Advertisement

Finite Integration Method and Discrete Electromagnetism

  • Thomas Weiland
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 28)

Summary

We review some basic properties of the Finite Integration Technique (FIT), a generalized finite difference scheme for the solution of Maxwell’s equations. Special emphasis is put on its relations to the Finite Difference Time Domain (FDTD) method, as both algorithms are found to be computationally equivalent for the special case of an explicit time-stepping scheme with Cartesian grids. The more general discretization approach of the FIT, however, inherently includes an elegant matrix-vector notation, which enables the application of powerful tools for the analysis of consistency, stability, and other issues. On the implementation side this leads to many important consequences concerning the basic method as well as all kinds of extensions.

Keywords

Finite Difference Time Domain Cartesian Grid Dual Facet Finite Integration Finite Integration Technique 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    K.S. Yee, Numerical Solution of Initial Boundary Value Problems Involving Maxwell’s Equations in Isotropic Media, IEEE Transactions on Antennas and Propagation, Vol.14 (1966), pp. 302–307.zbMATHGoogle Scholar
  2. 2.
    T. Weiland, A Discretization Method for the Solution of Maxwell’s Equations for Six-Component Fields, Electronics and Communication(AEU), Vol.31 (1977), pp. 116.Google Scholar
  3. 3.
    T. Weiland: On the Numerical Solution of Maxwell’s Equations and Applications in Accelerator Physics, Particle Accelerators, Vol. 15 (1984), pp. 245–291.Google Scholar
  4. 4.
    T. Weiland: Time Domain Electromagnetic Field Computation with Finite Difference Methods, International Journal of Numerical Modelling, Vol. 9 (1996), pp. 295–319.CrossRefGoogle Scholar
  5. 5.
    U. v. Rienen, T. Weiland, Triangular Discretization Method for the Evaluation of RF-Fields in Cylindrically Symmetric Cavities, IEEE Transactions on Magnetics, Vol. 21 (1985), pp. 2317–2320.CrossRefGoogle Scholar
  6. 6.
    R. Schuhmann, P. Schmidt, T. Weiland: A New Whitney-based Material Operator for the Finite Integration Technique on Triangular Grids, accepted for publication in IEEE Transactions on Magnetics (2002)Google Scholar
  7. 7.
    I. Munteanu: The Finite Volume Method for Electromagnetic Field Analysis in the Time Domain, Revue Roumaine des Sciences Techniques — lectrotechnique et nergtique, Vol. 42, No. 3 (1997), pp. 321–336.Google Scholar
  8. 8.
    M. Hano, T. Itoh: Three-Dimensional Time Domain Method for Solving Maxwell’s Equations based on Circumcenters of Elements, IEEE Transactions on Magnetics, Vol. 32, No. 3 (1996), pp. 946–949.CrossRefGoogle Scholar
  9. 9.
    R. Schuhmann, T. Weiland: Stability of the FDTD Algorithm on Nonorthogonal Grids Related to the Spatial Interpolation Scheme, IEEE Transactions on Magnetics, Vol. 34, No. 5 (1998), pp. 2751–2754.CrossRefGoogle Scholar
  10. 10.
    B. Krietenstein, R. Schuhmann, P. Thoma, T. Weiland: The Perfect Boundary Approximation Technique Facing the Big Challenge of High Precision Field Computation, Proceedings of the XIX International Linear Accelerator Conference (LINAC), Chicago, USA (1998), pp. 860–862.Google Scholar
  11. 11.
    A. Bossavit, L. Kettunen: Yee-Like Schemes on Staggered Cellular Grids: A Synthesis Between FIT and FEM Approaches, IEEE Transactions on Magnetics, Vol. 36, No. 4 (2000), pp. 861–867.CrossRefGoogle Scholar
  12. 12.
    J.A. Kong, F.L. Teixeira (ed.): Geometric Methods for Computational Electromagnetics, Progress In Electromagnetics Research (PIER) Monograph Series, Vol. 32, EMW Publishing, Cambridge, USA, 2001.Google Scholar
  13. 13.
    M. Clemens, R. Schuhmann, T. Weiland: Algebraic Properties and Conservation Laws in the Discrete Electromagnetism, Frequenz, Vol. 53, No. 11-12 (1999),pp. 219–225.CrossRefGoogle Scholar
  14. 14.
    S. Gutschling, H. Krger, T. Weiland: Time Domain Simulation of Dispersive Media with the Finite Integration Technique, International Journal of Numerical Modelling, Vol. 13, No. 4 (2000), pp. 329–348.zbMATHCrossRefGoogle Scholar
  15. 15.
    H. Spachmann, S. Gutschling, H. Krger, T. Weiland: FIT-Formulation for Nonlinear Dispersive Media, International Journal of Numerical Modelling, Special Issue, Vol. 12, No. 1/2 (1999), pp. 81–92.zbMATHCrossRefGoogle Scholar
  16. 16.
    T. Weiland, H. Krger, H. Spachmann: FIT-Formulation for Gyrotropic Media, International Conference on Electromagnetics in Advanced Applications (ICEAA), Torino, Italy (1999), pp. 737–740.Google Scholar
  17. 17.
    S. Drobny, T. Weiland: Iterative Algorithms For Nonlinear Transient Electromagnetic Field Calculation. Studies in Applied Electromagnetics and Mechanics, Vol. 18 (2000), IOS Press, pp. 385–388.Google Scholar
  18. 18.
    M. Clemens, T. Weiland: Discrete Electromagnetism with the Finite Integration Technique, Progress In Electromagnetics Research (PIER) Monograph Series, Vol. 32 (2001), pp. 65–87.CrossRefGoogle Scholar
  19. 19.
    R. Schuhmann, T. Weiland: Conservation of Discrete Energy and Related Laws in the Finite Integration Technique, Progress In Electromagnetics Research (PIER) Monograph Series, Vol. 32 (2001), pp. 301–316.CrossRefGoogle Scholar
  20. 20.
    A. Taflove, K.R. Umashankar, B. Beker, F.A. Harfoush, K.S. Yee: Detailed FDTD Analysis of Electromagnetic Fields Penetrating Narrow Slots and Lapped Joints in Thick Conducting Screens, IEEE Transactions on Antennas and Propagation, Vol. 36, No. 2 (1988), pp. 247–257.CrossRefGoogle Scholar
  21. 21.
    T.G. Jürgens, A. Taflove, K. Umashankar, T.G. Moore: Finite-Difference Time-Domain Modeling of Curved Surfaces, IEEE Transactions on Antennas and Propagation, Vol. 40, No. 4 (1992), pp. 357–366.CrossRefGoogle Scholar
  22. 22.
    S. Gedney, J.A. Roden: Well posed non-orthogonal FDTD methods, Digest of the IEEE Antennas and Propagation Society International Symposium (AP-S), Atlanta, Vol. 1 (1998), pp. 596–599.Google Scholar
  23. 23.
    R. Schuhmann, M. Hilgner, T. Weiland: Convergence Properties of the Nonorthogonal FDTD Algorithm. Proceedings of the 2000 USNC/URSI National Radio Science Meeting, Salt Lake City, USA (2000), p. 22.Google Scholar
  24. 24.
    I.S. Kim, W.J.R. Hoefer: A Local Mesh Refinement Algorithm for the Time Domain-Finite Difference Method Using Maxwell’s Curl Equations, IEEE Transactions on Microwave Theory and Techniques, Vol. 38, No. 6 (1990), pp. 812–815CrossRefGoogle Scholar
  25. 25.
    M. Okoniewski, E. Okoniewska, M.A. Stuchly: Three-dimensional Subgridding Algorithm for FDTD, IEEE Transactions on Antennas and Propagation, Vol. 45, No. 3 (1997), pp. 1512–1517.CrossRefGoogle Scholar
  26. 26.
    N. Chavannes, N. Küster: Numerical Optimization of EM Transmitters in Complex Environments by Application of a Novel FDTD Subgrid Scheme, Proceedings of the 2000 USNC/URSI National Radio Science Meeting, Salt Lake City, USA (2000), p. 86.Google Scholar
  27. 27.
    P. Thoma, T. Weiland: A Subgridding Method in Combination with the Finite Integration Technique, Proceedings of the 25th European Microwave Conference, Vol. 2 (1995), p. 770–774.Google Scholar
  28. 28.
    H. Spachmann, R. Schuhmann, T. Weiland: Higher Order Spatial Operators for the Finite Integration Theory, submitted to: ACES Journal, Special Issue on ‘Approaches to Better Accuracy / Resolution in Computational Electromagnetics’ (2001).Google Scholar
  29. 29.
    P. Thoma, T. Weiland: Numerical Stability of Finite Difference Time Domain Methods, IEEE Transactions on Magnetics, Vol. 34, No. 5 (1998), pp. 2740–2743.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Thomas Weiland
    • 1
  1. 1.Faculty of Electrical Engineering and Information TechnologyTechnische Universitt DarmstadtGermany

Personalised recommendations