2015-03-08
A Semi-Analytical Method to Calculate the Entries of the Method of Moments Matrix for the Mixed Potential Integral Equation of a Source Reconstruction Problem
By
Progress In Electromagnetics Research M, Vol. 41, 149-158, 2015
Abstract
In this article, the mixed potential integral equation is discretized using the Rao-Wilton-Glisson basis functions in order to obtain a method of moments matrix equation for a source reconstruction problem. The weighting functions used in the setup of the moments equation are Dirac delta functions. The entries of the moments matrix are computed using a semi-analytical method which is applicable to any method of moments problem with point matching. The analytical calculation is made possible by employing a differentiation property of the scalar Green function and the properties of the mesh elements of the source plane. The semi-analytical method makes it easier to increase the accuracy of the moments matrix elements. The accuracy of the method is shown by comparing the results obtained using the semi-analytical method to those obtained by a fully numerical procedure.
Citation
Saffet Sen, "A Semi-Analytical Method to Calculate the Entries of the Method of Moments Matrix for the Mixed Potential Integral Equation of a Source Reconstruction Problem," Progress In Electromagnetics Research M, Vol. 41, 149-158, 2015.
doi:10.2528/PIERM15012602
References

1. Rao, S. M., D. R. Wilton, and A. W. Glisson, "Electromagnetic scattering by surfaces of arbitrary shape," IEEE Trans. Antennas Propag., Vol. 30, No. 3, 409-428, 1982.
doi:10.1109/TAP.1982.1142818        Google Scholar

2. Abramowitz, M. and I. A. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, US Government Printing Office, 1965.

3. Paige, C. C. and M. A. Saunders, "LSQR: An algorithm for sparse linear equations and sparse least squares," ACM Transactions on Mathematical Software, Vol. 8, No. 1, 43-71, Mar. 1982.
doi:10.1145/355984.355989        Google Scholar

4. Hansen, P. C., Rank-deficient and Discrete Ill-posed Problems: Numerical Aspects of Linear Inversion, SIAM, 1997.

5. Saunders, M. A., "zlsqrmodule.f90,", Jun. 29, 2013, Online Available: http://web.stanford.edu/groupgroup/SOL/software/lsqr/f90/zlsqr.zip/.        Google Scholar

6. Dunavant, D. A., "High degree efficient symmetrical gaussian quadrature rules for the triangle," International Journal for Numerical Methods in Engineering, Vol. 21, 1129-1148, 1985.
doi:10.1002/nme.1620210612        Google Scholar

7. Petre, P. and T. K. Sarkar, "Planar near-field to far-field transformation using an equivalent magnetic current approach," IEEE Trans. Antennas Propag., Vol. 40, No. 11, 1348-1356, Nov. 1992.
doi:10.1109/8.202712        Google Scholar

8. Taaghol, A. and T. K. Sarkar, "Near-field to near/far-field transformation for arbitrary near-field geometry, utilizing an equivalent magnetic current," IEEE Trans. Electromagn. Compat., Vol. 38, No. 3, 536-542, Aug. 1996.
doi:10.1109/15.536088        Google Scholar

9. Sarkar, T. K. and A. Taaghol, "Near-field to near/far-field transformation for arbitrary near-field geometry, utilizing an equivalent electric current and MOM," IEEE Trans. Antennas Propag., Vol. 47, No. 3, 566-573, Mar. 1999.
doi:10.1109/8.768793        Google Scholar

10. Las-Heras, F., B. Galocha, and J. L. Besada, "Far-field performance of linear antennas determined from near-field data," IEEE Trans. Antennas Propag., Vol. 50, No. 3, 408-410, Mar. 2002.
doi:10.1109/8.999639        Google Scholar

11. Las-Heras, F. and T. K. Sarkar, "A direct optimization approach for source reconstruction and NF-FF transformation using amplitude-only data," IEEE Trans. Antennas Propag., Vol. 50, No. 4, 500-510, Apr. 2002.
doi:10.1109/TAP.2002.1003386        Google Scholar

12. Las-Heras, F. and T. K. Sarkar, "Radial field retrieval in spherical scanning for current reconstruction and NF-FF transformation," IEEE Trans. Antennas Propag., Vol. 50, No. 6, 866-874, Jun. 2002.
doi:10.1109/TAP.2002.1017669        Google Scholar

13. Alvarez, Y., F. Las-Heras, and M. R. Pino, "Reconstruction of equivalent currents distribution over arbitrary three-dimensional surfaces based on integral equation algorithms," IEEE Trans. Antennas Propag., Vol. 55, No. 12, 3460-3468, Dec. 2007.
doi:10.1109/TAP.2007.910316        Google Scholar

14. Alvarez, Y., F. Las-Heras, and M. R. Pino, "Probe-distortion correction for the sources reconstruction method," IEEE Antennas and Propagation Mag., Vol. 50, No. 6, 117-124, Dec. 2008.
doi:10.1109/MAP.2008.4768938        Google Scholar

15. Arrebola, M., Y. Alvarez, J. A. Encinar, and F. Las-Heras, "Accurate analysis of printed reflectarrays considering the near field of the primary feed," IET Microw. Antennas Propag., Vol. 3, No. 2, 187-194, 2009.
doi:10.1049/iet-map:20070325        Google Scholar

16. Eibert, T. F. and C. H. Schmidt, "Multilevel fast multipole accelerated inverse equivalent current method employing Rao-Wilton-Glisson discretization of electric and magnetic surface currents," IEEE Trans. Antennas Propag., Vol. 57, No. 4, 1178-1185, Apr. 2009.
doi:10.1109/TAP.2009.2015828        Google Scholar

17. Lopez, Y. A., F. Las-Heras, M. R. Pino, and T. K. Sarkar, "An improved super-resolution source reconstruction method," IEEE Trans. Instrum. Meas., Vol. 58, No. 11, 3855-3866, Nov. 2009.
doi:10.1109/TIM.2009.2020847        Google Scholar

18. Persson, K., M. Gustafsson, and G. Kristensson, "Reconstruction and visualization of equivalent currents on a radome using an integral representation formulation," Progress In Electromagnetics Research B, Vol. 20, 65-90, 2010.
doi:10.2528/PIERB10012109        Google Scholar

19. Lopez, Y. A., A. Dominguez-Casas, C. Garcia-Gonzalez, and F. Las-Heras, "Geometry reconstruction of metallic bodies using the sources reconstruction method," IEEE Trans. Propag. Lett., Vol. 9, 1197-1200, Dec. 2010.        Google Scholar

20. Alvarez, Y., M. Rodriguez, F. Las-Heras, and M. M. Hernando, "On the use of the source reconstruction method for estimating radiated EMI in electronic circuits," IEEE Trans. Instrum. Meas., Vol. 59, No. 12, 3174-3183, Dec. 2010.
doi:10.1109/TIM.2009.2036455        Google Scholar

21. Lopez-Fernandez, J. A., M. Lopez-Portugues, Y. Alvarez-Lopez, C. Garcia-Gonzalez, D. Martinez, and F. Las Heras Andres, "Fast antenna characterization using the sources reconstruction method on graphics processors," Progress In Electromagnetics Research, Vol. 126, 185-201, 2012.
doi:10.2528/PIER11121408        Google Scholar

22. Vazquez, C., C. Garcia, Y. Alvarez, V. Ver-Hoeye, and F. Las-Heras, "Near field characterization of an imaging system based on a frequency scanning antenna array," IEEE Trans. Antennas Propag., Vol. 61, No. 5, 2874-2879, May 2013.
doi:10.1109/TAP.2013.2244834        Google Scholar

23. Li, P., Y. Li, L. J. Jiang, and J. Hu, "A wide-band equivalent source reconstruction method exploiting the Stoer-Bulirsch algorithm with the adaptive frequency sampling," IEEE Trans. Antennas Propag., Vol. 61, No. 10, 5338-5343, Oct. 2013.
doi:10.1109/TAP.2013.2274032        Google Scholar

24. Li, P. and L. J. Jiang, "An iterative source reconstruction method exploiting phaseless electric field data," Progress In Electromagnetics Research, Vol. 134, 419-435, 2013.
doi:10.2528/PIER12102105        Google Scholar

25. Lopez-Portugues, M., Y. Alvarez, J. A. Lopez-Fernandez, C. Garcia-Gonzalez, R. G. Ayestaran, and F. Las Heras Andres, "A multi-GPU sources reconstruction method for imaging applications," Progress In Electromagnetics Research, Vol. 136, 703-724, 2013.
doi:10.2528/PIER12122104        Google Scholar

26. Quijano, J. L. A. and G. Vecchi, "Improved-accuracy source reconstruction on arbitrary 3-D surfaces," IEEE Trans. Propag. Lett., Vol. 8, 1046-1049, Sep. 2009.        Google Scholar

27. Quijano, J. L. A. and G. Vecchi, "Near- and very near-field accuracy in 3-D source reconstruction," IEEE Trans. Propag. Lett., Vol. 9, 634-637, Sep. 2010.        Google Scholar

28. Quijano, J. L. A. and G. Vecchi, "Field and source equivalence in source reconstruction on 3D surfaces," Progress In Electromagnetics Research, Vol. 103, 67-100, 2010.
doi:10.2528/PIER10030309        Google Scholar

29. Quijano, J. L. A., L. Scialacqua, J. Zackrisson, L. J. Foged, M. Sabbadini, and G. Vecchi, "Suppression of undesired radiated fields based on equivalent currents reconstruction from measured data," IEEE Trans. Propag. Lett., Vol. 10, 314-317, Apr. 2011.        Google Scholar

30. Foged, L. J., L. Scialacqua, F. Saccardi, J. L. A. Quijano, and G. Vecchi, "Application of the dual-equation equivalent-current reconstruction to electrically large structures by fast multipole method enhancement," IEEE Antennas and Propagation Mag., Vol. 56, No. 5, 264-273, Oct. 2014.
doi:10.1109/MAP.2014.6971966        Google Scholar