# Méthodes d'éléments finis d'ordre élevé pour la simulation numérique de la propagation d'ondes

Abstract : The purpose of this thesis is the construction of numerical schemes for the simulation of acoustic and electromagnetic wave propagation phenomena based on arbitrary high order efficient conforming finite elements. In the case of the scalar wave equation we develop an algorithm which generalizes the construction of mass-lumped triangular lagrangian finite elements (cf. Cohen-Joly-Tordjmann) which leads to the determination of a new mass-lumped $P_6$ element. We also present a new family of partial mass-lumped finite elements. In the case of electromagnetic waves propagation, we present a conforming coupling method between rectangular finite edge elements (with mass-lumping) and triangular finite edge elements, which permits the optimisation of the mass matrix profil (and thus its inversion) for the simulations in complex geometries. We also present an arbitrary high order time discretisation based on a Cauchy-Kowalewski procedure which we had to stabilise. All the discretisations presented where implemented, tested and compared, in a series of numerical tests, to discretisations usually used in this context as standard lagrangian finite elements in space, symplectic or Runge-Kutta in time
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https://tel.archives-ouvertes.fr/tel-00188739
Contributor : Sébastien Jund <>
Submitted on : Monday, December 3, 2007 - 8:19:05 AM
Last modification on : Friday, June 19, 2020 - 9:10:04 AM
Long-term archiving on: : Friday, November 25, 2016 - 5:04:56 PM

### Identifiers

• HAL Id : tel-00188739, version 2

### Citation

Sébastien Jund. Méthodes d'éléments finis d'ordre élevé pour la simulation numérique de la propagation d'ondes. Mathématiques [math]. Université Louis Pasteur - Strasbourg I, 2007. Français. ⟨NNT : 2007STR13125⟩. ⟨tel-00188739v2⟩

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