Publications

2013

• Fast non-overlapping Schwarz domain decomposition methods for solving the neutron diffusion equation
  
  • Jamelot Erell
  • Ciarlet Patrick
  Journal of Computational Physics, Elsevier, 2013, 241, pp.445--463. no abstract
• On the numerical computation of nonlinear normal modes for reduced-order modelling of conservative vibratory systems
  
  • Blanc F.
  • Touzé Cyril
  • Mercier Jean-François
  • Ege Kerem
  • Bonnet-Ben Dhia Anne-Sophie
  Mechanical Systems and Signal Processing, Elsevier, 2013, 36 (2), pp.520-539. Numerical computation of Nonlinear Normal Modes (NNMs) for conservative vibratory systems is addressed, with the aim of deriving accurate reduced-order models up to large amplitudes. A numerical method is developed, based on the center manifold approach for NNMs, which uses an interpretation of the equations as a transport problem, coupled to a periodicity condition for ensuring manifold's continuity. Systematic comparisons are drawn with other numerical methods, and especially with continuation of periodic orbits, taken as reference solutions. Three di erent mechanical systems, displaying peculiar characteristics allowing for a general view of the performance of the methods for vibratory systems, are selected. Numerical results show that invariant manifolds encounter folding points at large amplitude, generically (but not only) due to internal resonances. These folding points involve an intrinsic limitation to reduced-order models based on the center manifold and on the idea of a functional relationship between slave and master coordinates. Below that amplitude limit, numerical methods are able to produce reduced-order models allowing for a precise prediction of the backbone curve. (10.1016/j.ymssp.2012.10.016)
  DOI : 10.1016/j.ymssp.2012.10.016