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Berenger absorbing boundary condition with time finite-volume scheme for triangular meshes. (English) Zbl 0888.65132

The study of scattering problems gives an exterior problem. To solve this problem numerically, two methods to absorb the outgoing waves if the problem is posed in a bounded domain, are frequently used. The first one consists of finding an absorbing boundary condition on the artificial boundary, the second one consists of surrounding the computational domain with an artificial absorbing layer, in which artificial boundary layer equations allow to decrease parasitic reflections of the electromagnetic field. The second method was recently generalized by J.-P. Berenger [J. Comput. Phys. 114, No. 2, 185-200 (1994; Zbl 0814.65129)].
The authors present an extension of the Berenger perfectly matched absorbing layer, initially used for finite difference time domains, to a time finite volume scheme for triangular meshes. The presented method allows the authors to solve scattering problems numerically in an artifically bounded domain.

MSC:

65Z05 Applications to the sciences
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
35Q60 PDEs in connection with optics and electromagnetic theory
78A45 Diffraction, scattering

Citations:

Zbl 0814.65129
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References:

[1] Bendali, A.; Halpern, L., Conditions aux limites absorbantes pour le système de Maxwell dans le vide en dimension trois, C. R. Acad. Sci. Paris Ser. I Math., 307, 20 (1988) · Zbl 0692.35062
[2] Berenger, J. P., A perfectly matched layer for the absorption of electromagnetic waves, J. Comput. Phys., 114, 185-200 (1994) · Zbl 0814.65129
[3] J.P. Berenger, A perfectly matched layer for free-space simulation in finite-difference computer codes, Annales des Télécommunications; J.P. Berenger, A perfectly matched layer for free-space simulation in finite-difference computer codes, Annales des Télécommunications
[4] Cioni, J. P., Résolution numérique de équations de Maxwell instationnaires par une méthode de volumes finis, (Thèse (1995), Université de Nice Sophia-Antipolis) · Zbl 1428.35564
[5] J.P. Cioni, L. Fezoui and D. Issautier, High-order upwind schemes for solving time-domain Maxwell equation, Rech. Aérospat.; J.P. Cioni, L. Fezoui and D. Issautier, High-order upwind schemes for solving time-domain Maxwell equation, Rech. Aérospat. · Zbl 0874.76061
[6] Cioni, J. P.; Fezoui, L.; Steve, H., A parallel time-domain Maxwell solver using upwind schemes and triangular meshes, Impact Comput. Sci. Engrg., 165 (1993) · Zbl 0788.65119
[7] Collino, F., Conditions absorbantes d’ordre élevé pour les équations de Maxwell dans des domaines rectangulaires, (Rapport No. 1991 (1993), INRIA)
[8] de la Bourdonnaye, A., Sur le problème de Cauchy pour le système de Bérenger, C. R. Acad. Sci. Paris Ser. I Math., 322, 285-288 (1996) · Zbl 0844.65091
[9] Dervieux, A., Steady Euler simulations using unstructured meshes, Coursau Von Karman Institute, Lectures Series 85-04 (1985)
[10] Desideri, J. A.; Goudjo, A.; Selmin, V., Third-order numerical schemes for hyperbolic problems, (Rapport de Recherche No. 607 (1987), INRIA Sophia-Antipolis)
[11] Fezoui, L., Résolution des équations d’Euler par un schéma de Van Leer en éléments finis, (Rapport de Recherche No. 358 (1985), INRIA)
[12] Fezoui, L.; Stoufflet, B., A class of implicit upwind schemes for Euler simulations with unstructured meshes, J. Comput. Phys., 84, 174-206 (1989) · Zbl 0677.76062
[13] Gribbons, M.; Lee, S. K.; Cangellaris, A. C., Modification of Berenger’s perfectly matched layer for the absorption of electromagnetic waves in layered media, (Proceedings 11th Annual Review of Progress in Applied Computational Electromagnetics. Proceedings 11th Annual Review of Progress in Applied Computational Electromagnetics, Monterey (1995))
[14] Harrington, R. F., Time Harmonic Electromagnetic Fields (1961), McGraw-Hill
[15] Joly, P., Equations de Maxwell et ondes électromagnétiques, quelques aspects mathématiques et numériques (1989), Cours INRIA,: Cours INRIA, Rocquencourt
[16] Joly, P.; Mercier, B., Une nouvelle condition transparente d’ordre deux pour les équations de Maxwell en dimension trois, (Rapport No. 1047 (1989), INRIA)
[17] Katz, D. S.; Thiele, E. T.; Taflove, A., Validation and extension to three dimensions of the Berenger PML absorbing boundary condition for fd-td meshes, IEEE Microwave and Guided Wave Letters, 4, 268-270 (1994)
[18] Kingsland, D. M.; Sacks, Z. S.; Lee, J. F., Perfectly matched anisotropic absorbers for finite element, application in electromagnetics, (Proceedings 11th Annual Review of Progress in Applied Computational Electromagnetics. Proceedings 11th Annual Review of Progress in Applied Computational Electromagnetics, Monterey (1995))
[19] Lax, P. D.; Harten, A.; Van Leer, B., On upstream differencing and Godunov type schemes for hyperbolic conservation laws, SIAM Rev., 25, 1 (1983) · Zbl 0565.65051
[20] Oumansour, A., Conditions aux limites absorbantes pour l’équation de Maxwell en dimension trois (1989), Institut de Mathématiques U.S.T.H.B.,: Institut de Mathématiques U.S.T.H.B., Alger
[21] Sesques, M., Conditions aux limites artificielles pour le système de Maxwell, (Thèse (1990), Université de Bordeaux I)
[22] Yee, K., Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media, IEEE Trans. Antennas and Propagation (1966) · Zbl 1155.78304
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