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A fast certified parametric near-field-to-far-field transformation technique for electrically large antenna arrays

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Abstract

This paper presents a fast certified numerical method for computing radiation patterns of electrically large antenna arrays over broad frequency bands and wide ranges of look angles. The suggested scheme combines finite-element analysis with empirical interpolation and employs a sub-domain approach on the Huygens surface to reduce computational costs in the offline part of the algorithm. To assure the reliability of the numerical results, an accurate and efficiently computable a posteriori error bound for the radiation patterns is proposed. A real-world example is presented to demonstrate the efficiency and accuracy of the suggested approach.

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References

  1. Barrault, M., Maday, Y., Nguyen, N., Patera, A.: An empirical interpolation method: application to efficient reduced-basis discretization of partial differential equations. C. R. Math. Acad. Sci. Paris 339 (9), 667–672 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  2. Eftang, J., Grepl, M., Patera, A.: A posteriori error bounds for the empirical interpolation method. C. R. Math. Acad. Sci. Paris 348 (9), 575–579 (2010)

    Article  MATH  MathSciNet  Google Scholar 

  3. Eftang, J., Stamm, B.: Parameter multi-domain “hp” empirical interpolation. Int. J. Numer. Meth. Engng. 90 (4), 412–428 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  4. Fares, M., Hesthaven, J., Maday, Y., Stamm, B.: The reduced basis method for the electric field integral equation. J. Comput. Phys. 230 (14), 5532–5555 (2011)

    Article  MATH  MathSciNet  Google Scholar 

  5. Floch, O., Farle, O., Baltes, R., Dyczij-Edlinger, R.: A simplified domain-decomposition preconditioner for the finite-element discretization of the time-harmonic Maxwell equations. In Proceedings of the 2013 International Conference on Electromagnetics in Advanced Applications, pp 456–459. Turin, Italy (2013)

    Google Scholar 

  6. Grepl, M., Maday, Y., Nguyen, N., Patera, A.: Efficient reduced-basis treatment of nonaffine and nonlinear partial differential equations. M2AN Math. Model. Numer. Anal. 41 (3), 575–605 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  7. Hesthaven, J., Stamm, B., Zhang, S.: Certified reduced basis method for the electric field integral equation. SIAM J. Sci. Comput 34 (3), 1777–1799 (2012)

    Article  MathSciNet  Google Scholar 

  8. Industrial Information and Control Centre: OPTI Toolbox (2011–2014). http://www.i2c2.aut.ac.nz/Wiki/OPTI/

  9. Ingelström, P.: A new set of H (curl)-conforming hierarchical basis functions for tetrahedral meshes. IEEE Trans. Microw. Theory Techn. 54 (1), 106–114 (2006)

    Article  Google Scholar 

  10. Maday, Y., Nguyen, N., Patera, A., Pau, G.: A general multipurpose interpolation procedure: the magic points. Commun. Pure Appl. Anal 8 (1), 383–404 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  11. Orfanidis, S.: Electromagnetic waves and antennas. available at (2008). http://eceweb1.rutgers.edu/~orfanidi/ewa/

  12. Rothwell, E., Cloud, M., 2nd: Electromagnetics. CRC Press, Boca Raton, FL (2008)

    Google Scholar 

  13. Shin, J., Schaubert, D.H.: A parameter study of stripline-fed vivaldi notch-antenna arrays. IEEE Trans. Antennas Propag. 47 (5), 879–886 (1999)

    Article  Google Scholar 

  14. Sommer, A., Farle, O., Dyczij-Edlinger, R.: Efficient finite-element computation of far-fields of phased arrays by order reduction. COMPEL 32 (5), 1721–1734 (2013)

    Article  MathSciNet  Google Scholar 

  15. Sommer, A., Floch, O., Farle, O., Baltes, R., Dyczij-Edlinger, R.: An efficient parametric near-field-to-far-field transformation technique. In: Proceedings of the 2013 International Conference on Electromagnetics in Advanced Applications, pp 332–335. Turin, Italy (2013)

    Google Scholar 

  16. Vaz, A.I.F., Vicente, L.N.: A particle swarm pattern search method for bound constrained global optimization. J. Global Optim. 39 (2), 197–219 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  17. Zhu, Y., Cangellaris, A.: Multigrid finite element methods for electromagnetic field modeling. IEEE Press, Piscataway, NY (2006)

    Book  Google Scholar 

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Authors and Affiliations

  1. Chair for Electromagnetic Theory, Saarland University, Campus, Building C6 3, 11th floor, D-66123, Saarbrücken, Germany

    Alexander Sommer, Ortwin Farle & Romanus Dyczij-Edlinger

Authors
  1. Alexander Sommer
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  2. Ortwin Farle
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  3. Romanus Dyczij-Edlinger
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Correspondence to Alexander Sommer.

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Communicated by: Editors of Special Issue on MoRePas

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Sommer, A., Farle, O. & Dyczij-Edlinger, R. A fast certified parametric near-field-to-far-field transformation technique for electrically large antenna arrays. Adv Comput Math 41, 1015–1034 (2015). https://doi.org/10.1007/s10444-014-9373-0

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  • DOI: https://doi.org/10.1007/s10444-014-9373-0

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