This paper is the first contribution towards the rigorous justification of asymptotic 1D models for the time-domain simulation of the propagation of electromagnetic waves in coaxial cables. Our general objective is to derive error estimates between the “exact” solution of the full 3D model and the “approximate” solution of the 1D model known as the Telegraphist’s equation.

The present work aims at proposing a rigorous analysis of the mathematical and numerical modelling of ultrasonic piezoelectric sensors. This includes the well-posedness of the final model, the rigorous justification of the underlying approximation and the design and analysis of numerical methods. More precisely, we first justify mathematically the classical quasi-static approximation that reduces the electric unknowns to a scalar electric potential. We next justify the reduction of the computation of this electric potential to the piezoelectric domains only. Particular attention is devoted to the different boundary conditions used to model the emission and reception regimes of the sensor. Finally, an energy preserving finite element/finite difference numerical scheme is developed; its stability is analyzed and numerical results are presented.

In this paper we study a low frequency model for acoustic propagation in a 2D flow duct. For some Mach profile flow, we are able to give a well-posedness theorem. Its proof relies on a quasi-explicit expression of the solution which provides us an efficient numerical method. We give and comment numerical results for particular linear, tangent and quadratic profiles. Finally, we give a numerical validation of our asymptotic model.

We are concerned with a 2D time harmonic wave propagation problem in a medium including a thin slot whose thickness ε is small with respect to the wavelength. In a previous article, we derived formally an asymptotic expansion of the solution with respect to ε using the method of matched asymptotic expansions. We also proved the existence and uniqueness of the terms of the asymptotics. In this paper, we complete the mathematical justification of our work by deriving optimal error estimates between the exact solutions and truncated expansions at any order.

In this article, we derive a complete mathematical analysis of a coupled 1D-2D model for 2D wave propagation in media including thin slots. Our error estimates are illustrated by numerical results.

Météo-France is preparing the implementation of a revised graphical summary of the synoptic situation. This graphical product has been developed since 1993 as, as far as possible, an extension of the existing framework published by WMO. Graphics remain the best way to convey rapidly a lot of information. However, the existing graphical language for meteorology has seldom changed over the years, while our dynamical understanding has improved. Its current use is in fact poorer than the one allowed by the WMO reference definition. In an attempt to overcome these drawbacks, a richer graphical language is proposed. Its goal is to show and, often, to explain areas of synoptic weather activity in the initial spirit of the Norwegian method, since it has been so successful in shaping modern operational meteorology. However, it takes into account the present understanding of cyclogenesis and large-scale dynamics: the actual and potential baroclinic interactions replace the polar front concept. Dynamical meteorology also provides rather precise guidance for structuring and preparing the summary. The proposed code is described and explained. Examples are shown, with most cases taken from the recent FASTEX (Fronts and Atlantic Storm-Track Experiment) project.

In this work, we investigate the Perfectly Matched Layers (PML) introduced by Bérenger [3] for designing efficient numerical absorbing layers in electromagnetism. We make a mathematical analysis of this model, first via a modal analysis with standard Fourier techniques, then via energy techniques. We obtain uniform in time stability results (that make precise some results known in the literature) and state some energy decay results that illustrate the absorbing properties of the model. This last technique allows us to prove the stability of the Yee's scheme for discretizing PML's.

In this paper we are interested in the numerical modeling of absorbing ferromagnetic materials obeying the non-linear Landau-Lifchitz-Gilbert law with respect to the propagation and scattering of electromagnetic waves. In this work we consider the 1D problem. We first show that the corresponding Cauchy problem has a unique global solution. We then derive a numerical scheme based on an appropriate modification of Yee's scheme, that we show to preserve some important properties of the continuous model such as the conservation of the norm of the magnetization and the decay of the electromagnetic energy. Stability is proved under a suitable CFL condition. Some numerical results for the 1D model are presented.