Couplage de modeles et de methodes numeriques pour I' electromagnetisme en domaine temporel

Authors

  • Malika Remaki INRIA-CERMICS 2004 route des Lucioles, BP 93- Sophia Antipolis- F-06902 Valbonne
  • Frederic Poupaud Laboratoire Dieudonne- UMR 6621 du CNRS. Universite de Nice Sophia Antipolis, Pare Valrose-F- 06108 Nice cedex 2
  • Loula Fezoui INRIA-CERMICS 2004 route des Lucioles, BP 93- Sophia Antipolis- F-06902 Valbonne
  • Olivier Chanrion INRIA-CERMICS 2004 route des Lucioles, BP 93- Sophia Antipolis- F-06902 Valbonne

Keywords:

Electromagnetism, Maxwell equations, Vlasov-Poisson, Vlasov-Maxwell, Finite Volume, Finite Difference

Abstract

This paper deals with coupling models and/or methods in electromagnetism. The first part of the paper is devoted to the coupling of physical models (Vlasov-Poisson, VlasovMaxwell) which describe some field-particle interactions. In the second part, we present a new hybrid finite difference/ finite volume scheme applied to the time domain Maxwell equations.

Downloads

Download data is not yet available.

References

[AKU 86] ASANO K, KOYOSHI et UKAI S., On the Vlasov-Poisson limit of the VlasovMaxwell

equation. Pattern and waves. Qualitative analysis of nonlinear differential equations,

Stud. Math. Appl. 18, 369-383.

[ADS 96] Assous F.,DEGOND P. et SEGRE J., Numerical approximation of the Maxwell

equations in inhomogeneous media by a P 1 conforming finite element method. 1. Comput.

Phys. 128, no. 2, 363-380.

[BEZ 93] BEZARD M., Boundary value problems for the Vlasov-Maxwell system. Semin.

Equ. Deriv. Partielles, Ec. Polytech., Cent. Math., Palaiseau Semin. 1992-1993, Exp. No.4,

p.

[BON 97] BONNET F., FEZOUI L. , Methode PML en volumes finis pour Ia resolution des

equations de Maxwell en maillage hybride 2-D. Rapport de recherche Cermics no 97-92,

[BPO 97] BONNET F. et POUPAUD F., Berenger absorbing boundary condition with time

finite-volume scheme for triangular meshes. Appl. Nwner. Math. 25, No.4, 333-354.

[BOP 97] BOSTAN M. et POUPAUD F., Solutions periodique au systeme de Vlasov Poisson

avec conditions aux limites. C.R. Acad. Sci. Paris, Serie I 325 1333-1336.

[BOS 99] BOSTAN M., Etude numerique et theorique du systeme de Vlasov Maxwell. These

en mathematiques appliquees, Ecole Nationale des Ponts et Chaussees, janvier 1999.

[DEG 86] DEGOND P., Local existence of solutions of the Vlasov-Maxwell equations and

convergence to the Vlasov-Poisson equations for infinite light velocity. Math. Methods

Appl., Sci. 8, 533-558.

[DEP 95] DEPEYRE S. , Stability analysis for finite volume schemes on rectangular and triangular

meshes applied to the two-dimensional Maxwell system. Rapport de recherche

Cermics no 95-40, 1995.

[DIL 89] DIPERNA R.J et LIONS P.L., Global weak solution of Vlasov-Maxwell systems,

Commun. on Pure and Appl. Math, XVII., 729-757.

[GUO 93] Guo Y., Global weak solutions of the Vlasov-Maxwell system with boundary

conditions. Commun. Math. Phys., 154, No.2, 245-263.

[HOL 83] HOLLAND R., Finite-difference solutions of Maxwell's equation in generalizd nonorthogonal

coordinates, IEEE Trans. Nucl. Sci., vol.NS-30, pp. 4589-4591, 1983.

[!PC 95] ISSAUTIER D.,POUPAUD F.,CIONI J.P. et FEZOUI L., A 2-D Vlasov-Maxwell solver

on unstructured meshes. Cohen, Gary (ed.), Mathematical and numerical aspects of

wave propagation. Proceedings of the third international conference, Mandelieu-La Napoule,

France, April 24--28, 1995.

[PIE 98] Progress in Electromagnetics research Symposiun. Proceedings 13 - 17 july, Cite

des Congres Nantes, France.

[POU 92] POUPAUD F., Boundary value problems for the stationary Vlasov-Maxwell system.

Forum Math. 4, No.5, 499-527.

[REM 98] REMAKI M., FEZOUI L. et POUPAUD F., Un nouveau schema de type volumes finis

applique aux equations de Maxwell en milieu heterogene. Rapport de recherche INRIA

no 3351, janvier 1998.

[REM 99] REMAKI M., A New Finite Volume Scheme for Solving Maxwell System, rapport

de recherche INRIA no 3725, juillet 1999.

[SCH 86] SCHAEFFER J ., The classical limit of the relativistic Vlasov-Maxwell system. Commun.

Math. Phys. I 04, 403-421.

[TAF 75] TAFLOVE A. et BRODWIN M. E., Numerical Solution of Steady-State Electromagnetic

Scattering problems Using the Time-Dependent maxwell's equations, IEEE Trans.

Antenna Propagat, vol.MTT-23, no. 8, pp. 623-630, August 1975.

[YEE 66] YEE K. S., Numerical solution of initial boundary value problem in isotropic media,

IEEE Trans. Antenna Propagat, vol.AP-14, no. 3, pp. 302-307, May 1966.

[YEE 87] YEE K. S., Numerical solution to Maxwell's equations with non-orthogonal grids,

Lawrence Livermore National Laboratory Tech. Report. UCRL-93268, Apr. 1987.

[YEE 94] YEE K. S. et CHEN J. S., The Finite-Difference Time-Domain (FDTD) and The

Finite-Volume Time-Domain (FVTD) Methods in Solving Maxwell's Equations , IEEETrans.

Antenna Propagat, vol. 45, no. 3, pp. 354-363, March 1997.

Downloads

Published

1999-06-09

How to Cite

Remaki, M. ., Poupaud, F. ., Fezoui, L. ., & Chanrion, O. (1999). Couplage de modeles et de methodes numeriques pour I’ electromagnetisme en domaine temporel. European Journal of Computational Mechanics, 8(5-6), 639–658. Retrieved from https://journals.riverpublishers.com/index.php/EJCM/article/view/2993

Issue

Section

Original Article