Numerical analysis

I am interested in designing numerical schemes (mostly finite difference schemes) that preserve the physical properties of the underlying physical models.

  • Schemes for dispersive equations.
  • Finite differences for Maxwell-Debye and Maxwell-Lorentz equations.
  • Finite differences for Maxwell-Bloch equations.
  • Finite volumes for Maxwell equations.
  • Splitting and nonstandard methods.

Part of my Habilitation thesis deals with the theme. I also wrote a master-level book on models in nonlinear and quantum optics, including numerical issues.

Ongoing works deal with asymptotic preserving schemes for Bloch equations.