In this paper, a reduced basis approximation-based model order reduction for fast and reliable frequency sweep in the time-harmonic Maxwell's 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 element 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.

In this paper we investigate numerically the model for pedestrian traffic proposed in [B. Andreianov, C. Donadello, M.D. Rosini, Crowd dynamics and conservation laws with nonlocal constraints and capacity drop, Mathematical Models and Methods in Applied Sciences 24 (13) (2014) 2685-2722] . We prove the convergence of a scheme based on a constraint finite volume method and validate it with an explicit solution obtained in the above reference. We then perform ad hoc simulations to qualitatively validate the model under consideration by proving its ability to reproduce typical phenomena at the bottlenecks, such as Faster Is Slower effect and the Braess' paradox.

In this paper, we prove existence and uniqueness results for the Oseen problem in exterior domains of R 3 . To prescribe the growth or decay of functions at infinity, we set the problem in weighted Sobolev spaces.

This paper is devoted to a scalar model of the Oseen equations, a linearized form of the Navier-Stokes equations. To control the behavior of functions at infinity, the problem is set in weighted Sobolev spaces including anisotropic weights. In a first step, some weighted Poincaré-type inequalities are obtained. In a second step, we establish existence, uniqueness and regularity results. (2000). 76D05, 35Q30, 26D15, 46D35. Mathematics Subject Classification

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.

We introduce and analyze a class of models with nonlocal point constraints for traffic flow through bottlenecks, such as exit doors in the context of pedestrians traffic and toll gates in vehicular traffic. Constraints are defined based on data collected from non-local in space and/or in time observations of the flow. We propose a theoretical analysis and discretization framework that permits to include different data acquisition strategies; a numerical comparison is provided. Nonlocal constraint allows to model, e.g., the irrational behavior ("panic") near the exit observed in dense crowds and the capacity drop at tollbooth in vehicular traffic. Existence and uniqueness of solutions are shown under suitable and "easy to check" assumptions on the constraint operator. A numerical scheme for the problem, based on finite volume methods, is designed, its convergence is proved and its validation is done with an explicit solution. Numerical examples show that nonlocally constrained models are able to reproduce important features in traffic flow such as self-organization.

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To cite this version:Antoine Perasso, Ulrich Razafison. Asymptotic behavior and numerical simulations for an infection load-structured epidemiological model; Application to the transmission of prion pathologies. SIAM Journal on Applied Mathematics, Society for Industrial and Applied Mathematics, 2014, 74 (5) The goal of such epidemiological models is to describe the propagation of an infectious disease in a population, by incorporating in the model a susceptible class S linked to an infective class I and potentially a recovered class R. Various SIR epidemics models are described either by ordinary differential equations (ODEs) or by partial differential equations (PDEs), these latter models being structured according to other variables than the time (age, space... This article is devoted to the analysis of asymptotic properties and to the analysis of a numerical scheme for an infection load-structured epidemiological SI model that describes an infection process with an exponential growth of a fatal-issued disease. As illustrated at the end of the article, such a structuration allows to model the transmission of prion pathologies (BSE, scrapie...).Denoting by i the infection load in the infective class, it is supposed that, identically to size-structured models (see Arino [4], Cushing [11], Webb [48] and references therein), the following evolution equation is satisfied with respect to time t ≥ 0,