High-Order Discontinuous Galerkin Methods for Computational Electromagnetics and Uncertainty Quantification

  • J. S. Hesthaven
  • T. Warburton
  • C. Chauviere
  • L. Wilcox
Conference paper
Part of the Mathematics in Industry book series (MATHINDUSTRY, volume 14)


We discuss the basics of discontinuous Galerkin methods (DG) for CEM as an alternative of emerging importance to the widely used FDTD. The benefits of DG methods include geometric flexibility, high-order accuracy, explicit time-advancement, and very high parallel performance for large scale applications. The performance of the scheme shall be illustrated by several examples. As an example of particular interest, we further explore efficient probabilistic ways of dealing with uncertainty and uncertainty quantification in electromagnetics applications. Whereas the discussion often draws on scattering applications, the techniques are applicable to general problems in CEM.


Discontinuous Galerkin Discontinuous Galerkin Method Radar Cross Section FDTD Method Perfect Electric Conductor 
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  1. 1.
    Cameron R.H., Martin, W.T.: The Orthogonal Development of Nonlinear Functionals in Series of Fourier-Hermite Functionals. Ann. Math. 48, 385–392 (1947)CrossRefMathSciNetGoogle Scholar
  2. 2.
    Chauvière, C., Hesthaven, J.S., Lurati, L.: Computational modeling of uncertainty in time-domain electromagnetics. SIAM J. Sci. Comput. 28, 751–775 (2006)zbMATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Chauvière, C., Hesthaven, J.S., Wilcox, L.: Efficient Computation of RCS from Scatters of Uncertain Shapes. IEEE Trans. Antennas Propagat. 55, 1437–1448 (2007)CrossRefGoogle Scholar
  4. 4.
    Hagstrom, T., Warburton, T.: A New Auxiliary Variable Formulation of High-Order Local Radiation Boundary Conditions: Corner Compatibility Conditions and Extensions to First Order Systems. Wave Motion (2007) – to appear.Google Scholar
  5. 5.
    Hesthaven, J.S., Warburton, T.: High-order nodal methods on unstructured grids. I. Time-domain solution of Maxwell’s equations. J. Comput. Phys. 181, 1–34 (2002)Google Scholar
  6. 6.
    Hesthaven, J.S., Warburton, T.: Discontinuous Galerkin methods for the time-domain Maxwell’s equations: An introduction. ACES Newsletter 19 10-29 (2004)Google Scholar
  7. 7.
    Hesthaven, J.S., Warburton, T.: High Order Nodal Discontinuous Galerkin Methods for the Maxwell Eigenvalue Problem. Royal Soc. London Ser A 362 493–524 (2004)zbMATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Hesthaven, J.S., Warburton, T.: Nodal Discontinuous Galerkin Methods: Algorithms, Analysis, and Applications. Springer Texts in Applied Mathematics 54, Springer Verlag, New York (2008)Google Scholar
  9. 9.
    Kreiss, H.O., Oliger, J.: Comparison of Accurate Methods for the Integration of Hyperbolic Problems. Tellus 24, 199–215 (1972)CrossRefMathSciNetGoogle Scholar
  10. 10.
  11. 11.
    Taflove, A.: Computational Electrodynamics. The Finite-Difference Time-Domain Method. Artech House, Boston (1995)zbMATHGoogle Scholar
  12. 12.
    Taflove, A. (Ed.): Advances in Computational Electrodynamics: The Finite-Difference Time-Domain Method. Artech House, Boston (1998)zbMATHGoogle Scholar
  13. 13.
    Volakis, J.L.: Benchmark Plate Radar Targets for the Validation of Computational Electromagnetics Programs. IEEE Antennas Propagat. Mag. 34, 52–56 (1992)CrossRefGoogle Scholar
  14. 14.
    Yee, K.S.: Numerical Solution of Initial Boundary Value Problems involving Maxwells Equations in Isotropic Media. IEEE Trans. Antennas Propag. 14, 302–307 (1966)zbMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • J. S. Hesthaven
    • 1
  • T. Warburton
    • 2
  • C. Chauviere
    • 3
  • L. Wilcox
    • 4
  1. 1.Division of Applied MathematicsBrown UniversityProvidenceUSA
  2. 2.Department of Computational and Applied MathematicsRice UniversityHoustonUSA
  3. 3.Laboratoire de MathématiquesUniversité Blaise PascalAubièreFrance
  4. 4.Institute for Computational Engineering and Sciences (ICES)University of Texas at AustinAustinUSA

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