VALENTIN , Frédéric

This work proposes a novel multiscale finite element method for acoustic wave propagation in highly heterogeneous media which is accurate on coarse meshes. It originates from the primal hybridization of the Helmholtz equation at the continuous level, which relaxes the continuity of the unknown on the skeleton of a partition. As a result,...

The flux variable determines the approximation quality of hybridizationbased numerical methods. This work proves that approximating flux variables in discontinuous polynomial spaces from the L2 orthogonal projection is super-convergent on meshes that are not aligned with jumping coefficient interfaces. The results assume only the local...

The wave propagation phenomena in heterogeneous media is an actual challenging problem to numerical simulation. In today's scenario of increasing computing power and advent of exascale computing, machines provide good environments to obtain solutions to tough problems. However, it is necessary to construct good algorithms that can enjoy this...

In this work, we address time dependent wave propagation problems with strong multiscale features (in space and time). Our goal is to design a family of innovative high performance numerical methods suitable to the simulation of such multiscale problems. Particularly, we extend the Multiscale Hybrid-Mixed finite element method (MHM for short)...

International audience

In this work, we are interested in the propagation of electromagnetic waves in complex media. Moreprecisely, we would like to study time dependent wave propagation problems with strong multiscalesfeatures (possibly in space and time). In this context we would like to contribute in the design ofinnovative numerical methods particularly...

We establish the equivalence between the Multiscale Hybrid-Mixed (MHM) and the Multiscale Hybrid High-Order (MsHHO) methods for a variable diffusion problem with piecewise polynomial source term. Under the idealized assumption that the local problems defining the multiscale basis functions are exactly solved, we prove that the equivalence holds...

International audience

International audience

This work proposes a Multiscale Hybrid-Mixed (MHM) method for the Maxwell equation in time domain. The MHM method is a consequence of a hybridization procedure, and emerges as a method that naturally incorporates multiple scales while provides solutions with high-order precision. The computation of local problems is embedded in the upscaling...

This work proposes a Multiscale Hybrid-Mixed (MHM) method for the Maxwell equation in time domain. The MHM method is a consequence of a hybridization procedure, and emerges as a method that naturally incorporates multiple scales while provides solutions with high-order precision. The computation of local problems is embedded in the upscaling...

The Physics-Informed Neural Network (PINN) corresponds to a machinelearning strategy to approximate the solution of partialdifferential equations by in- cluding the residual PDE in the lossfunction. In a previous work, we found that adding physicalcoefficients as predictor variables in a PINN for boundary layerlinear...