Amélioration des performances de méthodes Galerkin discontinues d'ordre élevé pour la résolution numérique des équations de Maxwell instationnaires sur des maillages simplexes

Download or read book Amélioration des performances de méthodes Galerkin discontinues d'ordre élevé pour la résolution numérique des équations de Maxwell instationnaires sur des maillages simplexes written by Joseph Charles and published by . This book was released on 2012 with total page 213 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work is concerned with the development of a flexible and efficient arbitrary high-order Discontinuous Galerkin Time Domain (DGTD) method for solving time-domain Maxwell’s equations on unstructured simplicial meshes, relying on explicit time integration schemes. Electromagnetic field components are approximated locally by polynomial interpolation methods and continuity between neighbouring, elements is weakly enforced by a centred scheme for the calculation of the numerical flux across mesh interfaces. The aim of this PhD thesis is to fulfil two complementary objectives. On one hand, to improve the polynomial approximation flexibility in view of the development of p-adaptive DGTD methods by studying various polynomial interpolation methods. Several aspects such as the modal or nodal nature of the associated set of basis functions, their possible hierarchical structure, the conditioning of the elementary matrices to be inverted, the spectral properties of the interpolation or the programming simplicity are investigated. On the other hand, to increase the efficiency of the temporal approximation on locally refined meshes by using a local time stepping strategy. We finally develop in this work a high performance computing methodology to exploit the inherent locality and parallelism of DGTD methods combined with the GPU computing capabilities. The combination of these brand features result in worth improvement of efficiency and in significant reduction of the computational time.