Publications

2013

• Qualitative identification of cracks using 3D transient elastodynamic topological derivative: formulation and FE implementation
  
  • Bellis Cédric
  • Bonnet Marc
  Computer Methods in Applied Mechanics and Engineering, Elsevier, 2013, 253, pp.89-105. A time-domain topological derivative (TD) approach is developed for transient elastic-wave imaging of buried cracks. The TD, which quantifies the sensitivity of the misfit cost functional to the creation at a specified location of an infinitesimal trial crack, is expressed in terms of the time convolution of the free field and an adjoint field as a function of that specified location and of the trial crack shape. Following previous studies on cavity identification in similar conditions, the TD field is here considered as a natural and computationally efficient approach for defining a crack location indicator function. This study emphasizes the implementation and exploitation of TD fields using the standard displacement-based FEM, a straightforward exploitation of the relevant sensitivity formulation established here. Results on several numerical experiments on 3D elastodynamic and acoustic configurations are reported and discussed, allowing to assess and highlight many features of the proposed TD-based fast qualitative crack identification, including its ability to identify multiple cracks and its robustness against data noise. (10.1016/j.cma.2012.10.006)
  DOI : 10.1016/j.cma.2012.10.006
• Higher-Order Discontinuous Galerkin Method for Pyramidal Elements using Orthogonal Bases
  
  • Bergot Morgane
  • Duruflé Marc
  Numerical Methods for Partial Differential Equations, Wiley, 2013, 29 (1), pp.144-169. We study arbitrarily high-order finite elements defined on pyramids on discontinuous Galerkin methods. We propose a new family of high-order pyramidal finite element using orthogonal basis functions which can be used in hybrid meshes including hexahedra, tetrahedra, wedges and pyramids. We perform a comparison between these orthogonal functions and nodal functions for affine and non-affine elements. Different strategies for the inversion of mass matrix are also considered and discussed. Numerical experiments are conducted for 3-D Maxwell's equations. (10.1002/num.21703)
  DOI : 10.1002/num.21703