Publications

2008

• A spurious-free space-time mesh refinement for elastodynamics
  
  • Rodríguez Jerónimo
  International Journal for Multiscale Computational Engineering, Begell House, 2008, 6 (3), pp.263-279. We propose a generalization of the space-time mesh refinement technique for elastodynamics presented by 14 to the case where the discretization step (in space and time) on the fine grid is q N times finer than the one on the coarse grid. This method uses the conservation of a discrete energy to ensure the stability under the usual CFL condition. Some numerical examples show that the method is only first order accurate (and thus suboptimai with respect to the second-order interior scheme we have used) when the ratio of refinement is higher than 2. A Fourier analysis of the computed signals exhibits the presence of high-frequency waves (aliasing phenomena) polluting the fields on the fine grid. Those results provide valuable information with which to build a postprocessing by averaging that removes the spurious phenomena. Finally, we introduce a new numerical scheme, computing the postprocessed solution directly. This method is stable and second-order consistent, regardless of the ratio of refinement. Its performance is shown through a numerical simulation of the diffraction of elastic waves by small cracks. © 2008 by Begell House, Inc. (10.1615/intjmultcompeng.v6.i3.60)
  DOI : 10.1615/intjmultcompeng.v6.i3.60
• The linear sampling method in a waveguide: A formulation based on modes
  
  • Bourgeois Laurent
  • Lunéville Éric
  Journal of Physics: Conference Series, IOP Science, 2008, 135 (-), pp.012023. This paper concerns the Linear Sampling Method to retrieve obstacles in a 2D or 3D acoustic waveguide. We derive a modal formulation of the LSM which is suitable for the waveguide configuration. Despite the ill-posedness of the inverse problem is increased owing to the evanescent modes, numerical experiments show good reconstruction of obstacles by using the far field. © 2008 IOP Publishing Ltd. (10.1088/1742-6596/135/1/012023)
  DOI : 10.1088/1742-6596/135/1/012023