La toile de BD

Bruno Despres, email

Professor at the Jacques-Louis Lions Laboratory et Institut universitaire de France 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.

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

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
Polynomials with bounds and numerical approximation, Numerical Algorithms 2017 and Erratum (with M. Herda).
Algorithms for positive polynomial approximation, with F. Charles and M. Campos-Pinto, Siam Numer. Anal. 2019
A functional equation with polynomial solutions and application to Neural Networks, with Matthieu Ancellin HAL 2020

Numerical methods/scientific computing

Machine Learning design of Volume of Fluid schemes for compressible flows, with H. Jourdren, HAL 2020, accepted in JCP
TDG method for Friedrichs systems and the P N model in 2D, with G. Morel and C. Buet, HAL 2019
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
High-order staggered schemes for compressible hydrodynamics. Weak consistency and numerical validation, with G. Dakin and S. Jaouen, JCP 2019
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 for fusion

Degenerate elliptic equations for resonant wave problems, with A. Nicolopoulos, P. Ciarlet Jr. and M. Campos-Pinto, accepted in IMA Journal of Applied Mathematics 2019
A Stable Formulation of Resonant Maxwell's Equations in Cold Plasma, with A. Nicolopoulos and M. Campos-Pinto, Journal of Computational and Applied Mathematics 2019
Scattering structure and Landau damping for linearized Vlasov equations with inhomogeneous Boltzmannian states, published in AHP 2019
Trace class properties of the non homogeneous linear Vlasov-Poisson equation in dimension 1+1, accepted in J. Spectral theory, 2019
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

Master M2A: Analyse numerique et Neural Networks
Le poly (incomplet) est au lien ici .
Les transparents du 21/01 ont au lien ici .