J. Electromagnetic Analysis & Applications, 2009, 1: 254-258 doi:10.4236/jemaa.2009.14039 Published Online December 2009 (http://www.SciRP.org/journal/jemaa) Copyright © 2009 SciRes JEMAA Monte Carlo Integration Technique for Method of Moments Solution of EFIE in Scattering Problems Mrinal MISHRA, Nisha GUPTA Department of Electronics and Communication Engineering, Birla Institute of Technology, Mesra, India Email: mrinal.mishra@gmail.com, ngupta@bitmesra.ac.in Received May 8 th , 2009; revised July 10 th , 2009; accepted July 18 th , 2009. ABSTRACT An integration technique based on use of Monte Carlo Integration is proposed for Method of Moments solution of Elec- tric Field Integral Equation. As an example numerical analysis is carried out for the solution of the integral equation for unknown current distribution on metallic plate structures. The entire domain polynomial basis functions are em- ployed in the MOM formulation which leads to only small number of matrix elements thus saving significant computer time and storage. It is observed that the proposed method not only provides solution of the unknown current distribution on the surface of the metallic plates but is also capable of dealing with the problem of singularity efficiently. Keywords: Scattering, EFIE, Method of Moments, Monte Carlo Integration 1. Introduction The Method of Moments (MoM) [1] is one of the widely used numerical techniques employed for the solution of Integral Equations. The MoM is based upon the trans- formation of an integral equation, into a matrix equation. However, the application of the spatial-domain MoM to the solution of integral equation is quite time consuming. The matrix-fill time would be significantly improved if these integrals can be evaluated efficiently. The MoM employs expansion of the unknown function inside the integral in terms of known basis functions with unknown coefficients to be determined. Point matching technique or Galerkin’s technique commonly employed in MoM results in a system of linear equations equal in number to that of unknown coefficients. This leads to a matrix equation for the coefficients. The matrix thus obtained is called the ‘moment’ matrix. The unknown coefficients can then be obtained by matrix inversion. The MoM method involves two approaches, the sub domain [2,3] and the entire domain [4,5] approaches, essentially based on the two kinds of basis functions em- ployed for the expansion of the unknown function on the metal surface. The entire domain basis functions extend over the whole region occupied by the structure, whereas the sub domain basis functions are defined to exist over a section of the structure and have a zero value over the rest of its portion. The choice of the type of basis func- tion depends upon the size and shape of the metallic structure in the problem. The advantage with the sub domain basis functions is that due to their flexibility to be defined over small polygonal domains of varying sizes. The whole structure under investigation can be modeled as consisting of large number of such polygonal sub domains, thus making possible the analysis of com- plicated shaped structures. The disadvantage with these basis functions is that they are limited to electrically small and moderately large structures, as the number of sub domains required to model large structures accu- rately becomes very large. This results in the moment matrix of a large size increasing the computation costs in terms of memory and CPU time. The entire domain basis functions, on the other hand, require a very few number of expansion terms. These are also capable of analyzing electrically large structures and the solution obtained with these functions are more ac- curate than the sub domain basis functions. This results in a faster and more accurate solution, thus reducing the computational cost. One of the requirements of the entire domain basis functions is a prior knowledge of the dis- tribution of the unknown quantity for the kind of the structure under consideration. The effectiveness of a MoM numerical solution depends on a judicious choice of basis functions. The optimal choice of the basis func- tion is one that provides solutions with the fewest num- ber of expansion terms and in shortest computational time. These functions should incorporate as closely as possible the physical conditions of the actual distribution of the unknown quantity on the region of interest. In this paper, entire domain polynomial basis function is utilized