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Traitement de couche limite et méthodes Pic : algorithmes et approche objet

Abstract : The work exposed in this document is made up of two relatively independant parts. The first part deals with mathematical and numerical simulations for a model of high frequency electromagnetic shaping of liquid metals. The asymptotic analysis gives prominence to the existence of singular perturbation problems with a weak layer closeness of the conductor surface. From our numerical model simplified formulation emerge two kinds of singular perturbation problems, classical elliptic problem and elliptic problem with electromagnetic transmission. We study in details a domain decomposition without recovering based on finite difference framework in one dimensional space to solve the transmission problem. We show that, for a good choice of the domain decomposition and boundary conditions at the artificial interface, we obtain a uniform approximation of the solution and the iterative procedure convergence rate which is superlinear. Then, we generalize these results into a two dimensional space for the radial case and we apply our results to enhanced finite element computations. We obtained rigorous convergence and accuracy estimates which seems to indicate that these schemes could be extended to more general geometries . The second part deals with a problem in computer science from ? a computer science point of view: underlining opportunities of the objectoriented paradigm for advanced P.LC (Particle-In-Cell in plasma physic) modelling, with these known advantages : increased fiexibility, extensibility, robustness and so on. A two-dimensional relativistic electromagnetic PIC code implementation has been made . ? a numerical point of view : a comparative study about electrical field correction in electromagnetic PIC plasma simulations is done. We analyze two techniques for reducing electric field error: the first one consists in using a charge conservating method to compute charge and current density onto the Maxwell discretization mesh, the second one is to use one divergence correction of electric fields based on the reformulated Maxwell system.
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Laurence Viry. Traitement de couche limite et méthodes Pic : algorithmes et approche objet. Mathématiques générales [math.GM]. Université Henri Poincaré - Nancy 1, 2000. Français. ⟨NNT : 2000NAN10015⟩. ⟨tel-01748191⟩

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