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A \(p\)-strategy with a local time-stepping method in a discontinuous Galerkin approach to solve electromagnetic problems. (English) Zbl 1309.78008

The present paper is concerned with a \(p\)-strategy with a local time-stepping strategy for a particular discontinuous Galerkin method to solve Maxwell’s equations in the time domain. The authors use a method based on the frequency spectrum of the source and on a characteristic size of the cells in order to evaluate the spatial approximation order to be applied on each cell of the mesh. The stability of the method is also studied, and a stability condition is also established. In the final part of this paper, the method is applied to study the electromagnetic fields scattered by a 3D object typical of aeronautic applications.

MSC:

78M20 Finite difference methods applied to problems in optics and electromagnetic theory
78M10 Finite element, Galerkin and related methods applied to problems in optics and electromagnetic theory
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
35Q61 Maxwell equations
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References:

[1] G. Cohen, X. Ferrieres, and S. Pernet, “A spatial high-order hexahedral discontinuous Galerkin method to solve Maxwell’s equations in time domain,” Journal of Computational Physics, vol. 217, no. 2, pp. 340-363, 2006. · Zbl 1160.78004
[2] E. Montseny, S. Pernet, X. Ferriéres, and G. Cohen, “Dissipative terms and local time-stepping improvements in a spatial high order Discontinuous Galerkin scheme for the time-domain Maxwell’s equations,” Journal of Computational Physics, vol. 227, no. 14, pp. 6795-6820, 2008. · Zbl 1144.78330
[3] M. Dumbser, M. Käser, and E. F. Toro, “An arbitrary high-order Discontinuous Galerkin method for elastic waves on unstructured meshes-V. Local time stepping and p-adaptivity,” Geophysical Journal International, vol. 171, no. 2, pp. 695-717, 2007.
[4] A. Taube, M. Dumbser, C.-D. Munz, and R. Schneider, “A high-order discontinuous Galerkin method with time-accurate local time stepping for the Maxwell equations,” International Journal of Numerical Modelling, vol. 22, no. 1, pp. 77-103, 2009. · Zbl 1156.78012
[5] S. Pernet, Étude de méthodes d’ordre élevé pour résoudre les équations de Maxwell dans le domaine temporel. Application à la détection et à la compatibilité électromagnétique [Ph.D. thesis], Université de Paris IX, 2004.
[6] J.-P. Berenger, “Three-dimensional perfectly matched layer for the absorption of electromagnetic waves,” Journal of Computational Physics, vol. 127, no. 2, pp. 363-379, 1996. · Zbl 0862.65080
[7] G. Cohen and P. Monk, “Mur-Nédélec finite element schemes for Maxwell’s equations,” Computer Methods in Applied Mechanics and Engineering, vol. 169, no. 3-4, pp. 197-217, 1999. · Zbl 0956.78008
[8] G. C. Cohen, Higher-Order Numerical Methods for Transient Wave Equations, Springer, Berlin, Germany, 2002. · Zbl 0985.65096
[9] K. S. Yee, “Numerical solution of initial boundary value problem involving Maxwell’s equations in isotropic media,” IEEE Transactions on Antennas and Propagation, vol. AP-14, no. 3, pp. 302-307, 1966. · Zbl 1155.78304
[10] A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, Artech House, 3rd edition, 2005. · Zbl 0963.78001
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