Ulrich Razafison

Reliable Fast Frequency Sweep for Microwave Devices via the Reduced-Basis Method

In this paper, a reduced-basis-approximation-based model-order reduction for fast and reliable frequency sweep in the time-harmonic Maxwells equations is detailed. Contrary to what one may expect by observing the frequency response of different microwave circuits, the electromagnetic field within these devices does not drastically vary as frequency changes in a band of interest. Thus, instead of using computationally inefficient, large dimension, numerical approximations such as finite- or boundary-element methods for each frequency in the band, the point in here is to approximate the dynamics of the electromagnetic field itself as frequency changes. A much lower dimension, reduced-basis approximation sorts this problem out. Not only rapid frequency evaluation of the reduced-order model is carried out within this approach, but also special emphasis is placed on a fast determination of the error measure for each frequency in the band of interest. This certifies the accurate response of the reduced-order model. The same scheme allows us, in an offline stage, to adaptively select the basis functions in the reduced-basis approximation and automatically select the model-order reduction process whenever a preestablished accuracy is required throughout the band of interest. Finally, real-life applications will illustrate the capabilities of this approach.

Riemann problems with non--local point constraints and capacity drop.

In the present note we discuss in details the Riemann problem for a one-dimensional hyperbolic conservation law subject to a point constraint. We investigate how the regularity of the constraint operator impacts the well--posedness of the problem, namely in the case, relevant for numerical applications, of a discretized exit capacity. We devote particular attention to the case in which the constraint is given by a non--local operator depending on the solution itself. We provide several explicit examples. We also give the detailed proof of some results announced in the paper [Andreianov, Donadello, Rosini, Crowd dynamics and conservation laws with nonlocal constraints and capacity drop], which is devoted to existence and stability for a more general class of Cauchy problems subject to Lipschitz continuous non--local point constraints.

A reduced basis method applied to the Restricted Hartree–Fock equations

In this Note, we describe a reduced basis approximation method for the computation of some electronic structure in quantum chemistry, based on the Restricted Hartree-Fock equations. Numerical results are presented to show that this approach allows for reducing the complexity and potentially the computational costs.

ON THE OSEEN PROBLEM IN THREE-DIMENSIONAL EXTERIOR DOMAINS

In this paper, we prove existence and uniqueness results for the Oseen problem in exterior domains of ℝ3. To prescribe the growth or decay of functions at infinity, we set the problem in weighted Sobolev spaces. The analysis relies on a Lp-theory for any real p such that 1 < p < ∞.

Asymptotic behavior and numerical simulations for an infection load-structured epidemiological model; Application to the transmission of prion pathologies

This article studies an infection load-structured SI model with exponential growth of the infection, that incorporates a potential external source of contamination. We perform the analysis of the time asymptotic behavior of the solution by exhibiting epidemiological thresholds, such as the basic reproduction number, that ensure extinction or persistence of the disease in the contagion process. Moreover, a numerical scheme adapted to the model is developed and analyzed. This scheme is then used to illustrate the model with numerical simulations, applying this last to the transmission of prion pathologies.

Weighted estimates for the Oseen problem in R 3

Abstract In this Note, we present some existence results of the Oseen equations set in R 3 proved in a previous work. In order to control the behavior at infinity of functions, we use as functional framework weighted Sobolev spaces. The asymptotic of some solutions is then studied.

Identifiability problem for recovering the mortality rate in an age-structured population dynamics model

In this article is studied the identifiability of the age-dependent mortality rate of the Von Foerster–Mc Kendrick model, from the observation of a given age group of the population. In the case where there is no renewal for the population, translated by an additional homogeneous boundary condition to the Von Foerster equation, we give a necessary and sufficient condition on the initial density that ensures the mortality rate identifiability. In the inhomogeneous case, modelled by a non-local boundary condition, we make explicit a sufficient condition for the identifiability property, and give a condition for which the identifiability problem is ill-posed. We illustrate this latter case with numerical simulations.

Isotropically and Anisotropically Weighted Sobolev Spaces for the Oseen Equation

This contribution is devoted to the Oseen equations, a linearized form of the Navier-Stokes equations. We give here some results concerning the scalar Oseen operator and we prove Hardy inequalities concerning functions in Sobolev spaces with anisotropic weights that appear in the investigation of the Oseen equations.

Numerical Scheme for a Viscous Shallow Water System Including New Friction Laws of Second Order: Validation and Application

In this work, we are interested in the derivation of a new shallow water model with a diffusion source term. Analytical solutions for steady flow regimes are first presented to validate a numerical method designed to solve this new model. Then this model is applied on real data and seems to give better results than the classical shallow water system.