A 3D Meshless Approach for Transient Electromagnetic PDEs

Conference paper
Part of the Mathematics in Industry book series (MATHINDUSTRY, volume 17)

Abstract

A full wave three dimensional meshless approach for electromagnetic transient simulations is presented. The smoothed particle hydrodynamic (SPH) method is used by considering the particles as interpolation points, arbitrarily placed in the computational domain. Maxwell’s equations in time domain with the assigned boundary and initial conditions are numerically solved by means of the proposed method. The computational tool is assessed and, for the first time, a 3D test problem is simulated in order to validate the proposed approach.

Keywords

Smooth Particle Hydrodynamic Smooth Particle Hydrodynamic Meshless Method Smoothing Kernel Smooth Particle Hydrodynamic Method 
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.

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References

  1. 1.
    Liu, G.R., Liu, M.B.: Smoothed Particle Hydrodynamics – A Mesh-Free Particle Method. World Scientific Publishing, Singapore (2003)Google Scholar
  2. 2.
    Laguna, P.: Smoothed particle interpolation. Astrophys. J. 439, 814–821 (1994)Google Scholar
  3. 3.
    Monaghan, J.J.: An introduction to SPH. Comp. Phys. Commun. 48, 89–96 (1988)Google Scholar
  4. 4.
    Liu, M.B., Liu, G.R., Lam, K.Y.: Constructing smoothing functions in smoothed particle hydrodynamics with applications. J. Comput. Appl. Math. 155, 263–284 (2003)Google Scholar
  5. 5.
    Belytschko, T., Krongauz, Y., Organ, D., Fleming, M., Krysl, P.: Meshless methods: An overview and recent developments. Comput. Meth. Appl. Mech. Eng. 139, 3–47 (1996)Google Scholar
  6. 6.
    Mirzaei, D., Dehghan, M.: A meshless based method for solution of integral equations. Appl. Numer. Math. 60(3), 245–262 (2010)Google Scholar
  7. 7.
    Monaghan, J.J., Lattanzio, J.C.: A refined particle method for astrophysical problems. Astron. Astrophys. 149, 135–143 (1985)Google Scholar
  8. 8.
    Monaghan, J.J.: Smoothed particle hydrodynamics. Annu. Rev. Astronom. Astrophys. 30, 543–574 (1992)Google Scholar
  9. 9.
    Liu, M.B., Liu, G.R.: Smoothed particle hydrodynamics (SPH): An overview and recent developments. Arch. Comput. Meth. Eng. 17(1), 25–76 (2010)Google Scholar
  10. 10.
    Ala, G., Spagnuolo, A., Viola, F.: An advanced gridless method for electromagnetic transient simulation. In: Proceedings of EMC Europe 2004, pp. 54–59 (2004)Google Scholar
  11. 11.
    Ala, G., Francomano, E., Tortorici, A., Toscano, E., Viola, F.: A smoothed particle interpolation scheme for transient electromagnetic simulation. IEEE Trans. Magn. 42(4), 647–650 (2006)Google Scholar
  12. 12.
    Ala, G., Francomano, E., Tortorici, A., Toscano E., Viola, F.: Smoothed particle electromagnetics: A mesh-free solver for transients. J. Comput. Appl. Math. 191(2), 194–205 (2006)Google Scholar
  13. 13.
    Ala, G., Francomano, E., Tortorici, A., Toscano, E., Viola, F.: A mesh-free particle method for transient full-wave simulation. IEEE Trans. Magn. 43(4), 1333–1336 (2007)Google Scholar
  14. 14.
    Ala, G., Francomano, E., Tortorici, A., Toscano, E., Viola, F.: Corrective meshless particle formulations for time domain Maxwell’s equations. J. Comput. Appl. Math. 210(1), 34–46 (2007)Google Scholar
  15. 15.
    Ala, G., Francomano, E., Tortorici, A., Toscano, E., Viola, F.: On the use of a meshless solver for PDEs governing electromagnetic transients. Appl. Math. Comput. 209(1), 42–51 (2009)Google Scholar
  16. 16.
    Liu, M.B., Liu, G.R.: Restoring particle consistency in smoothed particle hydrodynamics. Appl. Numer. Math. 56, 19–36 (2006)Google Scholar
  17. 17.
    Taflove, A., Hagness, S.: Computational Electrodynamics: The Finite-Difference Time-Domain Method. Artech House, Boston (2000)Google Scholar
  18. 18.
    Sullivan, D.M.: Electromagnetic Simulation Using the FDTD Method. IEEE press, New York (2000)Google Scholar
  19. 19.
    Elsherbeni, A., Demir, V.: The Finite-Difference Time-Domain Method for Electromagnetics with Matlab Simulations. SciTech Publishing, Raleigh (2009)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Guido Ala
    • 1
  • Elisa Francomano
    • 2
  • Antonino Spagnuolo
    • 1
  1. 1.Dipartimento di Ingegneria Elettrica, Elettronica e delle Telecomunicazioni, di Tecnologie Chimiche, Automatica e Modelli MatematiciUniversitá degli Studi di PalermoPalermoItaly
  2. 2.Dipartimento di Ingegneria Chimica, Gestionale, Informatica e MeccanicaUniversitá degli Studi di PalermoPalermoItaly

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