Abstract
The main distinction between one-dimensional and multi-dimensional hyperbolic systems is that in the case of the latter information propagates in an infinite number of directions. In this paper we present a new class of bicharacteristic methods which take all the infinitely many directions of propagation into account. The principal issue involved in constructing bicharacteristic methods reduces to evolving the system of equations approximately along the bicharacteristics. For the spatial approximation we mainly concentrate on a discontinuous Galerkin finite element discretisation. We exemplify the technique on Maxwell’s equations with constant coefficients in two space dimensions.
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References
Butler D S (1960). The Numerical Solution of Hyperbolic Systems of Partial Differential Equations in Three Independent Variables. Proceeding of the Royal Society of London, Series A. Mathematical and Physical Sciences, 255.
Chushkin P I (1968). Numerical Method of Characteristics for Three-Dimensional Supersonic Flows, Progress in Aeronautical Science, 9.
Cline M C and Hoffman J D (1972). Comparison of Characteristic Schemes for Three-dimensional, Steady, Isentropic Flow. AIAA Journal, 10.
Holt M (1956). The Methods of Characteristics for Steady Supersonic Rotational Flow in Three Dimensions, Journal of Fluid Mechanics, 1.
Lukáčová-Medvid’ová M, Morton K W and Warnecke G (2000). Evolution Galerkin Methods for Hyperbolic Systems in Two Space Dimensions, Mathematics of Computation (to appear).
Ostkamp S (1995). Multidimensional Characteristic Galerkin Schemes and Evolution Operators for Hyperbolic Systems. Ph.D. thesis, Universität Hannover.
Reddy A S, Tikekar V G and Prasad P (1982). Numerical Solution of Hyperbolic Equations by Methods of Bicharacteristic. Journal of Mathematical and Physical Sciences, 6.
Roe P (1998). Linear Bicharacteristic Schemes without Dissipation. Siam Journal on Scientific Computing, 19.
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© 2001 Springer Science+Business Media New York
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Pham, M.H., Rudgyard, M., Süli, E. (2001). Bicharacteristic Methods for Multi-Dimensional Hyperbolic Systems. In: Toro, E.F. (eds) Godunov Methods. Springer, New York, NY. https://doi.org/10.1007/978-1-4615-0663-8_70
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DOI: https://doi.org/10.1007/978-1-4615-0663-8_70
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4613-5183-2
Online ISBN: 978-1-4615-0663-8
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