Publications

2005

• Modèles asymptotiques pour la propagation des ondes dans des milieux comportant des fentes
  
  • Joly Patrick
  • Tordeux Sébastien
  , 2005, pp.54. Dans ce rapport, nous nous intéressons à la propagation d'ondes acoustiques dans des milieux comportant des fentes minces. Nous proposons un modèle approché permettant de ramener la fente mince à sa surface moyenne et nous menons une analyse détaillée de ce modèle approché (stabilité et estimation d'erreur), dans un cas académique particulier.
• Robust high order non-conforming finite element formulation for time domain fluid-structure interaction
  
  • Diaz Julien
  • Joly Patrick
  Journal of Computational Acoustics, World Scientific Publishing, 2005, 13 (3), pp.403-431. In this paper we present various numerical methods for solving time-dependent fluid-structure interaction problem in two or three dimensions that we claim to be efficient, robust and highly accurate. These methods, based on mixed variational formulations, are explicit and conservative and can be of arbitrary high order in space. Their accuracy will be illustrated via a comparison with analytical solutions in simple configuration. (10.1142/S0218396X05002736)
  DOI : 10.1142/S0218396X05002736
• AN ANALYSIS OF HIGHER ORDER BOUNDARY CONDITIONS FOR THE WAVE EQUATION
  
  • Diaz Julien
  • Joly Patrick
  SIAM Journal on Applied Mathematics, Society for Industrial and Applied Mathematics, 2005, 65 (5), pp.1547-1575. Thanks to the use of the Cagniard–De Hoop method, we derive an analytic solution in the time domain for the half-space problem associated with the wave equation with Engquist– Majda higher order boundary conditions. This permits us to derive new convergence results when the order of the boundary condition tends to infinity, as well as error estimates. The theory is illustrated by numerical results. (10.1137/S0036139903436145)
  DOI : 10.1137/S0036139903436145
• An Error Analysis of Conservative Space-Time Mesh Refinement Methods for the 1D Wave Equation
  
  • Joly Patrick
  • Rodríguez Jerónimo
  SIAM Journal on Numerical Analysis, Society for Industrial and Applied Mathematics, 2005, 43, pp.825-859. We study two space-time mesh refinement methods as the one introduced in [F. Collino, T. Fouquet, and P. Joly, Numer. Math., 95 (2003), pp. 197-221].The stability of such methods is guaranteed by construction through the conservation of a discrete energy. In this paper, we show the L 2 convergence of these schemes and provide optimal error estimates. The proof is based on energy techniques and bootstrap arguments. Our results are validated with numerical simulations and compared with results from plane wave analysis [F. Collino, T. Fouquet, and P. Joly, Numer. Math., 95 (2003), pp. 223-251]. (10.1137/040603437)
  DOI : 10.1137/040603437
• High Spatial Order Finite Element Method to Solve Maxwell's Equations in Time Domain
  
  • Pernet Sébastien
  • Ferrieres Xavier
  • Cohen Gary
  IEEE Transactions on Antennas and Propagation, Institute of Electrical and Electronics Engineers, 2005, 53 (9), pp.2889 - 2899. This paper presents a finite element method with high spatial order for solving the Maxwell equations in the time domain. In the first part, we provide the mathematical background of the method. Then, we discuss the advantages of the new scheme compared to a classical finite-difference time-domain (FDTD) method. Several examples show the advantages of using the new method for different kinds of problems. Comparisons in terms of accuracy and CPU time between this method, the FDTD and the finite-volume time-domain methods are given as well. (10.1109/TAP.2005.856046)
  DOI : 10.1109/TAP.2005.856046
• Another approach to linearized elasticity and a new proof of Korn's inequality
  
  • Ciarlet Patrick
  • Ciarlet Philippe G.
  Mathematical Models and Methods in Applied Sciences, World Scientific Publishing, 2005, 15 (02), pp.259-271. We describe and analyze an approach to the pure traction problem of three-dimensional linearized elasticity, whose novelty consists in considering the linearized strain tensor as the "primary" unknown, instead of the displacement itself as is customary. This approach leads to a well-posed minimization problem, constrained by a weak form of the St Venant compatibility conditions. Interestingly, it also provides a new proof of Korn's inequality. (10.1142/S0218202505000352)
  DOI : 10.1142/S0218202505000352
• Space-time mesh refinement for elastodynamics. Numerical results
  
  • Bécache Eliane
  • Joly Patrick
  • Rodríguez Jerónimo
  Computer Methods in Applied Mechanics and Engineering, Elsevier, 2005, 194, pp.355-366. We propose here a generalization to the elastodynamic equations of the spacetime mesh refinement technique introduced in [Raffinement de maillage spatio-temporel pour les eŽquations de Maxwell, Ph.D. thesis, Université de Dauphine, Paris, 2000] for the Maxwell's equations. This method uses a discrete energy conservation to ensure the stability. The method is presented in a variational way applicable to other type of hyperbolic systems. Several numerical experiments are provided to show the efficiency of this approach. (10.1016/j.cma.2004.02.023)
  DOI : 10.1016/j.cma.2004.02.023