The CEA–EDF–Inria summer schools are intended for researchers, engineers, and PhD students. They allow them to review the state-of-the-art of the proposed subjects and to confront their experience with recent developments. The lectures are dispensed in English. They are complemented by computer tutorials under supervision of assistants.
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
Scientific 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)
Program
Practical information:
Date
June 26 – June 30, 2023
Place
EDF Lab
Paris-Saclay
Boulevard Gaspard Monge
91120 Palaiseau
Registration
first introductions to quantum computation and we will discuss notions such as error correction, the latest advances in quantum algorithms as well as the representation formalism of quantum circuits. In particular :
- A general introduction to quantum computing
- Advances in optimization and combinatorial search
- An overview of the technologies
- Quantum formal methods
- The ZX Calculus
- Quantum walks and their use in the numerical solution of partial differential equations
- Error correction and quantum volume concepts
- Code compilation & languages
- Quantum Learning Theory
- Practiccal works and implementation and use on simple cases
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Scientific context :
If it were to happen in its most promising form, the quantum computer would constitute a major breakthrough for many of the algorithms used within the industry. This concerns algorithms as varied as the resolution of partial differential equations, the simulation of molecules, combinatorial optimization, machine learning or financial mathematics.
The development of quantum algorithms follows drastically different rules and logic than those used in the development of classical algorithms.
Moreover, the maturity of the technology means that questions that a classical algorithmicist has stopped asking are once again relevant in the quantum world. Error correction, circuit representation formalism, data encoding or circuit compilation are all questions that are still open and that need to be adapted to the case under study. In the absence of machines, a deep theoretical work is carried out by the scientific community to address not only these questions, but also questions in quantum algorithms, quantum complexity classes, quantum information theory and quantum formal methods.
Date
July 3 – July 7 , 2023
Registration
Contacts
Summer schools secretary
Régis Vizet – CEA
tel: 01 69 26 47 45
Fax: 01 69 26 70 05