Quasi Monte Carlo Integration Technique for Method of Moments Solution of EFIE in Radiation Problems
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Quasi Monte Carlo Integration Technique for Method of Moments Solution of EFIE in Radiation ProblemsAbstract
In this work, a Quasi Monte Carlo Integration (QMCI) Technique using Halton Sequence is proposed for the Method of Moments (MoM) solution of the Electric Field Integral Equation (EFIE) in radiation problem. It is found that this scheme is capable of handling the singularity issue in the EFIE automatically and at the same time provides solution to the radiation problems very efficiently.
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References
W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B.
P. Flannery, Numerical Recipes, second edition,
Cambridge University Press, 1992.
B. D. Ripley, Stochastic Simulation, John Wiley &
Sons, Inc., 1987.
H. Niederreiter, Random Number Generation and
Quasi-Monte Carlo Methods,. SIAM, Pennsylvania,
W. Cai, Y. Yu, and X. C. Yu, “Singularity treatment
and high-order RWG basis functions for integral
equations of electromagnetic scattering,” Int. J.
Numerical Methods Eng., vol. 53, pp. 31–47, 2002.
M. G. Duffy, “Quadrature over a pyramid or cube of
integrands with a singularity at a vertex,” SIAM Journal
on Numerical Analysis, vol. 19, pp. 1260 –1262,
December 1982.
M. A. Khayat and D. R. Wilton, “Numerical evaluation
of singular and near-singular potential integrals,” IEEE
Trans. Antennas Propagat., vol. 53, no. 10, pp. 3180 –
, October 2005.
M. Mishra and N. Gupta, “Singularity treatment for
integral equations in electromagnetic scattering using
Monte Carlo integration technique,” Microwave and
Optical Technology Letters, vol. 50, no. 6, pp. 1619-
, June 2008.
J. H. Halton, “On the efficiency of certain quasi-random
sequences of points in evaluating multi-dimensional
integrals,” Numer. Math., vol. 2, pp. 84-196, 1996.
B. M. Kolundzija and B. D. Popovic, “Entire domain
Galerkin method for analysis of generalized wire
antennas and scatterers,” IEE Proceedings Part-H, vol.
, pp. 17-24, Feb. 1992.
G. Fikioris and T. T. Wu, “On the application of
numerical methods to Hall ́en’s equation,” IEEE Trans.
Antennas Propagat., vol. 49, pp. 383–392, Mar. 2001.
D. H. Werner, “A method of moments approach for the
efficient and accurate modeling of moderately thick
cylindrical wire antennas,” IEEE Trans. Antennas
Propagat., vol. 46, pp. 373–382, Mar. 1998.
S. Alyones, C. W. Bruce, and A. K. Buin, “Numerical
methods for solving the problem of electromagnetic
scattering by a thin finite conducting wire,” IEEE
Transactions on Antennas and propagation, vol. 55, pp.
-1861, June 2007.
G. Fikioris and C. A. Valagiannopoulos, “Input
Admittance arising from explicit solution to integral
equations for infinite-length dipole antennas,” Progress
In Electromagnetics Research, PIER 55 , pp. 285-306,
P. J. Papakanellos and G. Fikioris, “A possible remedy
for the oscillations occurring in thin-wire MOM
analysis of cylindrical antennas,” Progress In
Electromagnetics Research, PIER 69, pp. 77–92, 2007.
W. X. Wang, “The exact kernel for cylindrical
antenna,” IEEE Trans. Antennas Propagat., vol. AP-39,
pp. 434–435, 1991.
C. A. Balanis, Antenna Theory: Analysis and Design,
Harper & Row, New York, 1982.
