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Leçons J.-L. Lions 2018 - 22 11 2018 11h00 - Mini-cours 2 : A. Buffa
Annalisa Buffa (Ecole Polytechnique Fédérale de Lausanne)
Leçons Jacques-Louis Lions 2018 - Mini-cours 2
The interplay of geometric modelling and numerical analysis of PDEs
Le mini-cours 2 (jeudi 22 novembre 2018 de 11h00 à 12h30) aura lieu
salle du séminaire du Laboratoire Jacques-Louis Lions,
barre 15-16, 3ème étage, salle 09 (15-16-309),
Sorbonne Université, Campus Jussieu, 4 place Jussieu, Paris 5ème
Résumé du mini-cours
The interplay of geometric modelling and numerical analysis of PDEs
Over the last fifty years, computer simulations have dramatically increased their impact on research, design and production, and are now an indispensable tool for development and innovation in science and technology. Partial Differential Equations (PDEs) offer a broad and flexible framework for modelling and analysing a number of phenomena arising in fields as diverse as physics, engineering, biology, and medicine. Not surprisingly, research on methods to simulate PDEs have a central role in modern science.
In reality, the simulation of PDEs is a brick within a workflow where, at the beginning, the geometrical entities are created, described and manipulated with a geometry processor, often through Computer-Aided Design systems (CAD), and then used as input in Computer-Aided Engineering systems (CAE) where they are handled and processed for the simulation. The representation of geometric entities has its roots in geometric modelling, and often the requirements of shape design are different from those of simulation, which is based on numerical methods for PDEs. The simulation of PDEs on CAD geometries (which are mainly represented through their boundaries) calls then for (re-)meshing and re-interpolation techniques that are computationally expensive and result in non-exact geometries as well as inaccurate solutions.
In this course, I will give an introduction to the recent scientific efforts devoted to tackle this bottleneck both from the perspective of geometric modelling and of the numerical analysis of PDEs. From volumetric modelling to the framework of isogeometric analysis, within a mathematical perspective, I will provide an overview of the state of the art and of the many questions that are still open.