2023 summer school on numerical analysis
Robust polyhedral discretizations for computational mechanics
Contents
Robust polyhedral discretizations for computational mechanics
The aim of this summer school is to present a set of new numerical methods (finite elements and finite volumes) recently developed in the academic world for the resolution of partial differential equations. The first results of these methods on industrial problems are promising.
- Presentation of different methods
- Numerical analysis and connection between them
- Industrial presentations
- Practical sessions
Scientifical context
It is necessary, currently and in the future, to have more and more realistic simulations in the industrial field. It is therefore essential to have accurate and robust numerical methods with respect to physical parameters (volumetric-locking for solid mechanics, irrotational forces and viscosity for fluid mechanics for example) and mesh quality. Moreover, as meshes are becoming more and more complex and consequent, it is useful to have methods that support very general meshes (polyhedral, non-conformal, …) in order to facilitate the adaptive mesh refinement and to make the mesh generation step simpler and less time consuming for the engineer.
Thus, many new low-order and high-order numerical methods have been developed in recent years that could meet these needs:
- discontinuous Galerkin (dG)
- hydridizable discontinuous Galerkin (HDG)
- hybrid high-order (HHO)
- virtual element method (VEM)
- gradient schemes (GS)
- compatible discrete operator (CDO)
All of these methods have a rigourous mathematical analysis. Many of them have been extented to non-linear problems (and even to industrial problems).
Practical information
Date
June 26 – June 30, 2023
Place
EDF Lab
Paris-Saclay
Boulevard Gaspard Monge
91120 Palaiseau
Registration
If you wish to join, please fill the registration form 
and send it before June, 2, 2023 to Régis Vizet.
Contacts
Summer schools secretary
Régis Vizet – CEA
tel: 01 69 26 47 45
Fax: 01 69 26 70 05
Coordinators of the numerical analysis 2023 school
Mickaël Abbas (EDF R&D)
Jérôme Bonelle (EDF R&D)
Alexandre Ern (ENPC, INRIA)
Nicolas Pignet (EDF R&D)
Registration fees including coffee break and lunch (pre-tax price)
CEA, EDF, industry: 1200 euros
Academia / university & public research: 600 euros
Ph.D. students (a limited number): 300 euros
Program
| Monday, June 26 | Tuesday, June 27 | Wednesday, June 28 | Thursday, June 29 | Friday, June 30 | |
|---|---|---|---|---|---|
| Discontinuous Galerkin methods | Gradient Scheme methods | Virtual Element Method | Discrete de Rham methods | Industrial employment | |
| 9h00-9h30 | Breakfast coffee | Breakfast coffee | Breakfast coffee | Breakfast coffee | Breakfast coffee |
| 9h30-12h | Lecture Emmanuil Georgoulis (National Technical University of Athens & Heriot-Watt University) hp-Version Discontinuous Galerkin methods on arbitrarily-shaped elements |
Lecture Robert Eymard (Université Gustave Eiffel) The gradient discretization method |
Lecture Marco Verani (Politecnico di Milano) |
Lecture Daniele Di Pietro (Université de Montpellier) |
Examples 9h30 Guillaume Enchery (IFPEN) Use of the virtual-element method in geosciences 10h15 Jérôme Bonelle (EDF R&D) Polyhedral methods in code_saturne 11h Antoine Gerschenfeld (CEA) Numerical schemes for multiphase flows on general meshes 11h45 Discussion, conclusions, and perspectives |
| 12h-14h | Lunch | Lunch | Lunch | Lunch | Lunch |
| 14h-15h30 | Scientific seminars Michele Botti (Politecnico di Milano) Discontinuous Galerkin methods for multiphysics simulation Jérôme Bonelle (EDF R&D) Introduction to Compatble Discrete Operator methods (CDO) |
Scientific seminars Cindy Guichard (Sorbonne Université) Title to come Nicolas Pignet (EDF R&D) Introduction to Hybrid High-Order methods (HHO) |
Scientific seminars Michele Visinoni (Universita di Milano) Some Virtual Element Methods for linear elasticity problems Stefano Berrone (Politecnico di Torino) Title to come |
Scientific seminars Simon Lemaire (INRIA Lille) Hybrid High-Order methods for Electromagnetics Pierre Jolivet (Sorbonne Université) Title to come |
|
| 15h30-16h00 | Coffee break | Coffee break | Coffee break | Coffee break | |
| 16h00h-18h00 | Computer tutorials on CDO | Computer tutorials on HHO | Computer tutorials on VEM | Computer tutorials on HHO |