volume | PIER Journals

Abstract

In this work, a Quasi Monte Carlo (QMC) Integration Technique using Halton Sequence is proposed for the Electric Field Integral Equation (EFIE) in the Method of Moments (MoM) solution for scattering problems. It is found that the Halton Sequence used in QMC integration scheme is capable of handling the singularity issue in the EFIE automatically and at the same time provides solution to the scattering problems very easily. Finally the proposed technique is applied to solve the scattering problem from a finite cylinder employing the entire domain basis function expansions. The results obtained show a good agreement between the proposed and conventional technique.

1. Press, W. H., S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes, 2 Ed., Cambridge University Press, 1992.

2. Ripley, B. D., Stochastic Simulation, John Wiley & Sons, Inc., 1987.

3. Niederreiter, H., Random Number Generation and Quasi-Monte Carlo Methods, SIAM, 1992.

4. Cai, W., 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, 31-47, 2002.
doi:10.1002/nme.390 Google Scholar

5. Duffy, M. G., "Quadrature over a pyramid or cube of integrands with a singularity at a vertex," SIAM Journal on Numerical Analysis, Vol. 19, 1260-1262, December 1982.
doi:10.1137/0719090 Google Scholar

6. Khayat, M. A. and D. R. Wilton, "Numerical evaluation of singular and near-singular potential integrals," IEEE Trans. Antennas Propagat., Vol. 53, No. 10, 3180-3190, October 2005.
doi:10.1109/TAP.2005.856342 Google Scholar

7. Mishra, M. 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, 1619-1623, June 2008.
doi:10.1002/mop.23457 Google Scholar

8. Mishra, M. and N. Gupta, "Monte Carlo integration technique for the analysis of electromagnetic scattering from conducting surfaces," Progress In Electromagnetic Research, Vol. 79, 91-106, 2008.
doi:10.2528/PIER07092005 Google Scholar

9. Halton, J. H., "On the efficiency of certain quasi-random sequences of points in evaluating multi-dimensional integrals," Numer. Math., Vol. 2, 84-196, 1996. Google Scholar

10. Mishra, M., N. Gupta, A. Dubey, and S. Shekhar, "Application of quasi Monte Carlo integartion technique in efficient capacitance computation," Progress In Electromagnetics Research, Vol. 90, 309-322, 2009.
doi:10.2528/PIER09011310 Google Scholar

Dr. Mrinal Mishra

Professor Nisha Gupta