Comparative analysis of acceleration techniques for 2-D and 3-D Green's functions in periodic structures along one and two directions

IEEE Transactions on Antennas and Propagation

Volumn 55, Issue 6 I, 2007, Pages 1630-1643

  Valerio, Guido ^a   Baccarelli, Paolo ^a   Burghignoli, Paolo ^a   Galli, Alessandro ^a  

^a SAPIENZA UNIVERSITY OF ROME   (Italy)

Author keywords

Acceleration techniques; Complex modes; Green's functions; Numerical methods; Periodic structures

Indexed keywords

ACCELERATION TECHNIQUES; COMPLEX MODES; FREE-SPACE CONFIGURATION;

GREEN'S FUNCTION; NUMERICAL METHODS; PHASE SHIFT;

PERIODIC STRUCTURES;

EID: 34250795618     PISSN: 0018926X     EISSN: None     Source Type: Journal    
DOI: 10.1109/TAP.2007.897340     Document Type: Article

References (40)

1. R. E. Collin, Field Theory of Guided Waves. New York: IEEE Press, 1991.
2. R. E. Collin and F. J. Zucker, Eds., Antenna Theory. New York: McGraw-Hill, 1969, ch. 19 and 20.
3. R. E. Jorgenson and R. Mittra, "Efficient calculation of the free-space periodic Green's function," IEEE Trans. Antennas Propag., vol. 38, no. 5, pp. 633-642, May 1990.
4. S. Singh, W. F. Richards, J. R. Zinecker, and D. R. Wilton, "Accelerating the convergence of series representing the free periodic Green's function," IEEE Trans. Antennas Propag., vol. 38, no. 12, pp. 1958-1962, Dec. 1990.
5. S. Singh and R. Singh, "On the use of ρ-algorithm in series acceleration," IEEE Trans. Antennas Propag., vol. 39, no. 10, pp. 1514-1517, Oct. 1991.
6. N. Kinayman and M. I. Aksun, "Comparative study of acceleration techniques for integrals and series in electromagnetic problems," Radio Sci., vol. 30, no. 6, pp. 1713-1722, Nov.-Dec. 1995.
7. P. P. Ewald, "Die Berechnung optischer und elektrostatischer Gitterpotentiale," Ann. Phys., vol. 64, pp. 253-287, 1921, Translated by A. Cornell, Atomics International Library, 1964.
8. K. E. Jordan, G. E. Richter, and P. Sheng, "An efficient numerical evaluation of the Green's function for the Helmholtz operator on periodic structures," J. Comp. Phys., vol. 63, pp. 222-235, 1986.
9. F. Capolino, D. W.Wilton, and W. A. Johnson, "Efficient computation of the 2-D Green's function for 1-D periodic structures using the Ewald method," IEEE Trans. Antennas Propag., vol. 53, no. 9, pp. 2977-2984, Sept. 2005.
10. M. E. Veysoglu, H. Yueh, R. Shin, and J. Kong, "Polarimetric passive remote sensing of periodic surfaces," J. Electromagn. Waves Appl. vol. 5, no. 3, pp. 267-280, Mar. 1991.
11. M.-J. Park and S. Nam, "Efficient calculation of the Green's function in rectangular waveguides," in IEEE Antennas Propag. Int. Symp. Dig., July 1997, vol. 4, pp. 2354-2357.
12. R. M. Shubair and Y. L. Chow, "Efficient computation of the periodic Green's functions in layered dielectric media," IEEE Trans. Microwave Theory Tech., vol. 41, no. 3, pp. 498-502, Mar. 1993.
13. M.-J. Park and S. Nam, "Efficient calculation of the Green's function for multilayered planar periodic structures," IEEE Trans. Antennas Propag., vol. 46, no. 10, pp. 1582-1583, Oct. 1996.
14. T. Tamir and A. A. Oliner, "Guided complex waves, parts 1 and 2," Proc. Inst. Elect. Eng., vol. 110, pp. 310-324, 325-334, Feb. 1963.
15. P. Baccarelli, C. Di Nallo, S. Paulotto, and D. R. Jackson, "A full-wave numerical approach for modal analysis of 1-D periodic microstrip structures," IEEE Trans. Microw. Theory Tech., vol. 54, no. 4, pp. 1350-1362, Apr. 2006.
16. F. Capolino, D. R. Wilton, and W. A. Johnson, "Efficient computation of the 3D Green's function with one dimensional periodicity using the Ewald method," presented at the IEEE APS Symp., Albuquerque, NM, Jul. 9-14, 2006.
17. A. Papoulis, Systems and Transforms with Application in Optics. Malabar: Kreiger, 1981.
18. R. Lampe, P. Klock, and P. Mayes, "Integral transforms useful for the accelerated summation of periodic, free-space Green's functions," IEEE Trans. Microw. Theory Tech., vol. 33, no. 8, pp. 734-736, Aug. 1985.
19. A. W. Mathis and A. F. Peterson, "A comparison of acceleration procedures for the two-dimensional periodic Green's function," IEEE Trans. Antennas Propag., vol. 44, no. 4, pp. 567-571, Apr. 1996.
20. A. F. Peterson, S. L. Ray, and R. Mittra, Computational Methods for Electromagnetics. New York: IEEE Press, 1998.
21. A. D. Wheelon, "On the summation of infinite series in closed form," J. Appl. Phys., vol. 25, no. 1, pp. 113-118, Jan. 1954.
22. J. P. Skinner and P. J. Collins, "A one-sided version of the poisson sum formula for semi-infinite array Green's functions," IEEE Trans. Antennas Propag., vol. 45, no. 4, pp. 601-607, Apr. 1997.
23. F. Capolino, M. Albani, S. Maci, and L. B. Felsen, "Frequency-domain Green's function for a planar periodic semi-infinite phased array - Part I and II," IEEE Trans. Antennas Propag., vol. 48, no. 1, pp. 67-74, 75-85, Jan. 2000.
24. V. G. Papanicolaou, "Ewald's method revisited: Rapidly convergent series representations of certain Green's functions," J. Comp. Anal. Appl., vol. 1, no. 1, pp. 105-114, Jan. 1999.
25. N. Bleistein and R. A. Handelsman, Asymptotic Expansions of Integrals New York: Dover, 1986, ch. 4.
26. D. Shanks, "Non-linear transformations of divergent and slowly convergent sequences," J. Math. Phys., vol. 34, pp. 1-42, 1955.
27. n) transformation," Math. Tabl. Aids Comp., vol. 10, pp. 91-96, 1956.
28. P. Winn, "A sufficient condition for the instability of the ε-algorithm," Nieuw Arch. Wisk., vol. 9, pp. 117-119, 1961.
29. P. Winn, "On the convergence and stability of the epsilon algorithm," SIAM J. Numer. Anal., vol. 3, no. 1, pp. 91-122, 1966.
30. S. Singh and R. Singh, "Application of transforms to accelerate the summation of periodic free-space Green's functions," IEEE Trans. Microw. Theory Tech., vol. 38, no. 11, pp. 1746-1748, Nov. 1990.
31. S. Singh and R. Singh, "On the use of Shanks's transform to accelerate the summation of slowly converging series," IEEE Trans. Microw. Theory Tech., vol. 39, no. 3, pp. 608-610, Mar. 1990.
32. S. Singh and R. Singh, "Efficient computation of the free-space periodic Green's function," IEEE Trans. Microw. Theory Tech., vol. 39, no. 7, pp. 1226-1229, July 1991.
33. N. Guèrin, S. Enoch, and G. Tayeb, "Combined method for the computation of the doubly periodic Green's function," J. Electromagn. Waves Appl., vol. 15, no. 2, pp. 205-221, Feb. 2001.
34. P. Winn, "On a procrustean technique for the numerical transformation of slowly convergent sequences and series," Proc. Camb. Philos. Soc. vol. 52, pp. 663-671, 1956.
35. M. Abramowitz and I. Stegun, Handbook of Mathematical Functions. New York: Dover, 1970.
36. C. M. Linton, "The Green's function for the two-dimensional Helmholtz equation in periodic domains," J. Eng. Math., vol. 33, no. 4, pp. 377-402, May 1998.
37. J. A. C. Weideman, "Computation of the complex error function," SIAM J. Numer. Anal., vol. 31, no. 5, pp. 1497-1518, Oct. 1994.
38. A. Kustepeli and A. Q. Martin, "On the splitting parameter in the Ewald Method," IEEE Trans. Microw. Guided Wave Lett., vol. 10, no. 5, pp. 168-170, May 2005.
39. M. Silveirinha and C. A. Fernandes, "A new acceleration technique with exponential convergence rate to evaluate periodic Green functions," IEEE Trans. Antennas Propag., vol. 53, no. 1, pp. 347-355, Jan. 2005.
40. I. S. Gradshteyn and I. M. Ryzhik, Tables of Integrals, Series and Products. New York: Academic, 1980.