des ondes dans des milieux comportant des fentes, INRIA, (2005)

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