Numerical analysis
Sep 1, 1998
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.
- Journal papers: A-BB01
- 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.
Publications
We are interested in numerically solving a transitional model derived from the Bloch model. The Bloch equation describes the time …
Brigitte Bidegaray-Fesquet,
Clément Jourdana,
Léopold Trémant
We extend to the N-level Bloch model the splitting scheme which use exact numerical solutions of sub-equations. These exact solutions …
Marc Songolo,
Brigitte Bidegaray-Fesquet
In this paper, we present a reformulation of Mickens rules for nonstandard finite difference (NSFD) scheme to adapt them to systems of …
Marc Songolo,
Brigitte Bidegaray-Fesquet
In this paper, we present splitting schemes for the two-level Bloch model. After proposing two ways to split the Bloch equation, we …
Marc Songolo,
Brigitte Bidegaray-Fesquet
This technical report yields detailed calculations of the paper [1] (B. Bidégaray-Fesquet, “Stability of FD-TD schemes for …
Brigitte Bidegaray-Fesquet
The stability of five finite difference-time domain (FD-TD) schemes coupling Maxwell equations to Debye or Lorentz models have been …
Brigitte Bidegaray-Fesquet
The stability analysis of Finite Difference-Time Difference (FD-TD) schemes can be reduced via the von Neumann approach to the study of …
Brigitte Bidegaray-Fesquet
Cet ouvrage présente les modèles d’interaction onde-matière faisant intervenir une description quantique de la matière (optique …
Brigitte Bidegaray-Fesquet
Brigitte Bidégaray,
Jean-Michel Ghidaglia
In this paper, we consider the nonlinear Schrödinger equation $u_t + i\Delta u − F(u) = 0$ in two dimensions. We show, by an …
Christophe Besse,
Brigitte Bidégaray,
Stéphane Descombes
Brigitte Bidégaray
The Bloch equation models the evolution of the state of electrons in matter described by a Hamiltonian. To model more physical …
Brigitte Bidégaray,
Antoine Bourgeade,
Didier Reignier
In this article we implement different numerical schemes to simulate the Schrödinger-Debye equations that occur in nonlinear optics. …
Christophe Besse,
Brigitte Bidégaray
We present the Maxwell-Bloch equations that are a model for the semi-classical description of laser-matter interactions. After having …
Brigitte Bidégaray,
Antoine Bourgeade,
Didier Reignier,
Richard Ziolkowski