High-order discontinuous galerkin methods for the maxwell equations

Fahs-H - Collection Omn.univ.europ.

208 pages, parution le 05/07/2010

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Résumé

This work is concerned with the development of a high-order discontinuous Galerkin time-domain (DGTD) method for solving Maxwell's equations on non-conforming simplicial meshes. First, we present a DGTD method based on high-order nodal basis functions for the approximation of the electromagnetic field within a simplex, a centered scheme for the calculation of the numerical flux at an interface between neighbouring elements, and a second-order leap-frog time integration scheme. Next, to reduce the computational costs of the method, we propose a hp-like DGTD method which combines local h-refinement and p-enrichment. Then, we report on a detailed numerical evaluation of the DGTD methods using several propagation problems. Finally, in order to improve the accuracy and rate of convergence of the DGTD methods previously studied, we study a family of high-order explicit leap-frog time schemes. These time schemes ensure the stability under some CFL-like condition. We also establish rigorously the convergence of the semi-discrete approximation to Maxwell's equations and we provide bounds on the global divergence error.

Caractéristiques techniques

	PAPIER
Éditeur(s)	Editions universitaires européennes
Auteur(s)	Fahs-H
Collection	Omn.univ.europ.
Parution	05/07/2010
Nb. de pages	208
Format	15.2 x 22.9
Couverture	Broché
Poids	313g
EAN13	9786131500206