Discretization via the Galerkin Method of Moments

  • Harold A. Sabbagh
  • R. Kim Murphy
  • Elias H. Sabbagh
  • John C. Aldrin
  • Jeremy S. Knopp
Part of the Scientific Computation book series (SCIENTCOMP)


We will discretize (3.22) by employing Galerkin’s method, which uses the same vector functions for expansion and testing. The spatial derivatives that cause problems will be removed by the testing process. In order to test these derivatives, we introduce special vector expansion functions, called “facet elements” and “edge elements,” that comprise products of pulse and tent functions.


Conjugate Gradient Discrete Fourier Transform Edge Element Tent Function Magnetic Equation 
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  1. 30.
    Rao, S.M., Wilton, D.R., Glisson, A.W.: Electromagnetic scattering by surfaces of arbitrary shape. IEEE Trans. Antenn. Propag. AP-30(3), 409–418 (May 1982)Google Scholar
  2. 31.
    Aubin, J-P.: Approximation of Elliptic Boundary-Value Problems. Wiley-Interscience, New York (1972)Google Scholar
  3. 32.
    Glisson, A.W., Wilton, D.R.: Simple and efficient numerical methods for problems of electromagnetic radiation and scattering from surfaces. IEEE Trans. Antenn. Propag. AP-29, 593–603 (1980)Google Scholar
  4. 33.
    Wertgen, W., Jansen, R.H.: Efficient direct and iterative electrodynamic analysis of geometrically complex MIC and MMIC structures. Int. J. Numer. Model. Electron. Network. Dev. Field. 2(3), 153–186 (September 1989)Google Scholar
  5. 36.
    Catedra, M.F., Gago, E., Nuño, L.: A numerical scheme to obtain the RCS of three-dimensional bodies of resonant size using the conjugate gradient method and the fast Fourier transform. IEEE Trans. Antenn. Propag. 37(5), 528–537 (May 1989)Google Scholar
  6. 37.
    Peter, A., Zwamborn, M., van den Berg, P.M., Mooibroek, J., Koenis, F.T.C.: Computation of three-dimensional electromagnetic-field distributions in a human body using the weak form of the CGFFT method. Appl. Comput. Electrom. 7(2), 26–42 (Winter 1992)Google Scholar
  7. 38.
    Zwamborn, P., van den Berg, P.M.: The three-dimensional weak form of the conjugate gradient FFT method for solving scattering problems. IEEE Trans. Microw. Theor. Tech. 40(9), 1757–1766 (September 1992)Google Scholar
  8. 39.
    Sabbagh, H.A.: Splines and their reciprocal-bases in volume-integral equations. IEEE Trans. Magn. 29(6), 4142–4152 (November 1993)Google Scholar
  9. 41.
    Dongarra, J.J., Moler, C.B., Bunch, J.R., Stewart, G.W.: LINPACK Users’ Guide. Society for Industrial and Applied Mathematics, Philadelphia (1979)Google Scholar
  10. 42.
    Hestenes, M.: Conjugate Direction Methods in Optimization. Springer, New York (1980)Google Scholar
  11. 43.
    Sarkar, T.P.: Application of the Conjugate Gradient Method in Electromagnetics and Signal Processing. Elsevier, New York (1991)Google Scholar
  12. 45.
    Peterson, A., Ray, S., Mittra, R.: Computational Methods for Electromagnetics. IEEE, New York (1998)Google Scholar
  13. 46.
    Chew, W.C., Jin, J.M., Michielsssen, E., Song, J.M.: Fast and Efficient Algorithms in Computational Electromagnetics. Artech House, Boston (2001)Google Scholar

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Harold A. Sabbagh
    • 1
  • R. Kim Murphy
    • 1
  • Elias H. Sabbagh
    • 1
  • John C. Aldrin
    • 2
  • Jeremy S. Knopp
    • 3
  1. 1.Victor Technologies, LLCBloomingtonUSA
  2. 2.Computational ToolsGurneeUSA
  3. 3.Air Force Research Laboratory (AFRL/RXLP)Wright-Patterson AFBUSA

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