Abstract
In this paper we demonstrate the efficiency of using the discontinuous Galerkin method for simulating electromagnetic scattering problems using Maxwell’s equations. We show that it is possible to use unstructured hp-finite elements in mixed-element (polymorphic) grids. We include examples of scattering from a two-dimensional cylinder and preliminary results from a three-dimensional F15 geometry.
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References
Baumann C.E. and Oden J. T. The Discontinuous Galerkin Method Applied to CFD Problems. In SIAM 45th Anniversary Meeting, High order methods for compressible flow calculations, July 14–18 1997.
Bey K.S. and Oden J.T. hp-Version discontinuous Galerkin methods for hyperbolic conservation laws Comp. Meth. Appl. Mech. Eng.,133:259–286, 1996
Bowman J.J., Senior T.B.A, and Uslenghi P.L.E. Electromagnetic and Acoustic Scattering by Simple Shapes. Hemisphere Publishing Corporation, 1987.
Cockburn B. and Shu C.-W. TVB Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws II: General framework. Math. Comp., 52: 411–435, 1989.
Cockburn B. and Shu C.-W. The Runge-Kutta discontinuous Galerkin method for conservation laws V: multidimensional systems. J. of Comp. Phys., 141: 199–224, 1998.
Dubiner M. Spectral methods on triangles and other domains. J. Sci. Comp.,6:345, 1991.
Karniadakis G. E. and Sherwin S. J. Spectral hpElement Methods for CFD. Oxford University Press, 1999.
Koornwinder T. Two-variable analogues of the classical orthogonal polynomials. In Askey R.A., editor, Theory and Applications of Special Functions. Academic Press, 1975.
Kopriva D.A., Woodruff S.L. and Hussaini M.Y. Discontinuous Spectral Element Approximation of Maxwell’s Equation International Symposium on Discontinous Galerkin Methods, Salve Regina University May 24–26, 1999
Lomtev I., Quillen C.B., and Karniadakis G. E. Spectral/hp methods for viscous compressible flows on unstructured 2d meshes. J. Comp. Phys., in press, 1998.
Owens R.G. Spectral approximations on the triangle. Proc. R. Sec. Lond. A, 1997. Submitted.
Proriol J. Sur une famille de polynomes á deux variables orthogonaux dans un triangle. C.R. Acad. Sci. Paris, 257: 2459–2461, 1957.
Reed W.H, and Hill T.R. Triangular mesh methods for the neutron transport equation Los Alamos Scientific Laboratory report LA-UR-73–479, Los Alamos, NM, 1973
Sherwin S.J. Hierarchical hp finite elements in hybrid domains. Finite Elements in Analysis and Design,27:109–119, 1997.
Warburton T.C.E. Spectral/hp Methods on Polymorphic Domains. PhD thesis, Brown University, Division of Applied Mathematics, in progress.
Wingate B. A. and Taylor M. A. The natural function space for triangular and tetrahedral spectral elements. 1998. submitted to SIAM J. Num. Anal.
Yang B., Gottlieb D., and Hesthaven J.S. Spectral simulations of electromagnetic wave scattering. J. Comput. Phys1997.
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Warburton, T. (2000). Application of the Discontinuous Galerkin Method to Maxwell’s Equations Using Unstructured Polymorphic hp-Finite Elements. In: Cockburn, B., Karniadakis, G.E., Shu, CW. (eds) Discontinuous Galerkin Methods. Lecture Notes in Computational Science and Engineering, vol 11. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-59721-3_47
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DOI: https://doi.org/10.1007/978-3-642-59721-3_47
Publisher Name: Springer, Berlin, Heidelberg
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