Francisco de la Hoz (2012)
ESAIM: Proceedings
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This paper describes a numerical method for the two-dimensional sine-Gordon equation over a rectangular domain using differentiation matrices, in the theoretical frame of matrix differential equations.
Antoine Bourgeade, Boniface Nkonga (2011)
ESAIM: Proceedings
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In order to get the fusion of small capsules containing a deuterium-tritium nuclear fuel, the MegaJoule laser (LMJ) will focus a large number of laser beams inside a cylinder (Hohlraum) which contains the fusion capsule. In order to control this process we have to know as well as possible the electromagnetic field created by the laser beams on both Hohlraum’s apertures. This article describes a numerical tool which computes this electromagnetic...
Vincent Calvez, Jean Gabriel Houot, Nicolas Meunier, Annie Raoult, Gabriela Rusnakova (2010)
ESAIM: Proceedings
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This article is devoted to the construction of a mathematical model describing the early formation of atherosclerotic lesions. The early stage of atherosclerosis is an inflammatory process that starts with the penetration of low density lipoproteins in the intima and with their oxidation. This phenomenon is closely linked to the local blood flow dynamics. Extending a previous work [5] that was mainly restricted to a one-dimensional setting,...
Vuk Milišić, Amélie Rambaud, Kirill Pichon Gostaf (2010)
ESAIM: Proceedings
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This work aims to extend in two distinct directions results recently obtained in [10]. In a first step we focus on the possible extension of our results to the time dependent case. Whereas in the second part some preliminary numerical simulations aim to give orders of magnitudes in terms of numerical costs of direct 3D simulations. We consider, in the first part, the time dependent rough problem for a simplified heat equation in a straight channel...
Pierre Degond, Fabrice Deluzet, Dario Maldarella, Jacek Narski, Claudia Negulescu, Martin Parisot (2011)
ESAIM: Proceedings
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In this paper a strategy is investigated for the spatial coupling of an asymptotic preserving scheme with the asymptotic limit model, associated to a singularly perturbed, highly anisotropic, elliptic problem. This coupling strategy appears to be very advantageous as compared with the numerical discretization of the initial singular perturbation model or the purely asymptotic preserving scheme introduced in previous works [3, 5]. The model problem...
Carla L. Dias (2012)
ESAIM: Proceedings
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We discuss the geometric structures defined by Young in [9, 10], which are used to prove the existence of an ergodic absolutely continuous invariant probability measure and to study the decay of correlations in expanding or hyperbolic systems on large parts.