Title: Finite element complexes for the Stokes equation. Abstract: We present a new mixed finite element for the Stokes equation. It is conforming and the natural degrees of freedom provide an interpolation operator that commutes with the divergence operator. We also present the framework of finite element systems, which sheds…
Construction of moment models for rarefied gas dynamics In this presentation, we will propose new moment models (BGK/ Fokker Planck) to solve rarefied gas dynamics problems. A formal framework will be proposed to create conservative models with entropy dissipation. It will be shown in particular that the ESBGK model of…
Well-balanced schemes for free surface fluid models We consider here integrated models for free surface flows (extensions of the Saint-Venant system). These models have in common the presence of source terms which result in the existence of non-trivial stationary states, in the sense that the unknowns of the system (flow…
Discussion of some simple examples of approximation spaces and linear or nonlinear, intrusive or non-intrusive reduced models After a very brief introduction to reduced models, the presentation focuses on very simple examples of parametric problems governed by partial differential equations in which the linear representation of the reduced space fails.…
Modeling and simulation of musical instruments: propagation, dissipation and coupling. Musical instruments are complex objects that involve various physical phenomena, coupled together and sometimes non-linear. The instrumental practice exerts a very fine control on these systems in order to obtain a variety of possible responses, all in a musical contexts,…
In this talk I will review some recent results (detailed in [1, 2]) on the stabilisation of linearised incom- pressible invisid flows (or, with a very small viscosity). The partial differential equation is a linearised incompressible equation similar to Euler’s equation, or Oseen’s equation in the vanishing viscosity limit. In…
Computational efficiency is still an open challenge in solving optimization and inverse uncertainty quantification problems in engineering and clinical settings. The techniques adopted for these problems usually rely on iterative or sampling procedures, which require, at each iteration, the numerical approximation of a differential problem describing the underlying physical process.…
Fast computations of Wasserstein gradient flows Abstract: Wasserstein gradient flows describe the evolution of a mass density flowing along a pressure gradient generated by an internal energy functional. This class of PDEs models various physical phenomena such as fluid flow, heat transfer, aggregation-diffusion and crowd motion. In general, these equations…
Titre: Consensus-based sampling Abstract: In the first part of this talk, I will present background material on Bayesian inverse problems, the associated challenges at the numerical level, and gradient-free sampling and optimization approaches for solving them. In the second part, I will present recent work [1] on a novel gradient-free…
Title: Exploiting Mixed Precision Arithmetic in the Solution of Linear Systems Abstract: The emergence of low precision arithmetic on modern hardware, such as the increasingly supported fp16 and bfloat16 floating-point arithmetics, provides new opportunities to accelerate linear algebra computations. A key challenge in doing so is to preserve the accuracy…
