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.
  • 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.

Numerics
Brigitte Bidegaray-Fesquet
Brigitte Bidegaray-Fesquet
Researcher

Publications

Nonstandard finite difference schemes for the two-level Bloch model
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
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Stability of FD-TD schemes for Maxwell-Debye and Maxwell-Lorentz equations
The stability of five finite difference-time domain (FD-TD) schemes coupling Maxwell equations to Debye or Lorentz models have been …
Brigitte Bidegaray-Fesquet
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Von-Neumann stability analysis of FD-TD methods in complex media
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
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Hiérarchie de modèles en optique quantique. De Maxwell-Bloch à Schrödinger non linéaire
Cet ouvrage présente les modèles d’interaction onde-matière faisant intervenir une description quantique de la matière (optique …
Brigitte Bidegaray-Fesquet
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Multidimensional corrections to cell-centered finite volume methods for Maxwell equations
Brigitte Bidégaray, Jean-Michel Ghidaglia
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Time Discretizations for Maxwell-Bloch Equations
In this article we derive new time discretizations for the numerical simulation of Maxwell-Bloch equations. These discretizations …
Brigitte Bidégaray
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Modèles d'interaction radiation-matière en milieu résonnant
La description semi-classique de l’interaction radiation-matière dans un contexte résonnant utilise le modèle de Maxwell-Bloch. …
Brigitte Bidégaray
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Order estimates in time of splitting methods for the nonlinear Schrödinger equation
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
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Contributions à l'électromagnétisme dans le domaine temporel. Modélisation classique et quantique en optique non linéaire
Brigitte Bidégaray
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Introducing physical relaxation terms in Bloch equations
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
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Numerical study of self-focusing solutions to the Schrödinger-Debye system
In this article we implement different numerical schemes to simulate the Schrödinger-Debye equations that occur in nonlinear optics. …
Christophe Besse, Brigitte Bidégaray
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Multi-level Maxwell-Bloch simulations
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
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Second order corrections to the finite volume upwind scheme for the 2D Maxwell equations
When computing solutions to Maxwell equations with finite volumes methods one often faces mesh dependent structures. We describe a way …
Brigitte Bidégaray, Jean-Michel Ghidaglia
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