×

zbMATH — the first resource for mathematics

Computation of electromagnetic scattering with a non-conforming discontinuous spectral element method. (English) Zbl 0994.78020
Summary: We solve electromagnetic scattering problems by approximating Maxwell’s equations in the time-domain with a high-order quadrilateral discontinuous spectral element method. The method is a collocation form of the discontinuous Galerkin method for hyperbolic systems where the solution is approximated by a tensor product Legendre expansion and inner products are replaced with Gauss-Legendre quadratures. To increase flexibility of the method, we use a mortar element method to couple element faces. Mortars provide a means for coupling element faces along which the polynomial orders differ, which allows the flexibility to choose the approximation order within an element by considering only local resolution requirements. Mortars also permit local subdivision of a mesh by connecting element faces that do not share a full side. We present evidence showing that the convergence of the non-conforming approximations is spectral along with examples of their use.

MSC:
78M25 Numerical methods in optics (MSC2010)
78A45 Diffraction, scattering
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Discontinuous spectral element approximation of Maxwell’s Equations. In Proceedings of the International Symposium on Discontinuous Galerkin Methods, New York, May, (eds). Springer: Berlin, 2000. · Zbl 0957.78023
[2] Mohammadian, Computer Physics Communications 68 pp 175– (1991)
[3] Fang, Journal of Computational Physics 151 pp 921– (1999) · Zbl 0933.65113
[4] Some remarks on the accuracy of the Discontinuous Galerkin Method. In Proceedings of the International Symposium on Discontinuous Galerkin Methods, New York, May, (eds). Springer: Berlin, 1999.
[5] On the mortar element method: generalization and implementation. Proceedings of the 3rd International Conference on Domain Decomposition Methods for Partial Differential Equations, 1990.
[6] A new nonconforming approach to domain decomposition: the mortar element method. In Nonlinear Partial Differential Equations and their Applications, (eds). Pitman: New York, 1994;13-51. · Zbl 0797.65094
[7] Funaro, Numerical Mathematics 52 pp 329– (1988) · Zbl 0637.65077
[8] Non-conforming mortar element methods: application to spectral discretizations. In Domain Decomposition Methods, (eds). SIAM: Philadelphia, 1989; 392-418.
[9] Kopriva, Journal of Computational Physics 128 pp 475– (1996) · Zbl 0866.76064
[10] Kopriva, Journal of Computational Physics 143 pp 125– (1998) · Zbl 0921.76121
[11] Lomtev, Journal of Computational Physics 144 pp 325– (1998) · Zbl 0929.76095
[12] Spectral Methods in Fluid Dynamics. Springer: New York, 1987. · Zbl 0636.76009
[13] Patera, Journal of Computational Physics 54 pp 468– (1984) · Zbl 0535.76035
[14] Williamson, Journal of Computational Physics 35 pp 48– (1980) · Zbl 0425.65038
[15] Fourth-order 2N-storage Runge-Kutta schemes. Technical Report NASA TM 109111, 1994.
[16] Stanescu, Journal of Computational Physics 143 pp 674– (1998) · Zbl 0952.76063
[17] Kopriva, Journal of Computational Physics 125 pp 244– (1996) · Zbl 0847.76069
[18] Stanescu, AIAA Journal 37 pp 296– (1999)
[19] Hesthaven, Journal of Computational Physics 142 pp 216– (1998) · Zbl 0933.76063
[20] Yang, Journal of Computational Physics 134 pp 216– (1997) · Zbl 0883.65098
[21] Nonconforming discretizations and a posterior error estimates for adaptive spectral element techniques. Ph.D. Thesis, MIT, Cambridge, MA, 1989.
[22] Classical Electrodynamics (2nd edn). Wiley: New York, 1975. · Zbl 0997.78500
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.