La toile de BD

Bruno Despres, email

Professor at the Jacques-Louis Lions Laboratory (and IUF 2016)

Address: Tower 15-25, third floor, office 17 University PARIS 6, UPMC 4 place Jussieu, Paris IV, 75015, Paris

Googlometry, 2020 Google scholar extraction. And CV.

Recent book with colleagues on "Transport et Diffusion". Recent book on "Neural Networks and Numerical Analysis".

Principal fields of interest: they come from the mathematical analysis and numerical solution of Partial Differential Equations.

Applications come from the mathematical physics (wave equations, compressible fluids) for various problems.
Specific applications in Plasma Physics (ICF-Inertial Confinement Fusion and MCF-Magnetic Confinement Fusion) are considered.

colloquim talk on Scattering theory (Lax, Kato, ...) interpretation of linearized Landau damping: recently given at IAMP

Notes for a Master 2 course on plasmas here

Long term interests in the construction of new numerical algorithms started in my PhD thesis.
It materialized recently in 2 directions

new approach to polynomials with sign: Recent Results In Positivity Preserving Polynomials here

Machine Learning and Scientific Computing: Machine Learning design of Volume of Fluid schemes for compressible flows, with H. Jourdren, HAL 2020, JCP 2020

colloquim talk on ML: recently given at LJLL/SU

Play with both polynomials and Machine Learning: A functional equation with polynomial solutions and application to Neural Networks, with Matthieu Ancellin HAL 2020

ANR MUFFIN 2019/2023 here : ITER oriented project
ANR CHROME 2012/2016 completed : ITER oriented project

Groupe de travail

Stability and boundary interactions for fusion plasmas

Recent 2019/2020 papers or preprints

Polynomials (positive, with Machine Learning, ...)

A projection algorithm on the set of polynomials with two bounds, with M. Campos-Pinto, F. Charles, Herda Numer. Algo. 2020
Iterative Calculation of Sum Of Squares, with Maxime Herda HAL 2018, accepted in SIAM J. Numerical Analysis 2020
A functional equation with polynomial solutions and application to Neural Networks, with Matthieu Ancellin HAL 2020

Machine Learning design of Volume of Fluid schemes for compressible flows, with H. Jourdren, HAL 2020, published in JCP

A convergent deep learning algorithm for approximation of polynomials, HAL 2022

Numerical methods/scientific computing

Implicit discretization of Lagrangian gas dynamics, with A. Plessier and S. del Pino, HAL 2021
Quadratic stability of flux limiters HAL 2021
Approximation with vectorial exponential functions of solutions of the P N model for the transport of particles with G. Morel and C. Buet, HAL 2021
Trefftz Discontinuous Galerkin basis functions for a class of Friedrichs systems coming from linear transport, with G. Morel and C. Buet, to appear in ACOMP
Sensitivity equation method for the Navier-Stokes equations applied to uncertainty propagation, with C. Fiorina and A. Puscas HAL 2020

Mathematical modeling in applied physics, with emphasis on plasma and fusion plasma

Trace class properties of the non homogeneous linear Vlasov-Poisson equation in dimension 1+1, to appear in J. Spectral theory, 2021
The Vlasov-Ampere system and the Bernstein-Landau paradox, with F. Charles, A. Rege and R. Weder, Hal 2020 , Arxiv 2020
Corners and stable optimized domain decomposition methods for the Helmholtz problem, with Anouk Nicolopoulos and Bertrand Thierry, HAL 2020
A variational sheath model for gyrokinetic Vlasov-Poisson equations, with Mehdi Badsi, Martin Campos-Pinto and Ludov Godard-Cadillac, HAL 2021
On Domain Decomposition Methods with optimized transmission conditions and cross-points, with Anouk Nicolopoulos and Bertrand Thierry, HAL 2021

M2, cours de base B004
le site du cours ici , le poly ici , et aussi le le poly étendu.
Texte TP1 (15/09/2022): ici . Avec quelques modifications (Despres) ici . Une correction Notebok (Dupuy) ici .
Texte TP2 (29/09/2022): ici .
Texte TP2 (13/10/2022): ici .