Calcul de fonctions de forme de haut degré par une technique de perturbation

Abstract : Most problems of physics and mechanics lead to partial differential equations. The many methods that exist are relatively low degree. In this thesis, we propose a method of very high degree. Our idea is to increase the order of interpolation function via a perturbation technique to avoid or reduce the difficulties caused by the high cost operations such as integrations. In dimension 1, the proposed technique is close to the P-version finite elements. At a basic level, approximates the solution by a power series of order p. In the case of a linear equation of order 2, the local resolution can build an element of degree, with two degrees of freedom per element. For nonlinear problems, a linearization of the problem by Newton's method is needed. Tests involving linear and nonlinear equations were used to validate the method and show that the technique has a similar convergence in the p-version finite elements. In dimension 2, the problem is discretized through reorganizing polynomials in homogeneous polynomials of degree k. After a definition of variables called principal and secondary combined with a vertical scanning field, the problem becomes a series of 1D problem. A collocation technique allows to take into account the boundary conditions and coupling conditions and determine the solution of the problem. The collocation technique coupled with the least-squares enabled to improve the initial results and has made more robust the perturbation technique
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Theses
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http://docnum.univ-lorraine.fr/prive/UPVM_T_2009_ZEZE_Djedje_Sylvain.pdf
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https://hal.univ-lorraine.fr/tel-01751321
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Submitted on : Thursday, March 29, 2018 - 1:16:11 PM
Last modification on : Monday, April 16, 2018 - 10:41:12 AM

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Djédjé Sylvain Zézé. Calcul de fonctions de forme de haut degré par une technique de perturbation. Autre [cond-mat.other]. Université Paul Verlaine - Metz, 2009. Français. ⟨NNT : 2009METZ056S⟩. ⟨tel-01751321⟩

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