| |
Table des matières de ce fascicule | Article précédent | Article suivant Piperno, Serge
$L^2$-stability of the upwind first order finite volume scheme for the Maxwell equations in two and three dimensions on arbitrary unstructured meshes. ESAIM : Modélisation Mathématique et Analyse Numérique, 34 no. 1 (2000), p. 139-158
Texte intégral djvu | pdf | Analyses MR 1735972 | Zbl 0949.65104 | 1 citation dans Numdam
URL stable: http://www.numdam.org/item?id=M2AN_2000__34_1_139_0
[1] J.J. Ambrosiano, S.T. Brandon, R. Löhner and C.R. DeVore, Electromagnetics via the Taylor-Galerkin finite element method on unstructured grids. J. Comput. Phys. 110 (1994) 310-319. Zbl 0795.65088 [2] D.A. Anderson, J.C. Tannehill and R.H. Pletcher, Computational fluid mechanics and heat transfer, Hemisphere, McGraw-Hill, New York (1984). MR 761171 | Zbl 0569.76001 [3] F. Bourdel, P.-A. Mazet and P. Helluy, Resolution of the non-stationary or harmonic Maxwell equations by a discontinuous finite element method. Application to an E.M.I. (electromagnetic impulse) case. Computing Methods in Applied Sciences and Engineering. Nova Science Publishers, Inc., New-York (1991) 405-422. [4] P.G. Ciarlet and J.-L. Lions Eds., Handbook of Numerical Analysis, Vol. 1. North Holland-Elsevier Science Publishers, Amsterdam, New York, Oxford (1991). MR 1115235 | Zbl 0689.65001 [5] J.-P. Cioni, L. Fezoui and H. Steve, Approximation des équations de Maxwell par des schémas décentrés en éléments finis. Technical Report RR-1601, INRIA (1992). [6] J.-P. Cioni and M. Remaki, Comparaison de deux méthodes de volumes finis en électromagnétisme. Technical Report RR-3166, INRIA (1997). [7] J.-P. Cioni, L. Fezoui, L. Anne and F. Poupaud, A parallel FVTD Maxwell solver using 3D unstructured meshes, in 13th annual review of progress in applied computational electromagnetics, Monterey, California (1997). [8] G. Cohen and P. Joly Eds., Aspects récents en méthodes numériques pour les équations de Maxwell, Collection didactique INRIA, INRIA Rocquencourt, France (1998) 23-27. [9] S. Depeyre, Étude de schémas d'ordre élevé en volumes finis pour des problèmes hyperboliques. Application aux équations de Maxwell, d'Buler et aux écoulements diphasiques dispersés. Mathématiques appliquées, ENPC, janvier (1997).
Article [10] R. Eymard, T. Gallouët and R. Herbin, The finite volume method. in Handbook for Numerical Analysis, North Holland-Elsevier Science Publishers, Amsterdam, New York, Oxford (to appear). MR 1804748 | Zbl 0981.65095 [11] L. Fezoui and B. Stoufflet, A class of implicit upwind schemes for euler simulations with unstructured meshes. J. Comput. Phys. 84 (1989) 174-206. MR 1015358 | Zbl 0677.76062 [12] A. Harten, High Resolution Schemes for Hyperbolic Conservation Laws. J. Comput. Phys. 49 (1983) 357-393. MR 701178 | Zbl 0565.65050 [13] A. Harten, P.D. Lax and B. van Leer, On upstream differencing and Godunov-type schemes for hyperbolic conservation laws, SIAM Rev. 25 (1983) 36-61. MR 693713 | Zbl 0565.65051 [14] A. Jameson, Artificial diffusion, upwind biasing, limiters and their effect on accuracy and multigrid convergence in transonic and hypersonic flows, in 11th AIAA Computational Fluid Dynamics Conference, Orlando, Florida, July 6-9 (1993), AIAA paper 93-3359. [15] P. Lesaint, Sur la résolution des systèmes hyperboliques du premier ordre par des méthodes d'éléments finis. Ph.D. thesis, Université de Paris VI, France (1975). [16] R. Löhner and J. Ambrosiano, A finite element solver for the Maxwell equations, in GAMNI-SMAI Conference on Numerical Methods for the Maxwell Equations, Paris, France (1989). SIAM, Philadelphia (1991). [17] M. Remaki, A new finite volume scheme for solving Maxwell System. Technical Report RR-3725, INRIA (1999). Zbl 0994.78021 [18] M. Remaki, L. Fezoui and F. Poupaud, Un nouveau schéma de type volumes finis appliqué aux équations de Maxwell en milieu hétérogène. Technical Report RR-3351, INRIA (1998). [19] J.S. Shang, A characteristic-based algorithm for solving 3D, time-domain Maxwell equations. In 30th Aerospace Sciences Meeting and Exhibit, Reno, Nevada. January 6-9 (1992), AIAA paper 92-0452. [20] J.S. Shang and R.M. Fithen, A comparative study of characteristic-based algorithms for the Maxwell equations. J. Comput. Phys. 125 (1996) 378-394. MR 1388152 | Zbl 0848.65087 [21] V. Shankar, W.F. Hall and A.H. Mohammadian, A time-domain differential solver for electromagnetic scattering problems. Proc. IEEE 77 (1989) 709-720. [22] A. Tafiove, Re-inventing electromagnetics: supercomputing solution of Maxwell's equations via direct time integration on space grids. AIAA paper 92-0333 (1992). [23] K.R. Umashankar, Numerical analysis of electromagnetic wave scattering and interaction based on frequency-domain integral equation and method of moments techniques. Wave Motion 10 (1988) 493. MR 972733 | Zbl 0672.73026 [24] B. Van Leer, Towards the ultimate conservative difference scheme v: a second-order sequel to Godunov's method. J. Comput. Phys. 32 (1979) 361-370. MR 1703646 | Zbl 0276.65055 [25] J.-P. Vila, Convergence and error estimates in finite volume schemes for general multidimensional scalr conservation laws. I. Explicite monotone schemes. RAIRO Modél. Math. Anal. Numér. 28 (1994) 267-295.
Numdam | MR 1275345 | Zbl 0823.65087 [26] J.-P. Vila and P. Villedieu, Convergence de la méthode des volumes finis pour les systèmes de Friedrichs. C.R. Acad. Sci. Paris Sér. I Math. 3(325) (1997) 671-676. MR 1473844 | Zbl 0888.65107 [27] R.F. Warming and F. Hyett, The modified equation approach to the stability and accuracy analysis of finite-difference methods. J. Comput. Phys. 14 (1974) 159-179. MR 339526 | Zbl 0291.65023 [28] K.S. Yee, Numerical solution of initial boundary value problems involving Maxwell's equations in isotropic media. IEEE Trans. Antennas and Propagation AP-16 (1966) 302-307. Zbl 1155.78304
|
|
Copyright Cellule MathDoc 2013 | Crédit | Plan du site
|