Optimizing a complex system arising from physics or engineering covers a vast spectrum in basic and applied sciences. Although we target a certain transversality from analysis to implementation, the particular fields in which we are trying to excell can be defined more precisely.
From the physical analysispoint of view, our expertise relies mostly on Fluid and Structural Mechanics and Electromagnetics. In the former project Sinus, some of us had contributed to the basic understanding of fluid mechanical phenomena (Combustion, Hypersonic NonEquilibrium Flow, Turbulence). More emphasis is now given to the coupling of engineering disciplines and to the validation of corresponding numerical methodologies.
From the mathematical analysispoint of view, we are concerned with functional analysis related to partialdifferential equations, and the functional/algebraic analysis of numerical algorithms. Identifying the Sobolev space in which the direct or the inverse problem makes sound sense, tailoring the numerical method to it, identifying a functional gradient in a continuous or discrete setting, analyzing iterative convergence, improving it, measuring multidisciplinary coupling strength and identifying critical numerical parameters, etc constitute a nonexhaustive list of mathematical problems we are concerned with.
Regarding more specifically the numerical aspects(for the simulation of PDEs), considerable developments have been achieved by the scientific community at large, in recent years. The areas with the closest links with our research are:
approximation schemes, particularly by the introduction of specialized Riemann solvers for complex hyperbolic systems in FiniteVolume/FiniteElement formulations, and highlyaccurate approximations (e.g. ENO schemes),
solution algorithms, particularly by the multigrid, or multilevel and multidomain algorithms bestequipped to overcome numerical stiffness,
parallel implementation and software platforms.
After contributing to some of these progresses in the former project Sinus, we are trying to extend the numerical approach to a more global one, including an optimization loop, and thus contribute, in the longterm, to modern scientific computing and engineering design. We are currently dealing mostly with geometrical optimization.
Software platformsare perceived as a necessary component to actually achieve the computational costefficiency and versatility necessary to master multidisciplinary couplings required today by size engineering simulations.
The project has several objectives : to analyze mathematically coupled PDE systems involving one or more disciplines in the perspective of geometrical optimization or control; to construct, analyze and experiment numerical algorithms for the efficient solution of PDEs (coupling algorithms, model reduction), or multicriterion optimization of discretized PDEs (gradientbased methods, evolutionary algorithms, hybrid methods, artificial neural networks, game strategies); to develop software platforms for codecoupling and for parallel and distributed computing.
Major applications include : the multidisciplinary optimization of aerodynamic configurations (wings in particular) in partnership with Dassault Aviation and Piaggio Aero France; the geometrical optimization of antennas in partnership with France Télécom and Thalès Air Défense (see Opratel Virtual Lab.); the development of Virtual Computing Environmentsin collaboration with CNES and Chinese partners (ACTRI).
A new activity has been launched by J.P. Zolesio and collaborators related to the control of Maxwell equations to locate radar targets by using a strong solution to the HamiltonJacobi equation.
A new collaboration with the Numerical Simulation in Aerodynamics and Aeroacoustics Department, DSNA, of ONERA (The French Aerospace Laboratory) has been initiated by J.A. Désidéri as a consultant. The major areas of this collaboration are: adjoint equations for coupled aerostructural models, fast multigrid solvers for adjoint equations, global multilevel optimization, reduced models for shape optimization and control of numerical uncertainties, game strategies for multidisciplinary optimization.
Optimization problems involving systems governed by PDEs, such as optimum shape design in aerodynamics or electromagnetics, are more and more complex in the industrial setting.
In certain situations, the major difficulty resides in the costly evaluation of a functional by means of a simulation, and the numerical method to be used must exploit at best the problem characteristics (regularity or smoothness, local convexity).
In many other cases, several criteria are to be optimized and some are non differentiable and/or non convex. A large set of parameters, sometimes of different types (boolean, integer, real or functional), are to be taken into account, as well as constraints of various types (physical and geometrical, in particular). Additionally, today's most interesting optimization preindustrial projects are multidisciplinary, and this complicates the mathematical, physical and numerical settings. Developing robust optimizersis therefore an essential objective to make progress in this area of scientific computing.
In the area of numerical optimization algorithms, the project aims at adapting classical optimization methods (simplex, gradient, quasiNewton) when applicable to relevant engineering applications, as well as developing and testing less conventional approaches such as Evolutionary Strategies (ES), including Genetic or ParticleSwarm Algorithms, or hybrid schemes, in contexts where robustness is a very severe constraint.
In a different perspective, the heritage from the former project Sinus in FiniteVolumes (or Elements) for nonlinear hyperbolic problems, leads us to examine costefficiency issues of large shapeoptimization applications with an emphasis on the PDE approximation; of particular interest to us:
best approximation and shapeparameterization,
convergence acceleration (in particular by multilevel methods),
model reduction (e.g. by Proper Orthogonal Decomposition),
parallel and grid computing; etc.
In view of enhancing the robustness of algorithms in shape optimization or shape evolution, modeling the moving geometry is a challenging issue. The main obstacle between the geometrical viewpoint and the numerical implementation lies in the basic fact that the shape gradients are distributions and measures lying in the dual spaces of the shape and geometrical parameters. These dual spaces are usually very large since they contain very irregular elements. Obviously, any finite dimensional approach pertains to the Hilbert framework where dual spaces are identified implicitly to the shape parameter spaces. But these finitedimensional spaces sometimes mask their origin as discretized Sobolev spaces, and ignoring this question leads to wellknown instabilities; appropriate smoothing procedures are necessary to stabilize the shape large evolution. This point is sharp in the “narrow band” techniques where the lack of stability requires to reinitialize the underlying level equation at each step.
The mathematical understanding of these questions is sought via the full analysis of the continuous modeling of the evolution. How can we “displace” a smooth geometry in the direction opposite to a non smooth field, that is going to destroy the boundary itself, or its smoothness, curvature, and at least generate oscillations.
The notion of Shape Differential Equationis an answer to this basic question and it arises from the functional analysis framework to be developed in order to manage the lack of duality in a quantitative form. These theoretical complications are simplified when we return to a Hilbert framework, which in some sense, is possible, but to the undue expense of a large order of the differential operator implied as duality operator. This operator can always be chosen as an ad hocpower of an elliptic system. In this direction, the key point is the optimal regularity of the solution to the considered system (aerodynamical flow, electromagnetic field, etc.) up to the moving boundary whose regularity is itself governed by the evolution process.
We are driven to analyse the fine properties concerning the minimal regularity of the solution. We make intensive use of the “extractor method” that we developed in order
to extend the I. Lasiecka and R. Triggiani “hidden regularity theory”. For example, it was well known (before this theory) that when a domain
has a boundary with continuous curvatures and if a “right hand side”
fhas finite energy, then the solution
uto the potential problem

u=
fis itself in the Sobolev space
H^{2}(
)
H_{0}^{1}(
)so that the normal derivative of
uat the boundary is itself square integrable. But what does this result become when the domain boundary is not smooth? Their theory permitted for example to establish that if the open set
is convex, the regularity property as well as its consequences still hold. When the boundary is only a Lipschitzian continuous manifold the solution
uloses the previous regularity. But the “hidden regularity” results developed in the 80's for hyperbolic problems, in which the
H^{2}(
)type regularity is never achieved by the solution (regardless the
boundary regularity), do apply. Indeed
without regularity assumption on the solution
u, we proved that its normal derivative has finite energy.
In view of algorithms for shape optimization, we consider the continuous evolution
_{t}of a geometry where
tmay be the time (governing the evolution of a PDE modeling the continuous problem); in this case, we consider a problem with dynamical geometry (non cylindrical problem) including the
dynamical free boundaries. But
tmay also be the continuous version for the discrete iterations in some gradient algorithm. Then
tis the continuous parameter for the continuous
virtualdomain deformation. The main issue is the validity of such a large evolution when
tis large, and when
t. A numerical challenge is to avoid the use of any “smoother” process and also to develop “shapeNewton” methods
. Our evolution field approaches permit to extend this viewpoint to the topological shape optimization (
).
We denote
G(
)the shape gradient of a functional
Jat
. There exists
such that
, where
Dis the universe (or “hold all”) for the analysis. For example
. The regularity of the domains which are solution to the shape differential equation is related to the smoothness of the
oriented distancefunction
which turns out to be the basic tool for intrinsic geometry. The limit case
(where
is a tubular neighborhood of the boundary
) is the important case.
If the domains are Sobolev domains, that is if
, then we consider a duality operator,
satisfying:
where
Hdenotes a root space. We consider the following problem: given
_{0}, find a non autonomous vector field
such that,
T_{t}(
V)being the flow mapping of
V,
Several different results have been derived for this equation under boundednessassumptions of the following kind:
The existence of such bound has first been proved for the problem of best location of actuators and sensors, and have since been extended to a large class of boundary value
problems. The asymptotic analysis (in time
t) is now complete for a 2D problem with help of V. Sverak continuity results (and extended versions with D. Bucur). These developments necessitate an intrinsic framework in order to
avoid the use of Christoffel symbols and local mappings, and to work at
minimalregularity for the geometries.
The intrinsic geometry is the main ingredient to treat convection by a vector field
V. Such a non autonomous vector field builds up a tube. The use of
BVtopology permits these concepts to be extended to non smooth vector fields
V, thus modeling the possible topological changes. The
transverse fieldconcept
Zhas been developed in that direction and is now being applied to fluidstructure coupled problems. The most recent results have been published in three books
,
,
.
Developing grid computing for complex applications is one of the priorities of the IST chapter in the 6th Framework Program of the European Community. One of the challenges of the 21st century in the computer science area lies in the integration of various expertise in complex application areas such as simulation and optimisation in aeronautics, automotive and nuclear simulation. Indeed, the design of the reentry vehicle of a space shuttle calls for aerothermal, aerostructure and aerodynamics disciplines which all interact in hypersonic regime, together with electromagnetics. Further, efficient, reliable, and safe design of aircraft involve thermal flows analysis, consumption optimisation, noise reduction for environmental safety, using for example aeroacoustics expertise.
The integration of such various disciplines requires powerful computing infrastructures and particular software coupling techniques. Simultaneously, advances in computer technology militate in favour of the use of massively parallel PCclusters including thousands of processors connected by highspeed gigabits/sec widearea networks. This conjunction makes it possible for an unprecedented crossfertilisation of computational methods and computer science. New approaches including evolutionary algorithms, parameterization, multihierarchical decomposition lend themselves seamlessly to parallel implementations in such computing infrastructures. This opportunity is being dealt with by the Opaleproject since its very beginning. A software integration platform has been designed by the Opaleproject for the definition, configuration and deployment of multidisciplinary applications on a distributed heterogeneous infrastructure . Experiments conducted within European projects and industrial cooperations using CAST have led to significant performance results in complex aerodynamics optimisation testcases involving multielements airfoils and evolutionary algorithms, i.e. coupling genetic and hierarchical algorithms involving game strategies. .
The main difficulty still remains however in the deployment and control of complex distributed applications on grids by the endusers. Indeed, the deployement of the computing grid infrastructures and of the applications in such environments still requires specific expertise by computer science specialists. However, the users, which are experts in their particular application fields, e.g. aerodynamics, are not necessarily experts in distributed and grid computing. Being accustomed to Internet browsers, they want similar interfaces to interact with grid computing and problemsolving environments. A first approach to solve this problem is to define componentbased infrastructures, e.g. the Corba Component Model, where the applications are considered as connection networks including various application codes. The advantage is here to implement a uniform approach for both the underlying infrastructure and the application modules. However, it still requires specific expertise not directly related to the application domains of each particular user. A second approach is to make use of grid services, defined as application and support procedures to standardise access and invocation to remote support and application codes. This is usually considered as an extension of Web services to grid infrastructures. A new approach, which is currently being explored by the Opaleproject, is the design of a virtual computing environment able to hide the underlying gridcomputing infrastructures to the users. It is currently deployed within the Collaborative Working Environments Unit of the DG INFSO F4 of the European Commission. It is planned to include Chinese partners from the aeronautics sector in 2009 to set up a project for FP7.
The demand of the aeronautical industry remains very strong in aerodynamics, as much for conventional aircraft, whose performance must be enhanced to meet new societal requirements in terms of economy, noise (particularly during landing), vortex production near runways, etc., as for highcapacity or supersonic aircraft of the future. Our implication concerns shape optimization of wings or simplified configurations.
Our current involvement with Space applications relates to software platforms for code coupling.
In the context of shape optimization of antennas, we can split the existing results in two parts: the twodimensional modeling concerning only the specific transverse mode TE or TM, and treatments of the real physical 3D propagation accounting for no particular symmetry, whose objective is to optimize and identify real objects such as antennas.
Most of the numerical literature in shape optimization in electromagnetics belongs to the first part and makes intensive use of the 2D solvers based on the specific 2D Green kernels. The 2D approach for the optimization of directivityled recently to serious errors due to the modeling defect. There is definitely little hope for extending the 2D algorithms to real situations. Our approach relies on a full analysis in unbouded domains of shape sensitivity analysis for the Maxwell equations (in the timedependent or harmonic formulation), in particular, by using the integral formulation and the variations of the Colton and Kreiss isomorphism. The use of the France Telecom software SR3D enables us to directly implement our shape sensitivity analysis in the harmonic approach. This technique makes it possible, with an adequate interpolation, to retrieve the shape derivatives from the physical vector fields in the time evolution processes involving initial impulses, such as radar or tomography devices, etc. Our approach is complementary to the “automatic differentiation codes” which are also very powerful in many areas of computational sciences. In Electromagnetics, the analysis of hyperbolic equations requires a sound treatment and a clear understanding of the influence of space approximation.
A particular effort is made to apply our expertise in solid and fluid mechanics, shape and topology design, multidisciplinary optimization by game strategies to biology and medecine. Two selected applications are priviledged : solid tumours and wound healing.
Opale's objective is to push further the investigation of these applications, from a mathematicaltheoretical viewpoint and from a computational and software development viewpoint as well. These studies are led in collaboration with biologists, as well as image processing specialists.
Our expertise in theoretical and numerical modeling, in particular in relation to approximation schemes, and multilevel, multiscale computational algorithms, allows us to envisage to contribute to integrated projects focused on disciplines other than fluid dynamics or electromagnetics such as biology and virtual reality, image processing, in collaboration with specialists of these fields.
Opale team is developing the platform FAMOSA, designed for shape optimization of 3D aerodynamic bodies. It integrates the following components:
a parameterization module implementing a 3D multilevel and adaptive Bézier parameterization (FreeForm Deformation) that allows to deform simultaneously the shape and the CFD mesh ;
an optimization library composed of various algorithms, such as the Multidirectional Search Algorithm from V. Torczon (deterministic), a Particle Swarm Optimization method (semistochastic) and a Krigingbased algorithm (global optimization) ;
a module managing the calls to CFD solvers ;
a metamodel library that contains tools to build a database and kriging models that are used to approximate the objective function and constraints (multilevel modelling technique) ;
a parallel library implementing the evaluations of the objective function in parallel (independent shapes or independent flow conditions).
To facilitate the development of the software and collaborative work between the different developers, a code managing framework based on the SVN version control system has been set up. The code is presently hosted at the inriaGforge.
The FAMOSA platform has been linked to the compressible NavierStokes solver NUM3SIS developed by Opale and Smash (see below), the Euler code NS3D used by Tropics for automatic differentiation tests and the incompressible flow solver ISIS developed at the Ecole Centrale de Nantes.
The NUM3SIS flow solver has been developed by Smash and Opale ProjectTeam for two years. This work is carried out with the support of a software development engineer since October 2008 in the framework of the ADT (Action de Développement Technologique) program.
The compressible NavierStokes solver has been designed for large scale parallel computations using the MPI library. Main features are:
Euler / NavierStokes modelling ;
Laminar / turbulent flows (SpalartAllmaras turbulence model) ;
Multiphase flows ;
Mixed finitevolume and finiteelement spatial discretization (cellvertex method)
Highorder reconstruction schemes (MUSCL reconstruction, Beta scheme, V6 scheme)
Physical fluxes (Godunov, Vanleer flux splitting, HLLC, AUSM+)
Explicit (Backward explicit, RungeKutta) or implicit (Matrixfree, residuals linearization, dual time stepping);
Domain decomposition method for parallel computing.
The code has been validated on various largescale computing facilities (Linux cluster, IBM and Bull supercomputers) for a use of several hundreds of processors.
Shape gradients with respect to 3D geometries in electromagnetic fields are computed by numerical code developments peripherical to the France Télécom SR3D code for the solution of the Maxwell equations. These developments, combined with interpolation in the frequency domain, permit to compute the derivative w.r.t. the frequency.
Additionally, a selfsufficient FORTRAN code is being developed for antenna optimization by parameterized levelset techniques. This code is to be latter interfaced with the code for array antenna optimization.
This activity corresponds to A. W. Bello's thesis work in codirection between the University of Cotonou, Benin, and INRIA, with the support of the French Embassy in Cotonou. The study aims at developing a numerical simulation method of the water network in the city of Cotonou. This network includes a canal connecting Lake Nokoué to the Atlantic Ocean, and various ducts in the city itself. This network is chronically flooded when important rains occur. In our perspective, the simulation code is meant to be used in the future as a control tool to identify ways to prevent flood, or reduce the damages it causes.
The flow has been simulated by solving the shallowwater equations with topography and friction by a finitevolume method, as it is customary in estuaryflowtype simulations. The computational domain is the space occupied by water and the floodplains. It is projected on a horizontal plane of reference, and discretized, and the governing equations are integrated on each grid cell. The numerical integration is carried out by a Godunovtype scheme using a twostep Riemann approximate solver of HLLC type which preserves the positivity the water height and which is well adapted to the treatment of the shock waves. To determine the height of the intermediate state in the Riemann solver, we propose an algorithm in a celerityspeeds formulation in which the governing equations are linearized; as a result, the positivity of the height is preserved, and this then allows to compute the speeds of the fastest waves.
The simulation method has been tested on academic problems first to demonstrate its adequacy. Then, a more realistic case has been treated to model the phenomenon of flood in the city of Cotonou (BENIN) by the water risings in the lagoon. The thesis was successfully defended in March .
Paola Goatin is on parttime leave from University of Toulon. She is preparing her Habilitation thesis on the "Analysis and numerical approximation of some macroscopic models of vehicular traffic". At present, she is working on a traffic flow model with phase transitions on a road network , , , and on the numerical approximation of scalar conservation laws with unilateral constraints to model highway gates. These studies are intended to contribute to the development of numerical schemes devised to model real traffic situations.
Design optimization stands at the crossroad of different scientific fields (and related software): ComputerAided Design (CAD), Computational Fluid Dynamics (CFD) or Computational Structural Dynamics (CSM), parametric optimization. However, these different fields are usually not based on the same geometrical representations. CAD software relies on Splines or NURBS representations, CFD and CSM software uses gridbased geometric descriptions (structured or unstructured), optimization algorithms handle specific shape parameters. Therefore, in conventional approaches, several information transfers occur during the design phase, yielding approximations and nonlinear transformations that can significantly deteriorate the overall efficiency of the design optimization procedure.
The isogeometric approach proposes to definitely overcome this difficulty by using CAD standards as unique representation for all disciplines. The isogeometric analysis consist in developing methods that use NURBS representations for all design tasks:
the geometry is defined by NURBS surfaces;
the computation domain is defined by NURBS volumes instead of meshes;
the solution fields are obtained by using a finiteelement approach that uses NURBS basis functions instead of classical Lagrange polynomials;
the optimizer controls directly NURBS control points.
Using such a unique data structure allows to compute the solution on the exact geometry (not a discretized geometry), obtain a more accurate solution (highorder approximation), reduce spurious numerical sources of noise that deteriorate convergence, avoid data transfers between the software. Moreover, NURBS representations are naturally hierarchical and allows to define multilevel algorithms for solvers as well as optimizers.
In the context of the EXCITING European project, Opale has initiated the development of a model finiteelement solver based on isogeometric concepts, in collaboration with Galaad ProjectTeam, to study hierarchical strategies for modelling and parameterization in this framework. This activity gives the projectteam an opportunity to develop our expertise in numerical approximation schemes for hyperbolic equations in a new application area.
The NUM3SIS flow solver has been developed by Smash and Opale ProjectTeam for two years. This work has been carried out with the support of a software development engineer since October 2008.
Some specific developments have been achieved in order to link the solver with the shape optimization platform FAMOSA and solve more complex aerodynamic problems (implementation of SpalartAllmaras turbulence model, dual timestepping procedure for unsteady flows).
A study of parallel performance has been carried out on National computational facilities (IDRIS, CINES, CCRT), including computations using large grids (until 16 millions nodes for 512 processors) .
Our research themes are related to optimization and control of complex multidisciplinary systems governed by PDEs. They include algorithmic aspects (shape parameterization, game strategies, evolutionary algorithms, gradient/evolutionary hybridization, model reduction and hierarchical schemes), theoretical aspects (control and domain decomposition), as well as algorithmic and software aspects (parallel and grid computing).
These general themes for Opale are given some emphasis this year through the involvement of our project in the ANR/RNTL National Network on MultiDisciplinary Optimization "OMD”.
We have proposed to exploit the classical degree–elevation process to construct a hierarchy of nested Bézier parameterizations. The construction yields in effect a number of rigorously–embedded search spaces, used as the support of multilevel shape–optimization algorithms mimicking multigrid strategies. In particular, the most general, FAMOSA, Full Adaptive Multilevel Optimum Shape Algorithm, is inspired by the classical Full Multigrid Method.
The FAMOSAmethod has been applied to the context of three–dimensional flow for the purpose of shape optimization of a transonic aircraft wing (pressure–drag minimization problem). This complex iterative strategy has been compared with the basic onelevel method, and with the simple “onewayup” algorithm based on degree–elevation only (without coarseparameterization correction steps). The FAMOSAmethod was found superior to both simpler alternatives .
Multilevel parameterization algorithms have been developed also in the framework of semistochastic optimization methods. In particular, we have experimented with success a ParticleSwarm Optimization (PSO) algorithm based on searches in design spaces of increasing dimension . PSO is inspired from the collective intelligence of birds flocks for food seeking or predators avoiding and is based on underlying rules that enable sudden direction changes, scattering, regrouping, etc. The developed multilevel algorithm relies on the use of the swarm memoryto transfer information from one level to the next. This strategy has been found very effective for a simple degree increase strategy. Especially, it was shown that the multilevel algorithm permits to use swarms of smaller size yielding a significant computational time reduction .
The previous hierarchical approach, based on the degreeelevation property of Bézier curves, has been extended to other parameterization types in order to be able to solve general parametric optimization problems. The proposed approach rely on the construction of a hierarchical basis of the design space, originating from the eigenmodes of the Hessian matrix of the cost functional.
We have experimented the method on simple analytic functions and then on shape reconstruction problems, using various approximations of the Hessian matrix (exact, finitedifference, local metamodel, global leastsquares). The application to the multidisciplinary design of a supersonic business jet (aerodynamics, structure, propulsion, flight mechanics) is currently in progress.
Multicriterion design is gaining importance in Aeronautics in order to cope with new needs of society. In the literature, contributions to single discipline and/or singlepoint design optimization abound. We propose to introduce a new approach combining the adjoint method with a formulation derived from game theory for multipoint aerodynamic design problems. Transonic flows around lifting airfoils are analyzed by Euler computations. Airfoil shapes are optimized according to various aerodynamic criteria. The notion of player is introduced. In a competitive Nash game, each player attempts to optimize its own criterion through a symmetric exchange of information with others. A Nash equilibrium is reached when each player constrained by the strategy of the others, cannot improve further its own criterion. Specific real and virtual symmetric Nash games are implemented to set up an optimization strategy for design under conflict.
When devising a numerical shape–optimization method in the context of a practical engineering situation, the practitioner is faced with an additional difficulty related to the participation of several relevant physical criteria in a realistic formulation. For some problems, a solution may be found by treating all but one criteria as additional constraints. In some other problems, mainly when the computational cost is not an issue, Pareto fronts can be identified at the expense of a very large number of functional evaluations. However the difficulty is very acute when optimumshape design is sought w.r.t. an aerodynamic criterion as well as other criteria for two main reasons. The first is that aerodynamics alone is costly to analyze in terms of functional evaluation. The second is that generally only a small degradation of the performance of the absolute optimum of the aerodynamic criterion alone is acceptable (sub–optimality) when introducing the other criteria.
First, following the thesis of B. Abou El Majd, a wingshape aerostructural optimization was successfully realized despite the strong antagonism of the criteria in conflict in the concurrent reduction of the wing drag in Eulerian flow and a stress integral of the structural element treated as a shell subject to linear elasticity, .
Secondly, at the occasion of a twomonth visit of F. Strauss, the stability of a hydrodynamic channel flow governed by the incompressible NavierStokes equations has been formulated classically as a problem of control of the positivity of the real part of an appropriate eigenvalue. This case has been treated as a constrained shape optimization problem in which the eigenvalue real part is maximized. By application of the splitting technique certain improvements of the original design have been achieved . This activity was launched to initiate a collaboration with the Karlruhe Institute of Technology.
Thirdly, J. Niel has analyzed a problem of aerodynamic design of a supersonic aircraft proposed by Dassault Aviation within the French Network on MultiDisciplinary Optimization (OMD). In a classical flightmechanics model, the main flight characteristics (mass, range, takeoff distance, landing velocity) are explicitly related to global aircraft design characteristics by the fundamental laws of aerodynamics, structural and propulsion analyses. These relations have been integrated by Dassault Aviation to the Scilab project platform as explicit functionalities of the dedicated software. J. Niel has conducted a number of optimization experiments by using these functionalities and by applying particleswarm optimization techniquues and territory splitting, and achieved certain viable designs .
The technique of territory splitting is now being extended to encompass cases where all the criteria are of comparable importance (“equitable splits”). In a more global optimization process under developement, the optimization is carried out in two phases. In the first, said to be “cooperative”, all the criteria under consideration are iteratively improved. In the second phase, said to be “competitive”, viable tradeoffs are identified as particular Nash equilibrium points.
Design optimization in Computational Fluid Dynamics or Computational Structural Mechanics is particularly time consuming, since several hundreds of expensive simulations are required in practice. Therefore, we are currently developing approaches that rely on metamodels, i.e. models of models, in order to accelerate the optimization procedure by using different modelling levels. Metamodels are inexpensive functional value predictions that use data computed previously and stored in a database. Different techniques of metamodelling (polynomial fitting, Radial Basis Functions, Kriging) have been developed and validated on various engineering problems. Our developments have been particularly focused on the construction of algorithms that use both metamodels and models based on PDE's solving to drive a semistochastic optimization, with various couplings :
A strong coupling approach consists in using metamodels to preevaluate candidate designs and select those which are exactly evaluated by simulation at each iteration. Then, the optimization algorithm relies only on exact evaluations. For the ParticleSwarm Optimization (PSO) algorithm, an adaptive method has been proposed, that allows the algorithm to automatically adjust the number of exact evaluations required at each iteration , .
A weak coupling approach consists in using metamodels only to solve a set of optimization subproblems iteratively. In that case, kriging is employed to predict both function value and modelling error. The subproblems considered (lower bound minimization, probability of improvement maximization, expected improvement maximization) indicate which simulations should be performed to improve the model as well as determine the best design.
A major issue in design optimization is the capability to take uncertainties into account during the design phase. Indeed, most phenomena are subject to uncertainties, arising from random variations of physical parameters, that can yield offdesign performance losses.
To overcome this difficulty, a methodology for robust designis currently developed and tested, that includes uncertainty effects in the design procedure, by maximizing the expectation of the performance while minimizing its variance.
Two strategies to propagate the uncertaintyare currently under study :
the use of metamodels to predict the uncertainties of the objective function from the uncertainties of the input parameters of the simulation tool. During the optimization procedure, a few simulations are performed for each design variables set, for different values of the uncertain parameters in order to build a database used for metamodels training. Then, metamodels are used to estimate some statistical quantities (expectation and variance) of the objective function and constraints, using a MonteCarlo method.
the use of the automatic differentiation tool Tapenade (developped by Tropics ProjectTeam) to compute first and second order derivatives of the performance with respect to uncertain parameters. The first order derivatives are computed by solving the adjoint system, that is built by using Tapenade in reverse mode. For the computation of the second derivatives, two strategies can be employed: the use of two successive tangent mode differentiations or the use of the tangent mode on the result of the reverse mode differentiation. The efficiency of these strategies depends on the number of the parameters considered. Once these derivatives have been computed, one can easily derive statistic estimations by integrating the Taylor series expansion of the performance multiplied by the probability density function. This work is carried out in collaboration with Tropics ProjectTeam.
These strategies have been applied to quantify the drag statistics for a wing shape of a business aircraft subject to uncertain flow conditions (Mach number and angle of attack) , . It has been shown that the approach based on automatic differentiation is more efficient from a computational point of view, but the metamodelbased approach is more general and more robust , . In particular, some difficulties with nondifferentiable programs have been reported in case of transonic Eulerian flows when using automatic differentation ( due to the use of Roe flux and limiters).
In order to reduce the computational time required by aerodynamic design procedures, we have developed a sophisticated parallelization strategy, that relies on a threelevel parallelization using MPI library. For a robust design optimization in aerodynamics, we compute in parallel:
the flow field using a domain decomposition approach (mesh partitionning);
the performance for different flow conditions (database filling for metamodelbased MonteCarlo);
the performance for different candidate design (parallel optimizer).
This strategy has been applied for the robust design of a business aircraft using several hundreds of processors .
The shape optimization algorithms developed by Opale have been applied to challenging problems in naval hydrodynamics, in collaboration with the fluid mechanics laboratory of Ecole Centrale de Nantes (CNRS UMR 6598).
The problem consists in optimizing the hull shape of a carrier cruise ship, with respect to two antagonistic critera : the total flow resistance and the wake caracteristics of the flow at the propeller. Analyses are performed by solving incompressible Reynoldsaveraged NavierStokes equations on threedimensional unstructured grids with several millions of nodes, using the ISIS flow solver from Ecole Centrale de Nantes. This is a particularly challenging problem because each evaluation takes several hours on a parallel machine. Moreover, complex and highly nonlinear constraints are taken into account, such as constant displacement, room for engine installation, etc. This problem was considered as testcase for a European workshop meeting organized in Lisbon in October, where the leading naval engineering labs in Europe have competed.
This activity aims at constructing efficient numerical methods for shape optimization of threedimensional axisymmetric radiating structures incorporating and adapting various general numerical advances (multilevel parameterization, multimodel methods, etc) within the framework of the timeharmonic Maxwell equations.
The optimization problem consists in finding the shape of the structure that minimizes a criterion related to the radiated energy. In a first formulation one aims at finding the structure whose far field radiation fits a target radiation pattern. The target pattern can be expressed in terms of radiated power (norm of the field) or directivity (normalized power). In a second formulation we assume that the structure is fed by a special device named the waveguide. In such a configuration one wants to reduce the socalled reflexion coefficient in the waveguide. Both formulations make sense when the feeding is monochrome (single frequency feeding). For multiple frequencies optimization, several classical criterions used in multipoints optimization are considered (minmax, linear combinaison, etc.).
Two models have been considered for the analysis problem: a simplified approximation model known as “Physical Optics” (PO) for which the far field is known explicitly for a given geometry; a rigorous model based on the Maxwell equations. For the latter, the equations are solved by SRSR, a 3D solver of the Maxwell equations for axisymmetric structures provided by France Télécom R&D.
A parametric representation of the shape based on FreeFormdeformation (FFD) has been considered. For the PO model, the analytical gradient w.r.t. the FFD parameters has been derived. An exact Hessian has been obtained by Automatic Differentiation (AD) using Tapenade (developed by Tropics ProjectTeam). Both gradient and Hessian have been validated by finite differences. For the Maxwell equations model, the gradient is computed by finite differences.
Both global and local point of view have been considered for solving the optimization problem. An original multilevel semistochastic algorithm showed robustness for global optimization. In the case of multiple frequencies optimization w.r.t. the radiation diagram, numerical experiments showed that a hierarchy in the frequency points can improve the robustness. For local optimization, a quasiNewton method with BFGS update of the Hessian with linear equality constraints has been developed. A numerical spectral analysis of the projected Hessian or quasiHessian for some shapes has exhibited the geometrical modes that are slow to converge. Based on this observation, several multilevel strategies to help this modes to converge have been developed. Successful results have been obtained for both PO and Maxwell model , .
In order to provide a theoretical basis to this multilevel method, a shape reconstruction problem has been considered. The convergence of an ideal twolevel algorithm has been studied. In a first step the matrix of the linear iteration equivalent to the bigrid cycle is computed. Then, by mean of similar transformations and with the help of Maple, the eigenvalues problem is solved. Hence, the spectral radius of the ideal cycle is deduced. Provided that an adequate prolongation operator is used we can show the independance of the convergence rate w.r.t. the dimension of the search space.
In addition, it has been observed that better results are obtained when the Bernstein polynomials are replaced by Legendre or Tchebychev polynomials in the FFD formulation.
In the future we intend to consider multiobjective problems together with original approaches based on game theory. Further realcase problems proposed by France Télécom will be considered.
In the framework of a research collaborative action COLOR 2005, involving three research teams specialized in cell biology (IPMC), image processing and mathematical modeling ( Epidaureand Opaleprojects), two testcases are defined : angiogenesis and wound healing. This latter application is given particular emphasis, since experimental results from biology can be obtained more easily.
Thus, several images and movies are quickly collected from experimental results in biology, concerning monolayer MDCK cell healing. The analysis of these images allows us to observe that the cell migration velocity is constant during the healing.
In order to numerically model the migration, Fisher's model (nonlinear parabolic equations) seems relevant to us. Indeed, it is characterized by a constant front velocity. The first results obtained are very promising and confirm the adequacy of Fisher's model. As a consequence of this work, new data are provided to biologists (diffusive coefficients) to describe the behavior of MDCK cells in presence of HGF and inhibitors.
Using the pseudo differential boundary operator T, « Dirichlet to Neumann » for any outgoing radiating solution of the Maxwell equation in the exterior of a bounded domain D with boundary S, we build an optimal control problem whose solution is the harmonic regime in the domain D. The optimal control is part of the initial data for the time depending solution. Under periodic excitation (with compact support in D) and lateral Neumann boundary condition on S, the operator T is involved. The optimal synthesis involves the time backward adjoint state which is captured by the Ricatti solution. The mathematical proof of the « device » requires sharp regularity analysis on the non homgeneous Neuman problem associated in D with the time depending 3D Maxwell system.
This is an confidential approach for the conception of a part of radar device. It involves A specific geometrical optimization.
After IIAM 19595 in Hamburg ( and several papers) we introduced the socalled « extractor technique » which permit to recover the hidden regularity results in wave equation Under Dirichlet Boundary Condition. These results were a kind of quantified Version of results derived by I.Lasiecka and R. Triggiani using some multiplicator techniques and were power full enough to derive shape dérivative Under weak regularity . Nevertheless this technique failed for the Neumann like boundary conditions. We introduce theew concept of « Pseudodifferential « tehcnic which recentely dropped this limitation. So we develop new sharp regularity results leading for shape dérivative existence for wave Under eumann boundary data in the space of finité energy on the boundary. The intrinsic character of the pseudo extractor permits toextend easily the results to the important situation of free time depending elastic shell equations.
Optimal control theory is classicaly based on the assumption that the problem to be controled has solutions and is well posed when the control parameter describes a whole set (say a closed convex set) of some functional linear space. Concerning moving domains in classical heat or wave equations with usual boundary conditions, when the boundary speed is the control parameter, the existence of solution is questionable. For example with homogeneous Neumann boundary conditions the existence for the wave equation is an open problem when the variation of the boundary is not monotonic. We derive new results in which the control forces the solution to exist.
The ongoing collaboration with the CRM in Montreal (mainly with Professor Michel Delfour) led to several extensions to the theory contained in the book . The emphasis is put on two main aspects: in order to avoidany relaxation approach but to deal with real shape analysis we extend existence results by the introduction of several new families of domains based on fine analysis. Mainly uniform cuspcondition, fatconditions and uniform non differentiabilityof the oriented distance function are studied. Several new compactness results are derived. Also the fine study of Sobolev domainsleads to several properties concerning boundaries convergences and boundaries integral convergence under some weak global curvature boundness.
The use of the transverse vector field governed by the Lie bracket enables us to derive the “first variation” of a free boundary. This result has led to the publication of a book.
An alternate approach to fluidstructure has been developed with P.U.L.V. (J. Cagnol) and the University of Virginia (I. Lasiecka and R. Triggiani, Charlottesville) on stabilization issues for coupled acousticshell modeling. .
It is well known that in 3D scattering, the geometrical singularities play a special role. The shape gradient in the case of such a singularity lying on a curve in 3D space has been derived mathematically and implemented numerically in the 3D code of France Télécom.
This work with P. Dubois is potentially applicable to more general singularities.
The
inverse scatteringproblem in electromagnetics is studied through the identification or "reconstruction" of the obstacle considered as a
smooth surfacein
R^{3}. Through measurement of the scattered electric field
E_{d}in a zone
we consider the classical minimization of a functional
measuring the distance beetwen
E_{d}and the actual solution
Eover
. Then, we introduce the continuous flow mapping
T_{r}, where r is the disturbance parameter which moves the domain
in
_{r}. We derive the expression for the shape derivative of the functional, using a
minmaxformulation.
Using the Rumsey integral formulation, we solve the Maxwell equation and we compute the shape gradient, verified by finite difference, using the SR3D software (courtesy of the France Telecom company).
Additionally, we have introduced the Level Set representation method in 3 dimensions. This technique, which comes from the image processing community, allows us to construct an optimization method based on the shape gradient knowledge. In this method, the 3D surface, defined by a homogenous triangulation, evolves to reduce the cost functional, easily encompassing certain topological changes. Using this technique, we have studied the inverse problem and evaluated sensibilities w.r.t. quantitative and qualitative criteria.
The former results by J.P. Zolésio and C. Trucchi have been extended to more general boundary conditions in order to derive shape stabilization via the energy “cubic shape derivative”. Further extension to elastic shell intrinsic modeling is foreseen.
We have developed a numerical code for the simulation of the damping of the wave equation in a moving domain. The cubic shape derivativehas been numerically verified through a new approximation taking care of the non autonomeous oprator in the order reduction technique.
The ongoing collaboration on the stability of wave morphing analysis for drones led to new modeling and sensitivity analyses . Any eigenmode analysis is out of the scope for moving
domains as we are faced with time depending operators. Then, we develop a new stability approach directely based ont a "Liapounov decay" by active shape control of the wave morphing. This
active control implies a backward adjoint variable and working on the linearized state ( through the
transverse vector filed
Zwhich is driven by the Lie brackets) we present a Ricattilike synthesis for the real time of the morphing.
We are developing a new approach for modeling array antennas optimization. This method integrates a Pareto optimization principle in order to account for the array and side lobes but also the antenna behavior. The shape gradient is used in order to derive optimal positions of the macro elements of the array antenna.
Since a 1981 NATO study from the University of Iowa, we know how to define the speed vector field whose flow mapping is used to build the level set of a timedependent smooth function
F(t,x) in any dimension. We consider the Galerkin approach when F(t,.) belongs to a finite dimensional linear space of smooth functions over the fixed domain D. Choosing an appropriate
basis (eigenfunctions, special polynomials, wavelets, ...), we obtain F(t,.) as a finite expansion over the basis with timedependent coefficients. The HamiltonJacobi equation for the
shape gradient descent method applied to an arbitrary shape functional (possessing a shape gradient) yields a non linear ordinary differential equation in time for these coefficients, which
are solved by the RungeKutta method of order four. This Galerkin approximation turns to be powerful for modeling the
topological changesduring the domains evolution. Jérome Picard has developed a code which is used by L.Blanchard (in the OpRaTel collaboration). Also they have together developed a
code for an optimal partionning procedure which is working on the same Galerkin principle but avoiding the use of calculus which would have been developed by the brut force technique.
Indeed, if the optimal partionning of a domain (e.g. an antenna) consisted in finding a decomposition by 100 subdomains, the level set approach would lead to 100 Hamilton Jacobi equations.
We introduced the concept of "multisaddle" potential function
F(
t,
x)and through the Galerkin technique we follow the evolution of the saddle points. This technique has been succesfully understood thanks to the various testing
developed by J. Picard and will be exploited in OpRaTel collaboration by L. Blanchard and F. Neyme (Thales TAD). The work of Jérome Picard has been very interactive and very important to
understand this multisaddle procedure which turns out to be very delicate in the parameters tuning. We developed a mathematical analysis to justify that trialserror method and some
existence results have been proved for the crossing of the singularity associated with the toplogical change in the Galerkin approximation (here the finite dimensional character is
fundamental).
We characterize the geodesic for the Courant metric on Shapes. The Courant Metric is described in the book . It furnishes an intrinsic metric for large evolutions. We use the extended weak flow approach in the Euler setting.
It is extended to larger class of sets and using the transverse flow mapping(see the book) we derive evolution equationwhich caracterises the Geodesic for that differentiable metric.
Applications are being developed for Radar image analysis as well as for various non cylindrical evolution problems including real time control for array antennas.
Based on the previous work on Virtual Computing Environments with CNES (20042006), the OPALE project/team is working on Virtual Collaborative Platforms which are specifically adapted to Multiphysics Collaborative projects. This is in particular studied in the framework of the European AEROCHINA2 support action. The approach considers not only code coupling for multiphysics applications in aeronautics, but includes also interactions between participant teams, knowledge sharing through numerical databases and communication tools using Wikies. The design of a proof of concept demonstrator is planned in the AEROCHINA2 project, started in October 2007. Indeed, large scale multiphysics problems are expected to be orders of magnitude larger than existing single discipline applications, like weather forcast which involve ocean and atmosphere circulation, environmental disaster prevention and emergency management. Their complexity requires new computing technologies for the management of multiscale and multiphysics problems, large amounts of data and heterogenous codes. Among these technologies are wide area networks and distributed computing, using cluster and gridbased environments. It is clear that supercomputers, PCclusters and, to a limited extent wide area grids, are currently used for demanding escience applications, e.g., nuclear and flight dynamics simulation. It is not so clear however what approaches are currently the best for developing multiphysics applications. We advocate the use of an appropriate software layer called upperware, which, combined with cluster and gridbased techniques, can support virtualization of multidiscipline applications when running multidisciplinary codes and business software, e.g., decision support tools. This paves the way for "Virtual Collaborative Platforms" , , . Unlike Wikis and other collaborative tools widely accepted for document editing, virtual collaborative platforms are used to deploy distributed and parallel multiphysics simulation tools. Their execution may be controlled and monitored by distributed workflow systems that may be hierarchically composed. Work in progress is done on this subject, particularly on workflow management system with faulttolerance, interaction and exception handling mechanisms, in partnership with other participants to European projects, e.g., AEROCHINA.
France Télécom (La Turbie); two contracts:
Optimization of antennas, which has partially supported L. Blanchard's thesis;
Shape Optimization Codes Platform by Hierarchical Methods, which partially supports B. Chaigne's thesis.
Thalès (Bagneux) : optimization of the most dangerous trajectories in radar applications.
This year, a new partnership with industry was launched with the R & D Automotive Applications Centreof Arcelor Mittal in Montataire, France. This partnership is related to the optimization of steel (automobile) elements with respect to mechanical criteria (crash, fatigue). The project team was solicited to audit the GEAR2 optimization team in Montataire . Additionally, a student interm from Arcelor, J.G. Moineau, was hosted and directed at INRIA for a fourmonths period.
Opale participates in the RNTL
To establish the status of multilevel strategies in shape optimization;
To develop efficient techniques for hierarchical model coupling for optimumshape design in Aerodynamics.
This contract provides the grant supporting the postdoctoral studies of P. Chandrashekarappa and J. Zhao.
The collaboration with France Télécom and Thalès Défense led to the creation of the elab Opratelin which we develop models for array antennas for telecommunication purposes. Our activity is divided in two main themes:
development of models of array antennas for telecommunication purposes; a patent will shortly be deposited;
frequency allocation, a difficult modeling topic of major importance for our industrial partners.
More specifically, the classical problem of frequency allocation is a main activity. This problem results in a very acute technological challenge today due to the numerous systems operating concurrently (interference of radar, surveillance systems, telephone, radio, television, domestic electronics, electromagnetic noise of WIFI, etc.). Since the channels are limited, special techniques are envisaged to support these systems (orthogonal waves, coding, dynamic occupation of the spectrum).
Opale ProjectTeam and the Department of Mathematical Information Technology (MIT) at University of Jyväskylä (Finland) have initiated a collaboration in the framework of INRIA Associated Teams program on the topic “Shape Optimization with Uncertainties and Multicriterion Optimization in Concurrent Engineering”. More precisely, the aim is to develop and experiment methodologies for largescale computations and shape optimization in challenging engineering problems relying on advanced numerical simulation tools, such as compressible CFD (Computational Fluid Dynamics), CEM (Computational Electromagnetics), computational material sciences. More precisely, the objective is to make progress in:
Numerical methods for twodiscipline shape optimization. Establish a better understanding of the relationship between the Pareto equilibrium front and designs originating from Nash games. Treat specific challenging engineering cases involving joint expertise.
Numerical methods for optimization subject to uncertainties. Assessment of stateoftheart methods for uncertainty estimation: metamodelbased MonteCarlo methods, approaches using sensitivity analysis (derivatives evaluated via Automatic Differentiation), etc. Develop new optimization algorithms accounting for these uncertainty estimates as criteria or constraint. Compare numerical strategies on a variety of engineering problems potentially at hand jointly.
The OPALE project is a member of the FP7 AEROCHINA2 coordination and support action (20072009) on multidiscipline design, simulation and optimization for the aeronautics sector. OPALE is responsible for the Largescale simulation Working Group 06 and COllaborative Platforms Work Package 07 in this project, formed by five Chinese (ACTRI, NUAA, SADRI, NPU and BUAA) and five European members (Airbus, EADS IW, Alenia, CIMNE, INRIA). Current investigations for the setup of a proposal answering to the Call 2009 in the Transport and Aeronautics Objective of the FP7 are undertaken concerning Multidiscipline Optimization calling for High performance computing services.
Opale and Tropics ProjectTeams participate to the European project NODESIM (NOn DEterministic SIMulation), whose topic is the study of the influence of uncertainty on simulation in aeronautics. Tropics ProjectTeam is in charge of computing first and second order derivatives of the flow characteristics with respect to uncertain parameters, whereas Opale ProjectTeam uses these computations to carry out robust design optimization exercises.
Opale and Galaad ProjectTeams participate to the European project EXCITING (EXaCtgeometry sImulTIoN for optimized desiGn of vehicules and vessels). The objective is to develop simulation and design methods and software based on the isogeometric concepts, that unify ComputerAided Design (CAD) and FiniteElements (FE) representation bases. Applications concern hull shape, turbine and car structure design.
A. Habbal is the French responsible for the Integrated Action Project FranceMorocco ANOPIC: new applications in optimization, inverse problems and control, granted from 2005 to 2008 (7650 euros in 2005). The project is gathering several teams from France (INRIA/ Opale, University of Nice, “École des Ponts et Chaussées” and technical University of Compiègne) and Morroco (Engineering School Mohammedia and “ École des Mines”, University Mohammed V in Rabat, and University Chouaib Doukkali in Settat). The research topic is the mathematical and numerical study of parametric, geometry or topology optimization problems.
This project has supported the organization of the workshop “New Applications, Shape Optimization, and Inverse Problems, PDEs and Applications”, Rabat, Morocco, November 7, 2007, during which J.A. Désidéri delivered an invited opening lecture.
The members of the Opaleproject participate in the Educational effort within different areas at the University of Nice SophiaAntipolis.
A. Habbal teaches the following courses:
Introduction to game theory and its application to economy (Master 1, 47hrs)
A. Habbal teaches the following courses (“Information Systems”):
Numerical Engineering methods (first year, 75 hrs)
Programming mathematics (first year, 16 hrs)
Shape optimization (15hrs)
Numerical Methods in Finance (third year, 18 hrs)
Introduction to biomathematics ( 2nd year, 14hrs)
J.A. Désidéri, R. Duvigneau and A. Habbal teach the following course (“Applied Mathematics and Modelling”):
Shape optimization (third year, 45hrs)
R. Duvigneau teaches the following courses (“Applied Mathematics and Modelling”):
Project on Partial Differential Equations (first year, 20 hrs)
B. Chaigne teaches the following courses (“Applied Mathematics and Modelling”):
Numerical Engineering methods (first year, 24 hrs)
A. Habbal delivered a shortcourse: "Introduction to game theory" Postgraduate level at Ecole Mohammedia of Engineers, Rabat, Morocco, during a one month stay in the framework of IMAGEEN European Window Cooperation Program, may 2008.
The following trainees have been, or are being supervised by the project:
University of Cotonou; topic: Finitevolume methods for the shallowwater equations with application to the simulation of the flow in the ducts system of the city of Cotonou, Benin.
University of Compiègne; topic: shape optimization of axisymetric reflectors in electromagnetism.
“École Mohammedia” Engineering School of Rabat, Marroco; topic: Nash games in topological optimization.
University of Nice SophiaAntipolis; topic: Mathematical modeling of cellular migration.
J.A. Désidéri has been appointed by the department of aerodynamics and aeronautics simulation (DSNA) of ONERA Châtillon. This appointment includes a monthly visit at ONERA.
R. Duvigneau is member of the CFD (Computational Fluid Dynamics) committee of ECCOMAS (European Community for Computational Methods in Applied Science).
A. Habbal is member of the specialists board for sections 252627 in IUFM of Nice SophiaAntipolis.
A. Habbal is member of the executive board of “Ecole Polytech Nice”.
T. Nguyen is member of the Advisory Board of the FrenchFinnish Association for Scientific Research.
T. Nguyen was member of the Scientific and Technical Committee of the Workshop NUAAEurope held at the Nanjing University of Aeronautics and Astronautics de Nanjing (PR China), 2224 october 2007.
J.P. Zolésio is chairman of Working Group IFIP 7.2 System Modelling and Optimization.
“Hierarchical Optimization: MultiLevel Algorithms, MultiDisciplinary Optimization, Robust Design and Software Environments”, 8th World Congress on Computational Mechanics WCCM8, 5th European Congress on Computational Methods in Applied Sciences and Engineering ECCOMAS 2008, Venice, Italy, 30 June4 July 2008; Special Technological Session: MDO Tools for High Quality Design in Aeronautics (J.A. Désidéri);
“Partage de territoire en optimisation concourante”, ONERADSNA, Châtillon sous Bâgneux, France, January 2008 (J.A. Désidéri);
“Shape Optimization in Aerodynamics”, Univerity of AbomeyCalavi (Benin), March 2008 (J.A. Désidéri);
“ShapeMorphing Metric by Variational Formulation for Incompressible Euler Flow”, International Workshop on Advances in Shape and Topology Optimization, Graz, Austria, October 2008 (J.P. Zolésio);
“Control Formulation for incompressible Euler Flow in 3D”, 50 Years of Optimal Control, Banach Institute Conference, Bedlewo, Polland, September 2008 (J.P. Zolésio).