6 papers · 1 filter
Hermite Semi-Lagrangian schemes on triangular meshes for advection equations
Ali Elarif, Michel Mehrenberger, Laurent Navoret
High-order Hermite semi-Lagrangian schemes on unstructured triangular grids are proposed for advection equations, based on Bell and Argyris finite elements. Nodal semi-Lagrangian s…
Neural semi-Lagrangian method for high-dimensional advection-diffusion problems
Emmanuel Franck, Victor Michel-Dansac, Laurent Navoret +1
This work is devoted to the numerical approximation of high-dimensional advection-diffusion equations. It is well-known that classical methods, such as the finite volume method, su…
Reduced Particle in Cell method for the Vlasov-Poisson system using auto-encoder and Hamiltonian neural
Emmanuel Franck, Laurent Navoret, Vincent Vigon +2
Hamiltonian particle-based simulations of plasma dynamics are inherently computationally intensive, primarily due to the large number of particles required to obtain accurate solut…
Hamiltonian reduction using a convolutional auto-encoder coupled to an Hamiltonian neural network
Raphaël Côte, Emmanuel Franck, Laurent Navoret +2
The reduction of Hamiltonian systems aims to build smaller reduced models, valid over a certain range of time and parameters, in order to reduce computing time. By maintaining the…
Fourth-order entropy-stable lattice Boltzmann schemes for hyperbolic systems
Thomas Bellotti, Philippe Helluy, Laurent Navoret
We present a novel framework for the development of fourth-order lattice Boltzmann schemes to tackle multidimensional nonlinear systems of conservation laws. As for other numerical…
Approximately well-balanced Discontinuous Galerkin methods using bases enriched with Physics-Informed Neural Networks
Emmanuel Franck, Victor Michel-Dansac, Laurent Navoret
This work concerns the enrichment of Discontinuous Galerkin (DG) bases, so that the resulting scheme provides a much better approximation of steady solutions to hyperbolic systems…