zbMATH — the first resource for mathematics

A new constrained formulation of the Maxwell system. (English) Zbl 0874.65097
The authors present a new constrained formulation of the Maxwell equations in order to improve the numerical verification of the divergence relations \(\roman {div} \;\mathbf B = 0, \;\text{div} \;\mathbf E = \frac{\varrho}{\epsilon_0}\). The stability of the finite volume schemes applied to the new constrained system using rectangular and triangular meshes is also studied. The authors present some numerical results in order to demonstrate the efficiency of this method.
Reviewer: K.Najzar (Praha)

65Z05 Applications to the sciences
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs
35Q60 PDEs in connection with optics and electromagnetic theory
78A25 Electromagnetic theory, general
Full Text: DOI EuDML
[1] F. ASSOUS, P. DEGOND, J. SEGRE, 1992, A particle-tracking method for 3D electromagnetic PIC codes on unstructured meshes, Comp. Phys. Comm., 72, pp. 105-114.
[2] R. CARPENTIER, A. de la BOURDONNAYE, B. LARROUTUROU, 1994, On the derivation of the modified equation for the analysis of linear numerical methods, CERMICS Report no 26. Zbl0806.65122 MR1300083 · Zbl 0806.65122 · doi:10.1093/imanum/14.2.233
[3] S. DEPEYRE, R. CARPENTIER, High-order upwind numerical methods in two space dimensions, CERMICS Report, to appear.
[4] S. DEPEYRE, Stability analysis for the finite volume schemes on rectangular and triangular meshes applied to the 2D Maxwell system, to appear. · Zbl 0956.78019
[5] J. P. CIONI, L. FEZOUI, H. STEVE, 1993, A parallel time-domain Maxwell solver using upwind schemes and triangular meshes, IMPACT in computing in science and engeenering No 165. Zbl0788.65119 MR1237286 · Zbl 0788.65119 · doi:10.1006/icse.1993.1010
[6] J. P. CIONI, L. FEZOUI, D. ISSAUTIER, High order upwind schemes for solving time domain Maxwell equation, La Recherche Aérospatiale, numéro spécial électromagnétisme.
[7] R. DAUTRAY, J. L. LIONS, 1987, Analyse mathématique et calcul numérique, Masson, 1, 68-127. MR918560
[8] J. A. DESIDERI, A. GOUJO, V. SELMIN, 1987, Third-order numerical schemes for hyperbolic problems, Rapport de recherche INRIA no. 607.
[9] L. FEZOUI, 1985, Résolution des équations d’Euler par un schéma de Van Leer en éléments finis, INRIA Report no. 358.
[10] N. GLINSKY, 1990, Simulation numérique d’écoulements hypersoniques réactifs hors-équilibre chimique, Thesis, University of Nice-Sophia Antipolis. Zbl0923.76078 · Zbl 0923.76078
[11] D. ISSAUTIER, J. P. CIONI, F. POUPAUD, L. FEZOUI, A 2-D Vlasov Maxwell solver on unstructured meshes, Third international conference on mathematical and numerical aspects of wave propagation phenomena, Mandelieu, avril 1995. Zbl0874.76061 MR1328210 · Zbl 0874.76061
[12] P. D. LAX, A. HARTEN, B. Van LEER, 1983, On upstream differencing and Godunov type schemes for hyperbolic conservation laws, SIAM Revue, Vol. 25, No 1. Zbl0565.65051 MR693713 · Zbl 0565.65051 · doi:10.1137/1025002
[13] S. LANTERI, 1991, Simulation d’écoulements aérodynamiques instationnaires sur une architecture massivement parallèle, Thesis, University of Nice Sophia-Antipolis.
[14] V. SELMIN, 1987, Finite element solution of hyperbolic equations, I : one dimensional case, II : two dimensional case, INRIA Report no 655.
[15] B. Van LEER, 1982, Flux vector splitting for the Euler equations, Lecture Notes in Physics, Vol. 170, pp 405-512.
[16] R. F. WARMING, HYETT, 1974, The modified equation approach to the stability and accuracy analysis of finite-difference methods, J. Comp. Phys., 14, (2), p 159. Zbl0291.65023 MR339526 · Zbl 0291.65023 · doi:10.1016/0021-9991(74)90011-4
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.