Publications

2014

• Numerical modeling of nonlinear acoustic waves in a tube connected with Helmholtz resonators
  
  • Lombard Bruno
  • Mercier Jean-François
  Journal of Computational Physics, Elsevier, 2014, 259, pp.421-443. Acoustic wave propagation in a one-dimensional waveguide connected with Helmholtz resonators is studied numerically. Finite amplitude waves and viscous boundary layers are considered. The model consists of two coupled evolution equations: a nonlinear PDE describing nonlinear acoustic waves, and a linear ODE describing the oscillations in the Helmholtz resonators. The thermal and viscous losses in the tube and in the necks of the resonators are modeled by fractional derivatives. A diffusive representation is followed: the convolution kernels are replaced by a finite number of memory variables that satisfy local ordinary differential equations. A splitting method is then applied to the evolution equations: their propagative part is solved using a standard TVD scheme for hyperbolic equations, whereas their diffusive part is solved exactly. Various strategies are examined to compute the coefficients of the diffusive representation; finally, an optimization method is preferred to the usual quadrature rules. The numerical model is validated by comparisons with exact solutions. The properties of the full nonlinear solutions are investigated numerically. In particular, the existence of acoustic solitary waves is confirmed. (10.1016/j.jcp.2013.11.036)
  DOI : 10.1016/j.jcp.2013.11.036
• A Branch and Bound algorithm for general mixed-integer quadratic programs based on quadratic convex relaxation
  
  • Billionnet Alain
  • Elloumi Sourour
  • Lambert Amélie
  Journal of Combinatorial Optimization, Springer Verlag, 2014, 28 (2), pp.376-399. Let (MQP) be a general mixed-integer quadratic program that consists of minimizing a quadratic function f(x) = x^TQx +c^Tx subject to linear constraints. Our approach to solve (MQP) is first to consider an equivalent general mixed-integer quadratic problem. This equivalent problem has additional variables y_{ij}, additional quadratic constraints y_{ij}=x_ix_j, a convex objective function, and a set of valid inequalities. Contrarily to the reformulation proposed in MIQCR, the equivalent problem cannot be directly solved by a standard solver. Here, we propose a new Branch and Bound process based on the relaxation of the non-convex constraints y_{ij}=x_ix_j to solve $(MQP)$. Computational experiences are carried out on pure- and mixed-integer quadratic instances. The results show that the solution time of most of the considered instances with up to 60 variables is improved by our Branch and Bound algorithm in comparison with MIQCR and with the general mixed-integer nonlinear solver BARON. (10.1007/s10878-012-9560-1)
  DOI : 10.1007/s10878-012-9560-1
• Mathematical modelling of multi conductor cables
  
  • Beck Geoffrey
  • Imperiale Sebastien
  • Joly Patrick
  Discrete and Continuous Dynamical Systems - Series S, American Institute of Mathematical Sciences, 2014, pp.26. This paper proposes a formal justification of simplified 1D models for the propagation of electromagnetic waves in thin non-homogeneous lossy conductor cables. Our approach consists in deriving these models from an asymptotic analysis of 3D Maxwell’s equations. In essence, we extend and complete previous results to the multi-wires case. (10.3934/dcdss.2015.8.521)
  DOI : 10.3934/dcdss.2015.8.521