Comparison of Two Explicit Time Domain Unstructured Mesh Algorithms for Computational Electromagnetics

  • Igor Sazonov
  • Oubay Hassan
  • Ken Morgan
  • Nigel P. Weatherill
Part of the Computational Methods in Applied Sciences book series (COMPUTMETHODS, volume 16)

Summary

An explicit finite element time domain method and a co-volume approach, based upon a generalization of the well-known finite difference time domain scheme of Yee to unstructured meshes, are employed for the solution of Maxwell’s curl equations in the time domain. A stitching method is employed to produce meshes that are suitable for use with a co-volume algorithm. Examples, involving EM wave propagation and scattering, are included and the numerical performance of the two techniques is compared.

Key words

computational electromagnetics Delaunay triangulation Voronoï tessellation co-volume mesh generation explicit schemes finite element method co-volume method EM wave propagation and scattering 

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References

  1. Ber94.
    J.-P. Berenger. A perfectly matched layer for absorption of electromagnetic waves. J. Comput. Phys., 114:185–200, 1994.MATHCrossRefADSMathSciNetGoogle Scholar
  2. BP97.
    F. Bonnet and F. Poupaud. Berenger absorbing boundary condition with time finite-volume scheme for triangular meshes. Appl. Numer. Math., 25:333–354, 1997.MATHCrossRefMathSciNetGoogle Scholar
  3. CFS93.
    J. P. Cioni, L. Fezoui, and H. Steve. A parallel time-domain Maxwell solver using upwind schemes and triangular meshes. Impact Comput. Sci. Engrg., 5:215–247, 1993.MATHCrossRefMathSciNetGoogle Scholar
  4. DBB99.
    A. Deraemaeker, I. Babuška, and P. Bouillard. Dispersion and pollution of the FEM solution for the Helmholtz equation in one, two and three dimensions. Internat. J. Numer. Methods Engrg., 46:471–499, 1999.MATHCrossRefGoogle Scholar
  5. DH03.
    J. Donéa and A. Huerta. Finite element methods for flow problems. John Wiley & Sons, 2003.Google Scholar
  6. DL97.
    E. Darve and R. Löhner. Advanced structured-unstructured solver for electromagnetic scattering from multimaterial objects. AIAA Paper 97–0863, Washington, 1997.Google Scholar
  7. EHM+03.
    M. El hachemi, O. Hassan, K. Morgan, D. P. Rowse, and N. P. Weatherill. Hybrid methods for electromagnetic scattering simulations on overlapping grids. Comm. Numer. Methods Engrg., 19:749–760, 2003.MATHCrossRefGoogle Scholar
  8. EL02.
    F. Edelvik and G. Ledfelt. A comparison of time-domain hybrid solvers for complex scattering problems. Internat. J. Numer. Model.: Elect. Net. Dev. Fields, 15:475–487, 2002.MATHCrossRefGoogle Scholar
  9. Geo91.
    P. L. George. Automatic mesh generation. Applications to finite element methods. John Wiley & Sons, 1991.Google Scholar
  10. GL93.
    S. Gedney and F. Lansing. Full wave analysis of printed microstrip devices using a generalized Yee algorithm. In Proceedings of the IEEE Antenas and Propagation Society International Symposium, pages 1179–1182, Ann Arbor, 1993. Pennsylvania State University.CrossRefGoogle Scholar
  11. LMHW02.
    P. D. Ledger, K. Morgan, O. Hassan, and N. P. Weatherill. Arbitrary order edge elements for electromagnetic scattering simulations using hybrid meshes and a PML. Internat. J. Numer. Methods Engrg., 55:339–358, 2002.MATHCrossRefGoogle Scholar
  12. Mad95.
    N. Madsen. Divergence preserving discrete surface integral methods for Maxwell’s equations using nonorthogonal unstructured grids. J. Comput. Phys., 119:35–45, 1995.CrossRefADSMathSciNetGoogle Scholar
  13. MHP94.
    K. Morgan, O. Hassan, and J. Peraire. An unstructured grid algorithm for the solution of Maxwell’s equations in the time domain. Internat. J. Numer. Methods Fluids, 19:849–863, 1994.MATHCrossRefADSGoogle Scholar
  14. MHP96.
    K. Morgan, O. Hassan, and J. Peraire. A time domain unstructured grid approach to the simulation of electromagnetic scattering in piecewise homogeneous media. Comput. Methods Appl. Mech. Engrg., 134:17–36, 1996.MATHCrossRefGoogle Scholar
  15. MHPW00.
    K. Morgan, O. Hassan, N. E. Pegg, and N. P. Weatherill. The simulation of electromagnetic scattering in piecewise homogeneous media using unstructured grids. Comput. Mech., 25:438–447, 2000.MATHCrossRefGoogle Scholar
  16. MM98.
    A. Monorchio and R. A. Mittra. A hybrid finite-element/finite-difference (FE/FDTD) technique for solving complex electromagnetic problems. IEEE Microwave Guided Wave Lett., 8:93–95, 1998.CrossRefGoogle Scholar
  17. MSH91.
    A. H. Mohammadian, V. Shankar, and W. F. Hall. Computation of electromagnetic scattering and radiation using a time-domain finite-volume discretization procedure. Comput. Phys. Comm., 68:175–196, 1991.CrossRefADSGoogle Scholar
  18. MWH+99.
    K. Morgan, N. P. Weatherill, O. Hassan, P. J. Brookes, R. Said, and J. Jones. A parallel framework for multidisciplinary aerospace engineering simulations using unstructured meshes. Internat. J. Numer. Methods Fluids, 31:159–173, 1999.MATHCrossRefADSGoogle Scholar
  19. NW98.
    R. A. Nicoladies and Q.-Q. Wang. Convergence analysis of a co-volume scheme for Maxwell’s equations in three dimensions. Math. Comp., 67:947–963, 1998.CrossRefADSMathSciNetGoogle Scholar
  20. PLeD92.
    B. Petitjean, R. Löhner, and C. R. Devore. Finite element solvers for radar cross section RCS calculations. AIAA Paper 92–0455, Washington, 1992.Google Scholar
  21. PPM99.
    J. Peraire, J. Peiró, and K. Morgan. Advancing front grid generation. In J. F. Thompson, B. K. Soni, and N. P. Weatherill, editors, Handbook of Grid Generation, pages 17.1–17.22. CRC Press, 1999.Google Scholar
  22. RB00.
    T. Rylander and A. Bondeson. Stable FEM–FDTD hybrid method for Maxwell’s equations. Comput. Phys. Comm., 125:75–82, 2000.MATHCrossRefADSMathSciNetGoogle Scholar
  23. RBT97.
    W. Ruey-Beei and I. Tatsuo. Hybrid finite-difference time-domain modeling of curved surfaces using tetrahedral edge elements. IEEE Trans. Antennas and Propagation, 45:1302–1309, 1997.CrossRefGoogle Scholar
  24. SWH+06.
    I. Sazonov, D. Wang, O. Hassan, K. Morgan, and N. P. Weatherill. A stitching method for the generation of unstructured meshes for use with co-volume solution techniques. Comput. Methods Appl. Mech. Engrg., 195:1826–1845, 2006.MATHCrossRefMathSciNetGoogle Scholar
  25. TH00.
    A. Taflove and S. C. Hagness. Computational electrodynamics: The finite-difference time domain method. Artech House, Boston, 2nd edition, 2000.MATHGoogle Scholar
  26. WH94.
    N. P. Weatherill and O. Hassan. Efficient three-dimensional Delaunay triangulation with automatic point creation and imposed boundary constraints. Internat. J. Numer. Methods Engrg., 37:2005–2040, 1994.MATHCrossRefGoogle Scholar
  27. Yee66.
    K. S. Yee. Numerical solution of initial boundary value problem involving Maxwell’s equation in isotropic media. IEEE Trans. Antennas and Propagation, 14:302–307, 1966.MATHCrossRefADSGoogle Scholar
  28. ZM06.
    O. C. Zienkiewicz and K. Morgan. Finite elements and approximation. Dover, 2006.Google Scholar

Copyright information

© Springer Science + Business Media B.V. 2008

Authors and Affiliations

  • Igor Sazonov
    • 1
  • Oubay Hassan
    • 1
  • Ken Morgan
    • 1
  • Nigel P. Weatherill
    • 1
  1. 1.Civil and Computational Engineering Centre, School of EngineeringUniversity of WalesSwanseaUK

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