CAIMAN is a joint project team with the "École Nationale des
Ponts et Chaussées" (French national civil engineering school) through
the Cermics ("Centre d'Enseignement et de Recherche en
Mathématiques, Informatique et Calcul Scientifique", Teaching and
Research Center on Mathematics, Computer Science and Scientific
Computing), with the CNRS (French National Center of Scientific
Research) and the Nice-Sophia Antipolis University (NSAU), through the
Dieudonné Laboratory (UMR 6621).

The project aims at proposing new and efficient solutions for the numerical simulation of physical phenomena related to electromagnetics and complex flows in interaction (fluid-structure interactions, epitaxy, etc.). Scientific activities sweep a large range from physical modelling to design and analysis of numerical methods. A particular emphasis is put on their validation on realistic configurations and their algorithmic - possibly parallel - implementation.

Research themes

Electromagnetics:

In the frequency domain, we investigate several aspects of integral equations (fast multipole method, multi-layer models, coupling with volumic discretizations). The designed applications are RCS and near-field computations of large bodies or antennas.

In the time domain, we construct numerical methods based on discontinuous finite element or finite volume methods, including coupling schemes with time and space multi-scale approaches. We also study the coupling of the Maxwell equations with the transport of charges in rarefied gases. The main application is the spatial environment of satellites.

Complex fluid dynamics:

In aeroacoustics, we adapt the numerical methods developed for the heterogeneous Maxwell equations, in order to propagate acoustic waves in a continuously varying steady flow, with no numerical dissipation added.

In fluid structure interaction, we study the coupling between algorithms for solving the fluid and the structure, aiming at constructing new, stable and efficient coupling algorithms (new applications with incompressible fluids: wind in civil engineering and blood or air in biomedical engineering).

We intend to simulate epitaxy (cristal growth) on complex geometries via unstructured finite elements grids. This also requires the treatment of complex state laws formulated.

International and industrial relations

Industrial contracts with EADS CCR, Alcatel Space, France Telecom R&D, Centre d'Études de Gramat.

Collaborations with Dassault-Aviation, Cerfacs, ENST, Ecole Polytechnique, universities of Nice, Provence, Paris VI.

- Glossary
numerical methods based on a partition of the computational domain into control volumes, where an approximate for the average value of the solution is computed. These methods are very well suited for conservation laws, especially when the problem solution has very low regularity. These methods find natural extensions in discontinuous finite elements approaches.

a conservation law is a partial differential balance equation of a scalar field (system of conservation laws for a vector field), where all terms are first-order space or time derivatives of functions of the unknown (for example,

${\partial}_{t}u+{\partial}_{x}f\left(u\right)=0$ ).a Riemann solver yields an exact or approximate solution of a local Riemann problem (initial value problem with two constant states). It is used in finite volume methods, for example in Godunov-type numerical fluxes.

Many different PDEs are considered by team members. However, they are
mainly similar to fluid dynamics equations, because they can be
rewritten as hyperbolic systems of conservation laws or balance
equations (Euler, Navier-Stokes, Maxwell equations). Fluid Dynamics
equations are a non linear strictly hyperbolic system of conservation
laws. Computational Fluid Dynamics started decades ago (see

Finite volume methods can easily deal with complex geometries and
irregular solutions. They can simply lead to conservative method
(where for example no fluid mass is lost). They are based on numerical
flux functions, yielding an accurate approximation of the variable
flux through control volume interfaces (these interfaces separate to
distinct field average values on the two control volumes). The
construction of these numerical flux functions is itself based on
approximate Riemann solvers

These methods can be used in many application fields: complex CFD
(with several species or phases), wave propagation in the time-domain
in heterogeneous media

We have proposed a simple and very efficient finite volume method for
the numerical simulation of wave propagation in heterogeneous media,
which can be used on arbitrary unstructured meshes and compares well
with the FDTD

Finally, we should recall here that finite volume methods can very
simply deal with moving meshes (classically, for fluid-structure
interaction simulations, Fluid Dynamics equations are rewritten in an
Arbitrary Lagrangian-Eulerian form, allowing the use of deforming
meshes past a deforming structure). We currently make some effort to
propose finite volume extensions on variable meshes (both the
coordinates and the topology of the unstructured mesh vary), excluding
classical remeshings of mesh adaptation

The efficient use of modern parallel computing platforms implies a
careful adaptation of the underlying numerical algorithms. In
practice, this translates into two main types of activities: most
often, existing methods are parallelized with no modification to the
numerical ingredients; however, in certain situations, new numerical
methods have to be designed in order to fully benefit from the
capabilities of these computers. The solution of the algebraic
systems resulting from the discretization of partial differential
equations is a classical context which is witnessing a large number of
research activities worldwide that aim at developing new parallel
solvers. These are for a great part based on domain decomposition
principles

Moreover, the popularity of the Internet as well as the availability
of powerful computers and high-speed network technologies as low-cost
commodity components is changing the way we use computers today. These
technological opportunities have led to the possibility of using
distributed computing platforms as a single, unified resource, leading
to what is popularly known as grid
computing

- Glossary
interaction between several subsystems with simultaneous evolutions depending on each another. For example, a physical coupling can take place between different sub-systems. Similarly, different numerical methods solving different PDE can be coupled to solve a coupled physical problem.

particular algorithm, built for the numerical simulation of a coupled problem, allowing the modular use of existing numerical procedures. If no particular attention is paid to the construction of the algorithm, it does not inherit the numerical properties of the coupled procedures (in particular stability and accuracy).

Research themes in the team are widely spread: wave propagation, field-plasma coupling, fluid-structure interaction. All these research directions have in common the efficient, accurate coupling of different partial differential equations like the Maxwell system, the Vlasov and Poisson equations, the Navier-Stokes equations and equations for structural dynamics...

The coupled transient solution of different PDEs is still an open
problem (from the theoretical and numerical points of view). The
general approach is based on staggered algorithm (problems are solved
separately and one after each other). This allows the use of existing
codes and procedures. This kind of staggered partitioned procedure
allows also the iterative solution of difficult coupled problems,
where time scales are similar in different subsystems. Finally, one
more and more important aspect of coupling is the transient coupling
of numerical methods (the question of coupling the same method on
several subdomains is still very interesting). All these works are
motivated by the fact that the attention paid to the coupling
algorithm can prevent numerical efficiency, stability, and accuracy
breakdowns

- Glossary
a sparse matrix is almost only filled with zero (for example, a large tridiagonal matrix is sparse). On the contrary, a dense matrix is only filled with

a priorinon-zero terms.functional equation in which the functional unknown appears under the integration sign; in scientific computing, they play an important role in wave propagation in the frequency domain (acoustics, electromagnetics). The three-dimensional partial differential equations can be transformed into an integral equation on the boundary of the scattering object. This allows to reduce the space dimension of the problem and the mesh (from three to two). However, the induced linear systems are not sparse (like for volumic finite elements), but dense and complex.

recursive algorithm based on a octree which fastens and approximates the matrix-vector products appearing in surface discretizations of integral equations. The solution of linear systems are therefore solved using iterative algorithms.

One elementary problem in electromagnetics is the computation of
the field scattered by an object. For a perfectly conducting object
(find $\phi \in X$ such that
$\forall {\phi}^{t}\in X$,:

where

This variational equation is solved using boundary finite
elements. This leads to solving a dense (because of the
Green's kernel), complex, linear system. This can be done directly for
small systems (cpu time growing like

The fast multipole method

We develop numerical methods and algorithms for the numerical solution (in the time or frequency domain) of electromagnetic wave propagation. They can be applied to many different physical settings and several very rich application domains, like telecommunications, biomedical and transportation engineering (optimum design of antennas, electromagnetic compatibility, furtivity, modelling of new absorbing media).

In the time domain, we aim at proposing accurate and efficient methods
for complex geometries and heterogeneous materials (possibly with
small elements like point sources, lines, etc). We first adapted
existing finite volume methods, initially thought for the solution
of compressible fluid dynamics on unstructured grids. Their upwind
nature

In the frequency domain, we consider several developments of boundary
element methods for the numerical solution for integral equations. We
solve large problems (in terms of the size of the scattering object in
wavelengths) using a multilevel, parallel, out-of-core fast multipole
method

In the field of plasmas, we are highly interested in the study of the plasmic and electromagnetic environment of artificial satellites. Satellites receive and emit high energy electromagnetic waves, have many different potential levels on different parts and are evolving in a cloud of charged particles (which may induce electric discharges and other severe problems). Although the physical context is rather electrostatic (the Vlasov-Poisson equations), we use our own experience on the Vlasov-Maxwell system to couple a finite element approach with particle methods, in order to provide meaningful numerical simulations of the plasmic environment of satellites, in the framework of a continuous collaboration with an industrial partner, which pays attention to the physical meaning of both available experimental and numerical results.

We are interested in several physical problems where fluids dynamics are coupled to other phenomena: fluid-structure interactions, flows of real gases, aeroacoustics, etc.

In the field of fluid-structure interactions, many different
application domains appear, like aerospace engineering, biomedical
engineering, civil engineering. In aerospace engineering, the fluid
flow is compressible and light compared with the structure. The
stability properties of recent (both military and civil) airplanes is
strongly dependent on the coupled behavior of the structure and the
flow past itself. We have proposed with Charbel Farhat (Colorado
university at Boulder, Colorado) criteria for the design of efficient,
accurate and stable coupling algorithms in this
context macs and m3n projects).

We are also interested in realistic flows (reactive flows of multiphase
flows). For vapor phase epitaxy (industrial process of high importance
for growing of single crystals in which chemical reactions produce
thin layers of materials whose lattice structures are identical to
that of the substrate on which they are deposited), we have developed
a unstructured two-dimensional basic reactor
simulator

Finally, in connection with the general problem of the simulation of wave propagation, we have started a new research direction on aeroacoustics. We have chosen to limit our investigations to a context (validated by industrials) where the steady flow is known and the goal is to propagate acoustic waves in a non-uniform flow (then, we do not consider the modelling of noise generation, using DNS or turbulent models for example). This requires numerical methods able to deal with heterogeneous propagation properties and producing very few numerical dissipation. The method developed in the framework of electromagnetics and classical acoustics are being extended to this context.

AS_ELFIP is a software developed internally by EADS for solving Helmholtz equations in both the frequency domain and the time domain using integral equations. It is used to simulate acoustic waves propagations around aircrafts and engines. In the frequency domain, the EADS software AS_ELFIP_FMM we strongly contributed to is based on a full multilevel Fast Multipole Method and allows the solution of very large problems (up to 25,6 million of degrees of freedom, solved in 18 hours on a 64-processor IBM/SP3). In the time domain, it uses a time-marching solver and classical sparse matrices. We are in the process of implementing a multipole algorithm in this code in order to treat much larger problems in shorter execution times. The resulting software is for the moment called AS_ELFIP_TMM (TMM stands for "Time domain Multipole Method").

The platform ns3ifs allows the coupled simulation of a viscous
incompressible unsteady flow in a moving mesh and a deforming structure
(simple structural dynamics solver). Coupled in the framework of the
software coupleur modulef
library coupleur.

The team has developed a new version of the software
EM3D/VFC

The team has developed a discontinuous Galerkin version of the
software EM3D/VFC for the numerical simulation of
the three-dimensional Maxwell equations in time domain, for
heterogeneous media and on tetrahedral unstructured grids.
The software EM3D/GLK is based on a complete P1 discontinuous Galerkin
discretization (cells centered on tetrahedra) with centered fluxes and
a leap-frog explicit time-scheme

The retarded potentials

In a joint work with Alcatel, we have proposed ways to accelerate the
software Echo-light for the electromagnetic scattering of several
axisymmetric objects with different symmetry axes. The basic shell
script has been optimized and validated. The post processing was
accelerated using the multipole method

Electromagnetic problems often involve objects with complex geometries. Therefore, the use of unstructured tetrahedral meshes is mandatory for many applications.

We have proposed

Electromagnetic problems often involve objects of very different scales. In collaboration with France Télécom R&D, we have studied Discontinuous Galerkin Time Domain (DGTD) methods for the numerical simulation of the three-dimensional Maxwell equations on locally refined, possibly non-conforming meshes.

We have proposed

We have also proposed

The goal of this study, that has started in October 2003 with the
doctoral thesis of Hugo Fol, is to extend the finite
volume

Project team Caiman is the coordinator of the
HEADEXP

Biological effects of microwave radiation have been investigated both
from the experimental and numerical viewpoints. Concerning numerical
modelling, the power absorption in a user head is computed using
discretized models built from clinical MRI data. The great majority of
such numerical studies have been conducted using the widely known FDTD
(Finite Difference Time Domain) method due to Yee

The HEADEXP project aims at filling the gap between human head MRI images and the efficient and accurate numerical modelling of the interaction of electromagnetic waves emitted by mobile phones on biological tissues. This is made possible by the development of appropriate image analysis tools and automated unstructured mesh generation tools for the construction of realistic discretized human head models. Then, the numerical simulation of the propagation of electromagnetic waves throughout the head tissues calls for modern unstructured mesh solvers of the time domain Maxwell equations. A particular emphasis is put on the ability of the solvers to take into account the heterogeneity of the electromagnetic characteristics (conductivity, permittivity, permeability tensors) of the underlying media.

Numerical methods for the propagation of seismic waves have been
studied for many years. Most of these numerical codes rely on the
finite-element or the finite-difference methods. Among the most
popular schemes, we can cite the staggered-grid-finite-difference
scheme proposed by J. Virieux

To study the P-SV wave propagation in an heterogeneous medium, we solve the first-order hyperbolic system of elastic wave equations (Virieux, 1986) in a vertical 2D medium, supposed linearly elastic and isotropic

where

The validation of this method is actually done on academic test
cases. Firstly, we study the radial numerical displacement produced by
an explosive source. This solution is compared to the analytical
solution (provided by Géosciences Azur) of the propagation of a
P-wave in an infinite medium.
A second-test case, is the P-SV wave propagation in an homogeneous medium
with an horizontal free surface. Solutions are compared to analytical
seismograms for horizontal and vertical velocities

We are currently studying the propagation of acoustic waves in a steady inviscid flow. This subject is directly related to many research themes of the project. Starting from a steady solution of Euler equations in a given configuration (geometry, mesh, flow), we aim at propagating acoustic waves in this continuously heterogeneous medium. This is done by simulating the propagation of very small perturbations, following the linearized Euler equations. We then apply in this context of wave-advection equations the same kind of dissipation-free numerical methods which were developed by the team for electromagnetics in the time domain.

We have proved in

Similarly, a discontinuous Galerkin method was applied

We have developed a dynamic self-adaptative mesh method for
solving hyperbolic linear or non-linear equations in one space
dimension

The solutions adopted in one-dimensional problems were chosen for their natural extension to more than one space dimension (for example, working on mesh vortices rather than on control volumes interfaces, which is quite equivalent in one dimension, but strongly different in more than one dimension). The one-dimensional work is now being extended in two space dimensions. The main difficulties are the handling of an unstructured topology with appearing and disappearing elements, and the application of constraints on mesh adaptation and motion ensuring that control volume do not get strictly negative (leading to more than one approximate value for some portions of the space).

Gas flows arising in many engineering applications may be modeled
using the compressible Navier-Stokes equations. These equations
express the conservation of mass, momentum and energy and must be
completed by a thermodynamic model providing the pressure and the
temperature as a function of the conservative variables.
The simplest model is that of a thermically perfect and calorifically
perfect gas (TPCP, also referred to as polytropic ideal gas) in which,
firstly,
the pressure

Many gas flows require a more elaborate thermodynamic model (for instance, polyatomic gas flows or high pressure flows). The pressure and the temperature are then nonlinear functions of the specific internal energy, while the pressure is still bilinear in the density and the temperature. Such gases will be referred to as thermically perfect (TP).

An attractive approach to incorporate complex pressure and temperature
laws in the numerical simulation of gas flows is to consider a
relaxation method. For the Euler equations, a relaxation method has
been derived recently by Coquel and Perthame

We have developed a relaxation method for the compressible Navier-Stokes equations. The main difference with the Euler equations is that because of the presence of diffusive fluxes, it is necessary to account not only for pressure relaxation but also for temperature relaxation. Keeping the internal energy splitting and the same sub-characteristic conditions as for the Euler equations, we introduce a weighted decomposition of the diffusive flux contribution to the energy balance of both the real and the fictitious gas as well as a global temperature for the relaxation system. We have first specified general consistency conditions guaranteeing that the original Navier-Stokes system is recovered at equilibrium. We have then addressed the stability of the relaxation system and obtained an estimate for the entropy production under certain conditions on the weighting coefficients and the global temperature. A first-order asymptotic analysis around equilibrium states has confirmed the stability results.

The new system is solved using a mixed finite volume/finite element
method applicable to unstructured triangular meshes. The convective
fluxes are evaluated using a Roe scheme of order 3, thanks to a
combination of the MUSCL method and a

Recently, two test cases have been studied thoroughly
allowing publication of this work: the interaction of a temperature
spot with a weak shock for high temperatures (for a TPCP gas and two
different real gas) and the interaction of a reflected shock wave with
the incident boundary layer in a shock tube for a Reynolds number

We are interested here in the design, analysis and evaluation of
domain decomposition methods for the solution of algebraic systems
resulting from the discretization of hyperbolic or mixed
hyperbolic/parabolic systems of partial differential equations such as
those modelling compressible fluid mechanics problems.
This activity is carried out in the context of a collaboration that
was initiated during the doctoral thesis of Victorita
Dolean natural or
classical interface conditions), thus taking into account the
hyperbolic nature of the Euler equations. Here (see also

This study has been initiated during the postdoctoral stay of Zhongze
Li in the project team Caiman. The objective is to define an
effective strategy to benefit from both the numerical efficiency of a
multiplicative Schwarz algorithm and the parallel efficiency of an
additive Schwarz variant. Let

Finding a combination that works somewhat optimally is not an easy
task since, even when a combined preconditioner leads to fewer
iterations for the convergence of the Krylov method than a standard
preconditioner alone, it may be the case that the additional cost of
computing

Aiming at solving the Maxwell equations in the time domain with locally
refined grids (structured or unstructured), we study the possibility
of using both space and time locally refined subdomains. We first
reviewed in

In collaboration with Alcatel Space, we study problems related to the electrostatic charge of satellites. These charges are received periodically from the sun and from the plasmic propulsors (which will be more used in a near future). The presence of these charged particles can lead to undesired potential gaps and eventually to electrostatic discharges (able to destroy some parts of solar energy generators). Following the pioneering work of Olivier Chanrion, which provided a software for the pseudo-transient two-dimensional axisymmetric Vlasov-Poisson equations, Martine Chane-Yook is aiming at developing a three-dimensional code, including the same features and starting from a basis developed by Sébastien Clerc at Alcatel. During the last year, the use of infinite elements at the outside boundary for the Poisson equation has been validated in three space dimensions. At the same time, the spatial volumic discharge was everywhere taken into account and computed (the currents as well), in order to determine a boundary layer thickness. Finally, an algorithm for the determination of the electric potential of conductors (starting from magnetospheric currents, themselves evaluated using back-trajectories) has been proposed.

The NSI3FS software has been used to study the wind effect on bridge
decks and aeroelastic instabilities. In the continuity of validation
works on elementary geometries which have shown a good
aeroelastic coefficients prediction on laminar forced oscillation, we
went on with turbulent flows

The numerical simulation of realistic three-dimensional
electromagnetics problems typically translates into the processing of
very large amounts of data, especially for external problems. This is
essentially the result of two antagonistic parameters: the
characteristic space step of the mesh and the computational domain
size. For high frequency phenomena, the space step can be very small
while the artificial boundaries of the computational domain are
located near the scattering object whereas an opposite situation is
obtained for low frequency phenomena. Several numerical techniques can
be considered in order to partially cure this problem such as, for
instance, the reduction of the computational domain size through the
use of perfectly matched layers. However, these numerical modelling
adaptations are generally not sufficient and the computational power
and memory capacity that are required for the simulation of realistic
problems are such that the use of parallel computing platforms becomes
essential. With respect to this need, we have developed parallel
versions of our finite volume

This year, we have initiated a collaboration with the project team
Epidaure on various aspects of parallel computing for medical image
applications. These studies are carried out in the framework of
Yav++

Parallel computing can also benefit to other aspects of medical image
processing. This is for instance the case for certain aspects of
neurosurgery. Because of the accuracy required by a neurosurgical
procedure, tracking intra-operative deformations is a challenging
task. Therefore, clinical environment demand for fast non-rigid
registration have to be met in a very near future. With regards to
this need, we have been involved in a study whose general objective
was to combine a patient-specific biomechanical model with
block-matching features to register two MRI images of the same patient
in a parallel implementation

For scientific applications such as those considered in project team Caiman, the effective use of a heterogeneous, distributed, computing platform (i.e. a grid computing platform) requires new studies that must address several topics ranging from computer science concerns to more application related issues. This is for example the case for the development of numerical simulation tools that will be able to exploit several high performance computers (clusters of PCs, SMPs) geographically distributed. Indeed, from the computer science viewpoint, it is necessary to devise new parallelization strategies that will take into account the heterogeneity of the computational nodes (CPUs) and the interconnection networks. This characteristic could also be considered at the numerical modelling level through the design of hierarchical PDE solvers based on domain decomposition principles. However, grid computing also motivates the development of new generation collaborative tools that will allow several people located in different sites, to follow or even act on a running numerical simulation. Such a tool will ideally be based on different modules (PDE solver, visualization server, geometric modeler, etc.) that will be coupled and distributed on special purpose computers (clusters of PCs, SMPs, high performance graphical server).

Both of the applications discussed above could be designed as component based distributed applications and, in order to do so, it is necessary to adopt an appropriate programming paradigm. In 2002, we have initiated a collaboration with computer scientists from the project team Oasis at INRIA Sophia Antipolis whose general objective is to apply distributed object-oriented programming principles in the context of computational electromagnetism applications. Two main activities are considered so far.

For what concerns numerical simulation tools, we have developed
JEM3D

Beside this activity, we are also working on the development of a
collaborative tool for the interactive visualization of
three-dimensional numerical simulation results. Here, the objective is
to define a framework that allows for the coupling of a parallel PDE
solver with a visualization server. The visualization server is based
on the VTK

We compute the scattering of an electromagnetic wave by an object
using integral equations. The solution algorithm involves the inversion of a
dense linear system. The starting point of this study is provided by a
software library (developed by EADS, CERFACS and the team) making it
possible to solve linear systems on traditional parallel machines by
direct methods (LU, LDL factorizations), iterative methods (CG, GMRES)
and iterative multipole methods. The goal of this study is to adapt
these various methods to the concept of computational grids, aiming at
exploiting the idle periods of a great number of unused machines
without being concerned by their heterogeneity of their dispersion. We
show in

The team has taken an active part in the answer proposed by the group GERAC-BERTIN-INRIA to the open call of CEG (Centre d'Etudes de Gramat) on method hybridation solutions for the numerical solution of the three-dimensional Maxwell equations in the time-domain. Within this framework, the team was partially funded to promote the use of discontinuous finite volume and element methods, and show that complex computations (on possibly million-vertex unstructured tetrahedral meshes) on realistic configurations (electromagnetic vulnerability of metallic boxes designed to receive electronic devices). The final answer could lead to an important contract with CEG, including an actual industrialization of some of our softwares.

EADS (CCR) has been supporting our research and development effort for many years, mainly concerning the Fast Multipole Methods and their multiple extensions. This year, a new extension to FMM in the time domain has been considered. The goal is to obtain the well known acceleration factor of the fast multipole methods to boundary element formulations of integral equations in the time domain.

This short study aims at evaluating the possibility to include fast multiple methodology in the development process of Renault vehicles. Renault is interested in simulating acoustics in parts of vehicles (motor compartment, passenger space) with complex geometries and materials. The commercial code they use is limited in terms of number if degrees of freedom. The fast multipole method is currently the unique solution towards the solution of large integral equation systems.

Alcatel Space has developed its own software for the solution of integral equations for electromagnetics in the frequency domain, for special configurations where only axisymmetric elements (with possibly non parallel symmetry axes) are considered. These kind of simulations are mainly relevant for example for antennas and structures used on artificial satellites. In this study, ended at the beginning of the year, Nathalie Bartoli proposed an algorithm optimization for the iterative solution of coupled integral equations and, at the same time, provided an evaluation of possible gains given by the fast multipole methods for the computation of close and far fields and the interactions between objects (a multipole library developed at Cerfacs was used in that context).

In collaboration with Alcatel, we continue our effort on the numerical simulation of electrostatic charges and discharges of artificial satellites. After the PhD thesis of Olivier Chanrion, Alcatel partially supports the PhD thesis of Martine Chane-Yook, on the three-dimensional simulation of the Vlasov-Poisson equations around realistic satellites, starting from an Alcatel software basis from Sébastien Clerc.

France Télécom R&D (center of La Turbie) has developed an internal software for the numerical solution of three-dimensional electromagnetics in the frequency domain by integral equations. In this context, they have developed but not yet validated an approach allowing the simulation of multi-layered patch antennas, without any discretization of all interfaces between different media. This software is being validated, extended to magnetic currents and will help us to make accurate numerical comparisons between integral equation solutions and our discontinuous finite element solutions based on volumic formulations.

Numerical methods for the propagation of seismic waves have been
studied for many years. Most of these numerical codes relies on the
finite-element or the finite-difference methods. Among the most
popular schemes, we can cite the staggered-grid-finite-difference
scheme proposed by J. Virieux

In collaboration with Alcatel Space, we study the problems related to the electrostatic charge of satellites. These charges are received periodically from the sun and from the plasmic propulsors (which will be more used in a near future). The presence of these charged particles can lead to undesired potentials gaps and eventually to electrostatic discharges (able to destroy some parts of solar energy generators). Following the pioneering work of Olivier Chanrion, Martine Chane-Yook is aiming at developing a three-dimensional code, including the same features and starting from a basis developed by Sébastien Clerc at Alcatel. This PhD thesis work is advised by Anne Nouri (LATP, CMI, Université de Provence).

We maintain an active collaboration with the team "parallel computing" of Cerfacs on iterative solvers (flexible GMRES and multiple solution with several right-hand-sides) and preconditioners (SPAI and LRU) using the fast multipole method we have developed.

In the framework of a LCPC (Laboratoire Central des Ponts et
Chaussées) research theme on "Wind effects on Civil Engineering
flexible structures" (this work also concerns CSTB - scientific and
technical centre for buildings, and SETRA - service for technical
studies on highways), Emmanuel Briand (technical engineer) went on
with turbulent flows

The working group on "biological fluid dynamics"

Project team Caiman has been involved in the cooperative research
initiative "ICEMA-2"

Stéphane Lanteri is the coordinator of the HEADEXP

The HEADEXP project aims at filling the gap between human head MRI images and the efficient and accurate numerical modelling of the interaction of electromagnetic waves emitted by mobile phones on biological tissues. This is made possible by the development of appropriate image analysis tools and automated unstructured mesh generation tools for the construction of realistic discretized human head models. Then, the numerical simulation of the propagation of electromagnetic waves throughout the head tissues calls for modern unstructured mesh solvers of the time domain Maxwell equations. A particular emphasis is put on the ability of the solvers to take into account the heterogeneity of the electromagnetic characteristics (conductivity, permittivity, permeability tensors) of the underlying media.

Stéphane Lanteri is co-chairing the local club of parallel computing
users in Sophia Antipolis and PACA region

Stéphane Lanteri is a nominated member of CNU 26th section at University Claude Bernard Lyon 1.

Serge Piperno is a supplementary elected member of INRIA's evaluation board and participated to CR2 local admissibility boards at Rocquencourt and Sophia Antipolis, to CR1 and DR2 national admissibility boards.

Serge Piperno is member of the editing committee of "Progress in computational fluid dynamics" (Inderscience).

Serge Piperno is a member of the steering scientific committee of ONERA's federative research project "Couplage de Codes de Calcul Scientifique".

Introduction au calcul parallèle, Stéphane Lanteri, "Mastère de Mécanique Numérique", École Nationale Supérieure des Mines de Paris (18h).Calcul numérique parallèle, Stéphane Lanteri, École Supérieure des Sciences Informatiques, filière Calcul Scientifique pour l'Ingénieur (31h).Équations intégrales,Interactions fluide-structure,Électromagnétisme, Serge Piperno, "Mastère de Mécanique Numérique", École Nationale Supérieure des Mines de Paris (18h).Aéroélasticité, Serge Piperno, Ecole de Printemps de Mécanique des Fluides Numérique, CNRS (4h).Organization by Serge Piperno of an opening week at INRIA Sophia Antipolis pour ENPC students.

Organization by Anne Nouri, Frédéric Poupaud and Serge Piperno of "Journée simulation numérique pour les plasmas", CIRM, May 23-24.

Nicolas Canouet,

Schémas multi-échelles pour la résolution numérique des équations de Maxwell, Thèse de l'ENPC, soutenue le 15 décembre. Jury : Loula Fezoui et Serge Piperno (codirecteurs), Peter Monk (rapporteur), Éliane Bécache (rapporteur), Claude Dedeban, Isabelle Terrasse, Jean-Michel Ghidaglia.Stéphane Lanteri,

Méthodes numériques performantes en maillages non-structurés et applications en mécanique des fluides compressibles, Habilitation à Diriger des Recherches, Université de Nice-Sophia Antipolis, soutenue le 5 décembre. Jury : Olivier Pironneau (rapporteur), David Keyes (rapporteur), Frédéric Poupaud, Jacques Blum, Rémi Abgrall, Frédéric Desprez.

Marc Bernacki, Schémas en volumes finis avec flux centrés appliqués à l'aéroacoustique, ENPC

Martine Chane-Yook, Modélisation et simulation 3D de la charge d'un satellite en environnement plasmique, université de Provence.

Maud Mériaux-Poret, Méthodes en maillages mobiles auto-adaptatifs pour des systèmes hyperboliques en une et deux dimensions d'espace - Application aux interactions fluide-structure, ENPC

Hugo Fol, Couplage de schémas en volumes finis et de méthodes intégrales pour la propagation d ondes électromagnétiques, acoustiques et sismiques, Université de Nice-Sophia Antipolis.

Loula Fezoui has supervised the PhD of Nicolas Canouet.

Serge Piperno was second advisor for the thesis of Nicolas Canouet. He is supervising the theses of Marc Bernacki and Maud Poret, and co-supervising the one of Hugo Fol.

Stéphane Lanteri has supervised the post-doctoral research of Zhongze Li. He is supervising the action of Saïd El Kasmi and is co-supervisor of the thesis of Hugo Fol.

Jessy Aipert, "GRID Computing pour la résolution de systèmes linéaires : Application aux calculs de diffraction électromagnétique", DESS "Calcul Scientifique et Applications", University of Bordeaux 1.

Nathalie Bartoli, in a financially supported collaboration with Alcatel Space, in post-doctoral position till 2/1. Her contribution concerned the optimization and the validation of an Alcatel Space software of electromagnetic wave scattering past several axisymmetric objects. The study also dealt with the investigation on the possibility to accelerate computations using fast multipole methods (also in collaboration with Cerfacs).

Emmanuel Briand, as technical staff, in the framework of the LCPC research theme « Wind Effects on Civil Engineering Structures », till 2/1. Emmanuel Briand made a browsable synthesis of numerical results obtained with the NS3IFS software.

Zhongze Li, in postdoctoral position, within ARC ICEMA-2, till 9/1. He contributed to the acceleration of the software Yav++ developed at INRIA for the numerical simulation of the electromechanical cardiac activity, through parallelization of numerical methods and use of efficient solution algorithms.

Saïd El Kasmi, as junior technical staff, is contributing to our effort on Grid Computing for the simulation of large-scale electromagnetic problems, in strong collaboration with the Oasis project team.

Communications of Nicolas Canouet and Guillaume Sylvand at Waves 2003.

Posters of Nicolas Canouet, Serge Piperno, Stéphane Lanteri, Loula Fezoui at NUMELEC 2003, 4th Conference on Numerical Methods in Electromagnetism, Octobre 28-30.

Invited lecture of Serge Piperno at the colloquium "Fluid-structure coupling problems and non-linear PDEs", University of Haute Alsace, Mulhouse, october 9-10.

Seminars of Saïd El Kasmi and Jessy Aipert at INRIA Sophia Antipolis in a "Day on use of INRIA's cluster", July, 9.

Seminar of Martine Chane-Yook in a "Tropics/Caiman crossed seminar" at INRIA Sophia Antipolis, July 1.

Presentation of Marc Bernacki in a closed "Computational Aeroacoustics Seminar" with Dassault-Aviation, October 29.