Analytic Constraints on Electromagnetic Field Computations

IEEE Transactions on Microwave Theory and Techniques

Volumn 23, Issue 8, 1975, Pages 605-623

  Bates, R H T ^a  

^a UNIVERSITY OF CANTERBURY   (New Zealand)

Author keywords

[No Author keywords available]

Indexed keywords

ELECTROMAGNETIC WAVES;

EID: 0016544533     PISSN: 00189480     EISSN: 15579670     Source Type: Journal    
DOI: 10.1109/TMTT.1975.1128639     Document Type: Article

References (73)

1. P. Silvester and Z. J. Csendes “Numerical modeling of passive microwave devices,” IEEE Trans. Microwave Theory Tech. (Special Issue on Computer-Oriented Microwave Practices), vol. MTT-22, pp. 190–201, Mar. 1974.
2. F. L. Ng “Tabulation of methods for the numerical solution of the hollow waveguide problem,” IEEE Trans. Microwave Theory Tech. (Short Papers), vol. MTT-22, pp. 322–329, Mar. 1974.
3. P. Daly “Polar geometry waveguides by finite-element methods,” IEEE Trans. Microwave Theory Tech. (Special Issue on Computer-Oriented Microwave Practices), vol. MTT-22, pp. 202–209, Mar. 1974.
4. P. B. Johns “The solution of inhomogeneous waveguide problems using a transmission-line matrix,” IEEE Trans. Microwave Theory Tech. (Special Issue on Computer-Oriented Microwave Practices), vol. MTT-22, pp. 209–215, Mar. 1971.
5. F. M. Tesche “On the analysis of scattering and antenna problems using the singularity expansion technique,” IEEE Trans. Antennas Propagat., vol. AP-21, pp. 53–62, Jan. 1973.
6. D. S. Jones, The Theory of Electromagnetism. New York: Macmillan, 1964, sec. 1.10, 1.27, 1.34, 9.1, 9.2.
7. R. H. T. Bates and F. L. Ng “Polarisation-source formulation of electromagnetism and dielectric-loaded waveguides,” Proc. Inst. Elec. Eng., vol. 119, pp. 1568–1574, Nov. 1972.
8. G. N. Watson, Theory of Bessel Functions, 2nd ed. New York: Cambridge, 1958, ch. 3 and sec. 11.3.
9. E. T. Whittaker and G. N. Watson, Modern Analysis, 4th ed. New York: Cambridge, 1952, ch. 5.
10. S. Bochner and W. T. Martin, Several Complex Variables. Princeton, N. J.: Princeton Univ. Press, 1948, pp. 33–35.
11. P. C. Waterman “Symmetry, unitarity and geometry in electromagnetic scattering,” Phys. Rev. D, vol. 4, pp. 825–839, Feb. 1971.
12. R. Mittra and D. R. Wilton “A numerical approach to the determination of electromagnetic scattering characteristics of perfect conductors,” Proc. IEEE (Lett.), vol. 57, pp. 2064–2065, Nov. 1969.
13. W. A. Imbriale and R. Mittra “The two-dimensional inverse scattering problem,” IEEE Trans. Antennas Propagat., vol. AP-18, pp. 633–642, Sept. 1970.
14. V. H. Weston, J. J. Bowman, and E. Ar “On the electromagnetic inverse scattering problem,” Arch. Ration. Mech. Anal., vol. 31, pp. 199–213, 1968.
15. J V. H. Weston and W. M. Boerner “An inverse scattering technique for electromagnetic bistatic scattering,” Can. J. Phys., vol. 47, pp. 1177–1184, June 1969.
16. R. F. Millar, “The Rayleigh hypothesis and a related least-squares solution to scattering problems for periodic surfaces and other scatterers,” Radio Sci., vol. 8, pp. 785–796, Aug–Sept. 1973.
17. B. B. Baker and E. T. Copson, Mathematical Theory of Huygens' Principle, 2nd ed. New York: Oxford, 1953.
18. T. B. A. Senior “Impedance boundary conditions for imperfectly conducting surfaces,” Appl. Sci. Res. B, vol. 8, pp. 418–436, 1960.
19. M. Hashimoto and K. Fujisawa “Considerations on matrix methods and estimation of their errors,” IEEE Trans. Microwave Theory Tech., vol. MTT-18, pp. 352–359, July 1970.
20. R. F. Harrington, Field Computation by Moment Methods. New York: Macmillan, 1968.
21. A. E. H. Love “The integration of the equations of propagation of electric waves,” Phil. Trans. A, vol. 197, pp. 1–45, 1901.
22. J. de Goede and P. Mazur “On the extinction theorem in electrodynamics,” Physica (Utrecht), vol. 58, pp. 568–584, Apr. 1972.
23. D. N. Pattanayak and E. Wolf “General form and a new interpretation of the Ewald-Oseen extinction theorem,” Opt. Commun., vol. 6, pp. 217–220, Nov. 1972.
24. R. H. T. Bates and C. T. Wong “The extended boundary condition and thick axially symmetric antennas,” Appl. Sci. Res., vol. 29, pp. 19–43, Jan. 1974.
25. R. H. T. Bates, “New justification for physical optics and the aperture-field method,” in Proc. 20th AGAARD Meeting on Electromagnetic Wave Propagation Involving Irregular Surfaces and Inhomogeneous Media (The Hague, The Netherlands), Mar. 25–29, 1974, pp. 36-1–36-7, AGAARD Conf. Publication No. CPP-144.
26. —, “Modal expansions for electromagnetic scattering from perfectly conducting cylinders of arbitrary cross-section,” Proc. Inst. Elec. Eng., vol. 115, pp. 1443–1445, Oct. 1968.
27. J. W. Strutt (3rd Lord Rayleigh), The Theory of Sound, vol. II. New York: Dover, 1945.
28. M. Nevière, M. Cadilhac, and R. Petit “Applications of con-formal mappings to the diffraction of electromagnetic waves by a grating,” IEEE Trans. Antennas Propagat, vol. AP-21, pp. 37–46, Jan. 1973.
29. L. V. Kantorovich and V. I. Krylov, Approximate Methods of Higher Analysis. Groningen, The Netherlands: Noordhoff, 1958.
30. P. A. Laura, E. Romanelli, and M. J. Maurizi “On the analysis of waveguides of doubly-connected cross-section by the method of conformal mapping,” J. Sound Vib., vol. 20, pp. 27–38, Jan. 1972.
31. C. R. Mullin, R. Sandburg, and C. O. Velline “A numerical technique for the determination of scattering cross sections of infinite cylinders of arbitrary geometrical cross section,” IEEE Trans. Antennas Propagat., vol. AP-13, pp. 141–149, Jan. 1965.
32. H. Y. Yee and N. F. Audeh “Uniform waveguides with arbitrary cross-section considered by the point-matching method,” IEEE Trans. Microwave Theory Tech. (1965 Symp. Issue), vol. MTT-13, pp. 847–851, Nov. 1965.
33. R. H. T. Bates and F. L. Ng “Point matching computation of transverse resonances,” Int. J. Numerical Methods Eng., vol. 6, pp. 155–168, 1973.
34. R. H. T. Bates, J. R. James, I. N. L. Gallett, and R. F. Millar “An overview of point matching,” Radio Electron. Eng., vol. 43, pp. 193–200, Mar. 1973.
35. H. Ikuno and K. Yasuura “Improved point-matching method with application to scattering from a periodic surface,” IEEE Trans. Antennas Propagat., vol. AP-21, pp. 657–662, Sept. 1973.
36. J. C. Bolomey and A. Wirgin “Numerical comparison of the Green's function, Waterman and Rayleigh theories of scattering from a cylinder with arbitrary cross-section,” Proc. Inst. Elec. Eng., vol. 121, pp. 794–804, Aug. 1974.
37. J. B. Davies “A least-squares boundary residual method for the numerical solution of scattering problems,” IEEE Trans. Microwave Theory Tech., vol. MTT-21, pp. 99–104, Feb. 1973.
38. P. Vincent and R. Petit “Sur la diffraction d'une onde plane par un cylindre dielectrique,” Opt. Commun., vol. 5, pp. 261–266, July 1972.
39. R. Petit and D. Maystre “Application des lois d'électromagnétisme à l'étude des réseaux,” Rev. Phys. Appl., vol. 7, pp. 427–441, Dec. 1972.
40. A. Hizal and H. Tosun “State-space formulation of scattering with application to spherically symmetrical objects,” Can. J. Phys., vol. 51, pp. 549–558, May 1973.
41. A. Hizal “Formulation of scattering from conducting bodies of revolution as an initial value problem,” J. Phys. D: Appl. Phys., vol. 7, pp. 248–256, Jan. 1974.
42. K. Ogata, State Space Analysis of Control Systems. Englewood Cliffs, N. J.: Prentice-Hall, 1967.
43. N. Marcuvitz, Waveguide Handbook. New York: Dover, 1965, sec. 1.2 (reprint of 1951 McGraw-Hill ed.: M.I.T. Rad. Lab. Series, no. 10).
44. B. E. Spielman and R. F. Harrington “Waveguides of arbitrary cross section by solution of a nonlinear integral eigenvalue equation,” IEEE Trans. Microwave Theory Tech., vol. MTT-20, pp. 578–585, Sept. 1972.
45. F. L. Ng and R. H. T. Bates “Null-field method for waveguides of arbitrary cross section,” IEEE Trans. Microwave Theory Tech., vol. MTT-20, pp. 658–662, Oct. 1972.
46. R. F. Harrington “On the calculation of scattering by conducting cylinders,” IEEE Trans. Antennas Propagat. (Commun.), vol. AP-13, pp. 812–813, Sept. 1965.
47. R. H. T. Bates “The point-matching method for interior and exterior two-dimensional boundary value problems,” IEEE Trans. Microwave Theory Tech. (Corresp.), vol. MTT-15, pp. 185–187, Mar. 1967.
48. H. Y. Yee and N. F. Audeh “Cutoff frequencies of eccentric waveguides,” IEEE Trans. Microwave Theory Tech., vol. MTT-14, pp. 487–493, Oct. 1966.
49. J. A. Fuller and N. F. Audeh “The point-matching solution of uniform nonsymmetric waveguides,” IEEE Trans. Microwave Theory Tech. (Corresp.), vol. MTT-17, pp. 114–115, Feb. 1969.
50. R. H. T. Bates “The theory of the point-matching method for perfectly conducting waveguides and transmission lines,” IEEE Trans. Microwave Theory Tech., vol. MTT-17, pp. 294–301, June 1969.
51. R. F. Millar “Rayleigh hypothesis in scattering problems,” Electron. Lett., vol. 5, pp. 416–418, Aug. 1969.
52. D. M. Bolle and D. M. Fye, “Application of point-matching method to scattering from quadrilateral cylinders,” Electron. Lett., vol. 7, pp. 577–579, Sept. 1971.
53. J. R. James and I. N. L. Gallett “Point-matched solutions for propagating modes on arbitrarily-shaped dielectric rods,” Radio Electron. Eng., vol. 42, pp. 103–113, Mar. 1972.
54. L. Lewin “On the restricted validity of the point-matching techniques,” IEEE Trans. Microwave Theory Tech. (1970 Symp. Issue), vol. MTT-18, pp. 1041–1047, Dec. 1970.
55. J. D. Hunter “The surface current density on perfectly conducting polygonal cylinders,” Can. J. Phys., vol. 50, pp. 139–150, Jan. 1972.
56. B. H. McDonald, M. Friedman, and A. Wexler “Variational solution of integral equations,” IEEE Trans. Microwave Theory Tech. (Special Issue on Computer-Oriented Microwave Practices), vol. MTT-22, pp. 237–248, Mar. 1974.
57. L. Shafai “A improved integral equation for the numerical solution of two-dimensional diffraction problems,” Can. J. Phys., vol. 48, pp. 954–963, Apr. 1970.
58. J. H. Richmond “Scattering by a dielectric cylinder of arbitrary cross section shape,” IEEE Trans. Antennas Propagat., vol. AP-13, pp. 334–341, May 1965.
59. —, TE-wave scattering by a dielectric cylinder of arbitrary cross section shape, ibid., vol. AP-14, pp. 460–464, July 1966.
60. J. R. James and I. N. L. Gallett “Modal analysis of triangular-cored glass-fibre waveguide,” Proc. Inst. Elec. Eng., vol. 120, pp. 1362–1370, Nov. 1973.
61. R. Mittra, Ed., Computer Techniques for Electromagnetics. New York: Pergamon, 1973, sec. 4.3.1 and appendix to ch. 5.
62. N. C. Albertson, J. E. Hansen, and N. E. Jensen, “Computation of radiation from wire antennas on conducting bodies,” IEEE Trans. Antennas Propagat., vol. AP-22, pp. 200–206, Mar. 1974.
63. D. S. Jones “Truncation error in the solution of integral equations,” Proc. Roy. Soc. Edinburgh, vol. 71, pp. 263–273, Sept. 1973.
64. R. F. Harrington and J. R. Mautz “Theory of characteristic modes for conducting bodies,” IEEE Trans. Antennas Propagat., vol. AP-19, pp. 622–628, Sept. 1971.
65. — “Computation of characteristic modes for conducting bodies,” ibid., vol. AP-19, pp. 629–639, Sept. 1971.
66. A. Hizal and Z. Yasa “Scattering by perfectly conducting rotational bodies of arbitrary form excited by an obliquely incident plane wave or by a linear antenna,” Proc. Inst. Elec. Eng., vol. 120, pp. 181–182, Feb. 1973.
67. B. A. Howarth and T. J. F. Pavlasek “Multipole induction: A novel formulation of multiple scattering of scalar waves,” J. Appl. Phys., vol. 44, pp. 1162–1167, Mar. 1973.
68. J.-C. Bolomey and W. Tabbara “Numerical aspects on coupling between complementary boundary value problems,” IEEE Trans. Antennas Propagat., vol. AP-21, pp. 356–363, May 1973.
69. D. S. Jones “Integral equations for the exterior acoustic problem,” Quart. J. Mech. Appl. Math., vol. 27, pp. 129–142, Feb. 1974.
70. L. Marin “Natural-mode representation of transient scattering from rotationally symmetric bodies,” IEEE Trans. Antennas Propagat., vol. AP-22, pp. 266–274, Mar. 1974.
71. F. M. Tesche “Transient response of a thin-wire antenna or scatterer near a conducting ground plane,” IEEE Trans. Antennas Propagat. (Succinct Papers), vol. AP-22, pp. 352–355, Mar. 1974.
72. I. A. Cermak et al. “The status of computer-oriented microwave practices,” IEEE Trans. Microwave Theory Tech. (Special Issue on Computer-Oriented Microwave Practices), vol. MTT-22, pp. 155–160, Mar. 1974.
73. D. S. Jones “Numerical methods for antenna problems,” Proc. Inst. Elec. Eng., vol. 121, pp. 573–582, July 1974.