A Comparative Study of Expansion Functions Using the Boundary Residual Method on a Linear Dipole - Part I: Entire-Domain Functions
Keywords:
A Comparative Study of Expansion Functions Using the Boundary Residual Method on a Linear Dipole - Part I: Entire-Domain FunctionsAbstract
the Boundary Residual Method, which is a specialization of the Least Squares Method, is described. A significant benefit of the approach is that error in the residual satisfaction of the boundary condition is explicitly reported. Use of error values facilitates better monitoring of solution convergence as expansion functions are added to the underlying model. Furthermore, better discrimination between competing models is possible when errors are known. These concepts are explored and applied to dipoles of various lengths with key findings reported.
Downloads
References
R. King. “Linear Arrays: Currents, Impedances
and Fields”, IEEE Trans. Ant. & Prop., Vol. 7,
S440, 1959
R. W. P. King, R. B. Mack & S. S. Sandler,
Arrays of Cylindrical Dipoles, Cambridge
University Press, Chapter 2, 1967
R. H. Duncan & F. A. Hinchey, “Cylindrical
Antenna Theory”, J. Res. NBS, Vol. 64D, pp.
-584, Sept. 1960
R. Storm, “Investigations into modern aerial
theory and a new solution of Hallen’s integral
equation for a cylindrical aerial, dissertation,
Imperial College, London, 1953; summary in
Wireless Engineer (July 1953)
B. D. Popovic, “Polynomial approximation of
current along thin symmetrical cylindrical
dipoles”, Proc. IEE, Vol. 117, pp. 873-878,
J. H. Richmond, “Digital Computer Solutions of
the Rigorous Equations for Scattering
Problems”, Proc. IEEE, pp. 796-804, August,
B. A. Finlayson & L. E. Scriven, “The Method
of Weighted Residuals – A Review”, Applied
Mechanics Reviews, Vol. 19, No. 9, pp. 735-
, Sept., 1966
J. B. Davies, “A Least-Squares Boundary
Residual Method for the Numerical Solution of
Scattering Problems”, IEEE Trans. On
Microwave Theory & Techniques”, Vol. 21, No
, pp. 99-104, February 1973
F. H. Fenlon, “Calculation of the Acoustic
Radiation Field at the Surface of a Finite
Cylinder by the Method of Weighted
Residuals”, Proc. Of IEEE, Vol. 37, No 3, pp.
-306, March 1969
K. J. Bunch & R. W. Grow, “Numerical
Aspects of the Boundary Residual Method”,
Int. J. of Numerical Modelling: Electronic
Networks, Vol. 3, pp. 57-71, 1990
K. J. Bunch & R. W. Grow, “On the
Convergence of the Method of Moments, the
ACES JOURNAL, VOL. 17, NO. 1, MARCH 2002, SI: APPROACHES TO BETTER ACCURACY/RESOLUTION IN CEM52
Boundary Residual Method, and the Point-
Matching Method with a Rigorously
Convergent Formulation of the Point-Matching
Method”, Journal of the Applied Computational
Electromagnetics Society, Vol. 8, No 2, 1993,
pp. 188-202,
C. L. Lawson & R. J. Hanson, Solving Least-
Squares Problems, Prentice-Hall, Inc.,
Chapters 3 & 4, 1974
F. B. Hildebrand, Methods of Applied
Mathematics, Dover, pp. 286-292, 1992
G. H. Golub & C. F. Van Loan, Matrix
Computations, The John Hopkins University
Press, 1989
C. de Boor, A Practical Guide to Splines,
Springer-Verlag, 1978
LAPACK 3.0, available from
www.netlib.org/lapack/
TOMS644 available from www.netlib.org/toms/
J. H. Ma, V. Rohklin and S. Wandzura,
“Generalized Gaussian quadrature rules for
systems of arbitrary functions”, SIAM J.
Numer. Anal., Vol. 33, pp. 971-996, June 1996
A. F. Peterson, S. L. Ray, R. Mittra,
Computational Methods for Electromagnetics,
IEEE Press, 1998
E. Hallen, “Theoretical Investigations into the
Transmitting and Receiving Qualities of
Antennae”, Nova Acta Regiae Soc. Sci.
Upsaliensis, Ser. IV, No 4, pp.1-44, 1938
L. L. Tsai, “A Numerical Solution for the Near
and Far Fields of an Annular Ring of Magnetic
Current”, IEEE Trans. on Ant. & Prop., Vol. 20,
No 5, pp. 569-576, Sept., 1972
J. H. Richmond, “On the Edge Mode in the
Theory of Thick Cylindrical Monopole
Antennas”, IEEE Trans. on Ant. & Prop., Vol.
, No 6, pp. 916-920, Nov. 1980
J. Meixner, “The Behavior of Electromagnetic
Fields at Edges”, IEEE Trans. on Ant. & Prop.,
Vol. 20, No 4, pp. 442-446, 1972
