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International Journal of Antennas and Propagation
Volume 2016, Article ID 2417402, 7 pages
http://dx.doi.org/10.1155/2016/2417402
Research Article

Study on the Accuracy Improvement of the Second-Kind Fredholm Integral Equations by Using the Buffa-Christiansen Functions with MLFMA

1CAEP Software Center for High Performance Numerical Simulation, Beijing 100088, China
2Institute of Applied Physics and Computational Mathematics, Beijing 100094, China
3Center for Electromagnetic Simulation, Beijing Institute of Technology, Beijing 100081, China

Received 1 April 2016; Revised 12 July 2016; Accepted 26 July 2016

Academic Editor: Ananda S. Mohan

Copyright © 2016 Yue-Qian Wu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. I. Fredholm, “Sur une classe d’équations fonctionnelles,” Acta Mathematica, vol. 27, no. 1, pp. 365–390, 1903. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  2. A. J. Poggio and E. K. Miller, Integral Equation Solutions of Three-Dimensional Scattering Problems, MB Associates, 1970.
  3. T.-K. Wu and L. L. Tsai, “Scattering from arbitrarily-shaped lossy dielectric bodies of revolution,” Radio Science, vol. 12, no. 5, pp. 709–718, 1977. View at Publisher · View at Google Scholar · View at Scopus
  4. Y. Chang and R. F. Harrington, “A surface formulation for characteristic modes of material bodies,” IEEE Transactions on Antennas and Propagation, vol. 25, no. 6, pp. 789–795, 1977. View at Google Scholar · View at Scopus
  5. R. F. Harrington, “Boundary integral formulations for homogeneous material bodies,” Journal of Electromagnetic Waves and Applications, vol. 3, no. 1, pp. 1–15, 1989. View at Publisher · View at Google Scholar
  6. P. Ylä-Oijala and M. Taskinen, “Application of combined field integral equation for electromagnetic scattering by dielectric and composite objects,” IEEE Transactions on Antennas and Propagation, vol. 53, no. 3, pp. 1168–1173, 2005. View at Google Scholar
  7. Ö. Ergül and L. Gürel, “Comparison of integral-equation formulations for the fast and accurate solution of scattering problems involving dielectric objects with the multilevel fast multipole algorithm,” IEEE Transactions on Antennas and Propagation, vol. 57, no. 1, pp. 176–187, 2009. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  8. Ö. Ergül and L. Gürel, “Solid-angle factor in the magnetic-field integral equation,” Microwave and Optical Technology Letters, vol. 45, no. 5, pp. 452–456, 2005. View at Publisher · View at Google Scholar · View at Scopus
  9. L. Gürel and Ö. Ergül, “Singularity of the magnetic-field integral equation and its extraction,” IEEE Antennas and Wireless Propagation Letters, vol. 4, no. 1, pp. 229–232, 2005. View at Publisher · View at Google Scholar · View at Scopus
  10. B. M. Notaroš, “Higher order frequency-domain computational electromagnetics,” IEEE Transactions on Antennas and Propagation, vol. 56, no. 8, pp. 2251–2276, 2008. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  11. M. Djordjević and B. M. Notaros, “Double higher order method of moments for surface integral equation modeling of metallic and dielectric antennas and scatterers,” IEEE Transactions on Antennas and Propagation, vol. 52, no. 8, pp. 2118–2129, 2004. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  12. Ö. Ergül and L. Gürel, “Improving the accuracy of the magnetic field integral equation with the linear-linear basis functions,” Radio Science, vol. 41, no. 4, 2006. View at Publisher · View at Google Scholar · View at Scopus
  13. Ö. Ergül and L. Gürel, “Improved testing of the magnetic-field integral equation,” IEEE Microwave and Wireless Components Letters, vol. 15, no. 10, pp. 615–617, 2005. View at Publisher · View at Google Scholar · View at Scopus
  14. C. P. Davis and K. F. Warnick, “High-order convergence with a low-order discretization of the 2D MFIE,” IEEE Antennas and Wireless Propagation Letters, vol. 3, no. 1, pp. 355–358, 2004. View at Publisher · View at Google Scholar · View at Scopus
  15. K. Cools, F. P. Andriulli, F. Olyslager et al., “Improving the MFIE's accuracy by using a mixed discretization,” in Proceedings of the IEEE Antennas and Propagation Society international symposium; USNC/URSI National Radio Science Meeting, pp. 1–4, Charleston, SC, USA, June 2009. View at Publisher · View at Google Scholar
  16. P. Ylä-Oijala, S. P. Kiminki, K. Cools, F. P. Andriulli, and S. Järvenpää, “Mixed discretization schemes for electromagnetic surface integral equations,” International Journal of Numerical Modelling: Electronic Networks, Devices and Fields, vol. 25, no. 5-6, pp. 525–540, 2012. View at Publisher · View at Google Scholar · View at Scopus
  17. A. Buffa and S. H. Christiansen, “A dual finite element complex on the barycentric refinement,” Mathematics of Computation, vol. 76, no. 260, pp. 1743–1769, 2007. View at Publisher · View at Google Scholar · View at MathSciNet
  18. Ö. Ergül and L. Gürel, “Discretization error due to the identity operator in surface integral equations,” Computer Physics Communications, vol. 180, no. 10, pp. 1746–1752, 2009. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  19. S. Yan, J.-M. Jin, and Z. Nie, “Improving the accuracy of the second-kind Fredholm integral equations by using the Buffa-Christiansen functions,” IEEE Transactions on Antennas and Propagation, vol. 59, no. 4, pp. 1299–1310, 2011. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  20. S. Yan, J.-M. Jin, and Z. Nie, “Accuracy improvement of the second-kind integral equations for generally shaped objects,” IEEE Transactions on Antennas and Propagation, vol. 61, no. 2, pp. 788–797, 2013. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  21. S. M. Rao, D. R. Wilton, and A. W. Glisson, “Electromagnetic scattering by surfaces of arbitrary shape,” IEEE Transactions on Antennas and Propagation, vol. 30, no. 3, pp. 409–418, 1982. View at Publisher · View at Google Scholar · View at Scopus
  22. R. F. Harrington and J. L. Harrington, Field Computation by Moment Methods, Oxford University Press, 1996.
  23. F. P. Andriulli, K. Cools, H. Bağci et al., “A multiplicative Calderon preconditioner for the electric field integral equation,” IEEE Transactions on Antennas and Propagation, vol. 56, no. 8, pp. 2398–2412, 2008. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  24. X. Q. Sheng, J.-M. Jin, J. Song, W. C. Chew, and C.-C. Lu, “Solution of combined-field integral equation using multilevel fast multipole algorithm for scattering by homogeneous bodies,” IEEE Transactions on Antennas and Propagation, vol. 46, no. 11, pp. 1718–1726, 1998. View at Publisher · View at Google Scholar · View at Scopus