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Numerical simulations of the focal spot generated by a set of laser beams : LMJ⋆⋆⋆

Antoine Bourgeade, Boniface Nkonga (2011)

ESAIM: Proceedings

In order to get the fusion of small capsules containing a deuterium-tritium nuclear fuel, the MegaJoule laser (LMJ) will focus a large number of laser beams inside a cylinder (Hohlraum) which contains the fusion capsule. In order to control this process we have to know as well as possible the electromagnetic field created by the laser beams on both Hohlraum’s apertures. This article describes a numerical tool which computes this electromagnetic field...

Numerical solution of the Maxwell equations in time-varying media using Magnus expansion

István Faragó, Ágnes Havasi, Robert Horváth (2012)

Open Mathematics

For the Maxwell equations in time-dependent media only finite difference schemes with time-dependent conductivity are known. In this paper we present a numerical scheme based on the Magnus expansion and operator splitting that can handle time-dependent permeability and permittivity too. We demonstrate our results with numerical tests.

Numerical study by a controllability method for the calculation of the time-periodic solutions of the Maxwell and Vlasov-Maxwell systems

Mihai Bostan (2001)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

The topic of this paper is the numerical analysis of time periodic solution for electro-magnetic phenomena. The Limit Absorption Method (LAM) which forms the basis of our study is presented. Theoretical results have been proved in the linear finite dimensional case. This method is applied to scattering problems and transport of charged particles.

Numerical study by a controllability method for the calculation of the time-periodic solutions of the Maxwell and Vlasov-Maxwell systems

Mihai Bostan (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

The topic of this paper is the numerical analysis of time periodic solution for electro-magnetic phenomena. The Limit Absorption Method (LAM) which forms the basis of our study is presented. Theoretical results have been proved in the linear finite dimensional case. This method is applied to scattering problems and transport of charged particles.

Numerical study of self-focusing solutions to the Schrödinger-Debye system

Christophe Besse, Brigitte Bidégaray (2001)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

In this article we implement different numerical schemes to simulate the Schrödinger-Debye equations that occur in nonlinear optics. Since the existence of blow-up solutions is an open problem, we try to compute such solutions. The convergence of the methods is proved and simulations seem indeed to show that for at least small delays self-focusing solutions may exist.

Numerical study of self-focusing solutions to the Schrödinger-Debye system

Christophe Besse, Brigitte Bidégaray (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

In this article we implement different numerical schemes to simulate the Schrödinger-Debye equations that occur in nonlinear optics. Since the existence of blow-up solutions is an open problem, we try to compute such solutions. The convergence of the methods is proved and simulations seem indeed to show that for at least small delays self-focusing solutions may exist.

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