Lors du séminaire du Labex MS2T du vendredi 08 juin 2012, nous avons eu le plaisir d’écouter un exposé de Francisco CHINESTA, Professeur à l’Ecole Centrale de Nantes et responsable du pôle Matériaux et Procédés de fabrication du GeM (Institut de Recherche en Génie Civil et Mécanique, UMR CNRS - Ecole Centrale de Nantes - Université de Nantes).
Francisco CHINESTA est titulaire de la Chaire de la Fondation d’entreprise EADS, dont l’objectif est de mettre en place des projets de recherche en modélisation et simulation numérique avancées des procédés de fabrication des structures composites pour l’industrie aéronautique et spatiale et plus généralement de contribuer à relever les nombreux et grands défis technologiques de ces secteurs.
Résumé de l’exposé :
Today many problems in science and engineering remain intractable, in spite of the impressive progresses attained in mechanical modelling, numerical analysis, discretization techniques and computer science during the last decade, because their numerical complexity is simply unimaginable. We can distinguish different challenging scenarios :
• The first one concerns models that are defined in high dimensional spaces, usually encountered in quantum chemistry and kinetic theory descriptions of complex fluids. Model defined in high dimensional spaces suffer the so-called curse of dimensionality.
• The second problem category involves time-dependent problems not necessarily defined in high-dimensional spaces, but whose spectrum of characteristic times is so wide that standard incremental time discretization techniques cannot be applied.
• Real time simulators are needed in many applications, e.g. surgical simulators. Control, malfunctioning identification and reconfiguration of systems also need to run in real time.
• Problems of the fourth category are defined in degenerate geometrical domains, as plate or shell-like domains. Standard grid-based 3D discretization methods then quickly become impractical, in view of the compulsory discretization of the small length scales that yield extremely fine meshes.
• Many problems in process control, parametric modeling, inverse identification, and process or shape optimization, usually require, when approached with standard techniques, the direct computation of a very large number of solutions for particular values of the problem parameters.
• Traditionally, Simulation-based Engineering Sciences relied on the use of static data inputs to perform the simulations. A new paradigm emerged : Dynamic Data-Driven Application Systems (DDDAS) entails the ability to dynamically incorporate data into an executing application.
• Augmented reality is another area in which efficient (fast and accurate) simulation is urgently needed. The idea is supplying in real time appropriate information to the reality perceived by the user.
• Light computing platforms (tablets or smartphones) are appealing alternatives to heavy computing platforms that in general are expensive and whose use requires technical knowledge.
The main challenge is to address the modeling and simulation of “real” models encountered in science and engineering with all their complexity from the geometrical and constitutive points of view, some of them never until now solved because their computational complexity. These models should be solved very fast, in some cases in real time, by using light computing platforms. Classical simulation techniques fail to fulfill the above requirements. An appealing alternative consist of considering off-line solutions of parametric models, in which all the sources of variability – loads, boundary conditions, material parameters, geometrical parameters, etc. - will be considered as extra-coordinates. Thus, by solving only once the resulting multidimensional model, we have access to the solution of the model for any value of the parameters considered as extra-coordinates. Now, from this general solution computed only once and off-line we could perform on-line real time post-processing, optimization, inverse analysis, analysis of sensibilities, stochastic analysis … by using very light computing platforms as for example smartphones. We could also adapt the model on-line while its simulation is running within the framework of dynamic data-driven application systems – DDDAS. The price to be paid is the solution of parametric models defined in high dimensional spaces that could involve hundreds of coordinates. The use of the Proper Generalized Decomposition that we recently proposed and we are intensively developing, allows such solution, because thanks to the separated representation of the unknown fields the computational complexity scales linearly with the dimensionality, instead of growing exponentially which is characteristic of mesh-based discretization techniques. This off-line-on-line Proper Generalized Decomposition Based Dynamic Data-Driven Application Systems could constitute a new paradigm in computational sciences and engineering.