Localized adaptive radiation condition for coupling boundary with finite element methods applied to wave propagation problems

first published online October 3, 2013 doi:10.1093/imanum/drt038International audienceThe wave propagation problems addressed in this paper involve a relatively large and impenetrable surface on which is posed a comparatively small penetrable heterogeneous material. Typically the numerical solution of such kinds of problems is solved by coupling boundary and finite element methods. However, a straightforward application of this technique gives rise to some difficulties which mainly are related to the solution of a large linear system whose matrix consists of sparse and dense blocks. To face such difficulties, the adaptive radiation condition technique is modified by localizing the truncation interface only around the heterogeneous material. Stability and error estimates are established for the underlying approximation scheme. Some alternative methods are recalled or designed making it possible to compare the numerical efficiency of the proposed approach

Field behavior near the edge of a microstrip antenna by the method of matched asymptotic expansions

International audienceThe cavity model is a wide-spread powerful empirical approach for the numerical simulation of microstrip antennas. It is based on several hypotheses assumed a priori: a dimension reduction in the cavity, that is, the zone limited by a metallic patch and the ground plane in which is fed the antenna, supplied by the additional condition that the open sides of the cavity act as magnetic walls. An additional important assumption of this model consists in an adequate description of the singular field behavior in the proximity of the edge of the patch. A simplified two-dimensional problem incorporating the main features of the field behavior near the edge of the patch and inside the cavity is addressed. The method of matched asymptotic expansions is used to carry out a two-scale asymptotic analysis of the field relatively to the thickness of the cavity. All the empirical hypotheses at the basis of the derivation of the cavity model can thus be recovered. Proved error estimates are given in a simplified framework where the dielectric constants of the substrate are assumed to be 1 in order to avoid some unimportant technical difficulties

Algorithme exact pour le problème de l'indépendant faiblement connexe de cardinalité minimum.

International audienceLa gestion des communications radios entre des capteurs sans fil dépend de la topologie mise en place sur le réseau. Généralement, on utilise des architectures basées sur des objets combinatoires issus de la théorie des graphes comme les arbres, les ensembles dominants connexes ou faiblement connexes. Dans cet exposé, nous étudions la structure alternative d'indépendant faiblement connexe (\emph{weakly connected independent set} ou $wcis$) et précisons ses propriétés. Nous décrivons une heuristique qui permet de trouver un $wcis$ rapidement dans un graphe des communications $G=(V,E)$ connexe, ainsi qu'un algorithme d'énumération pour la recherche d'un $wcis$ de cardinalité minimum. Nous donnons enfin des résultats d'expérimentations numériques

Approximation by multipoles of the multiple acoustic scattering by small obstacles and application to the Foldy theory of isotropic scattering.

50 (avec 1,5 interligne)International audienceThe asymptotic analysis, carried out in this paper, for the problem of a multiple scattering of a time-harmonic wave by obstacles whose size is small as compared with the wavelength establishes that the effect of the small bodies can be approximated at any order of accuracy by the field radiated by point sources. Among other issues, this asymptotic expansion of the wave furnishes a mathematical justification with optimal error estimates of Foldy's method that consists in approximating each small obstacle by a point isotropic scatterer. Finally, it is shown how this theory can be further improved by adequately locating the center of phase of the point scatterers and taking into account of self-interactions

Numerical study of acoustic multiperforated plates

International audienceIt is rather classical to model multiperforated plates by approximate impedance boundary conditions. In this article we would like to compare an instance of such boundary conditions obtained through a matched asymptotic expansions technique to direct numerical computations based on a boundary element formulation in the case of linear acoustic

La communauté d'intérêt du Moulin de Rousty et son mode de communication

Visite organisée dans le cadre des travaux du groupe "Communication et forêt méditerranéenne" de Foresterranée'96, au Moulin de Rousty (propriété privée dans les Bouches-du-Rhône)

Matching of Asymptotic Expansions for a 2-D eigenvalue problem with two cavities linked by a narrow hole

One question of interest in an industrial conception of air planes motors is the study of the deviation of the acoustic resonance frequencies of a cavity which is linked to another one through a narrow hole. These frequencies have a direct impact on the stability of the combustion in one of these two cavities. In this work, we aim is analyzing the eigenvalue problem for the Laplace operator with Dirichlet boundary conditions. Using the Matched Asymptotic Expansions technique, we derive the asymptotic expansion of this eigenmodes. Then, these results are validated through error estimates. Finally, we show how we can design a numerical method to compute the eigenvalues of this problem. The results are compared with direct computations

From uprising to secession: a plea for a localized and processual approach to the avatars of the yellow vest movement

For about fifteen years now, so-called leaderless movements, often stemming from appeals via social networks and having recourse to lasting or episodic occupations of public spaces have flourished. This has had the effect of calling into question the usual toolkit used by social movement scholars to study them. More precisely, it is a question of which levels, dimensions and units of analysis are relevant, especially when it comes to describe movements’ social base and worldviews. In this paper, based on a localized and a long-term collective undertaking, begun from the very beginning of the Yellow Vests movement in November 2018, we discuss those shortcomings and suggest avenues for analysis. We rely on three sets of data in a concomitant manner: life history calendars, social media data (mainly Facebook) and field research (participant observation and biographical interviews). By considering time and place as key variables, we offer an innovative way to describe how the YVs movement has been constructed in a constant flux of change