Radio Science, Volume 29, Number 4, Pages 1023-1033, July-August 1994 A comparative study of two-dimensional multiple scattering techniques Atef Z. Elsherbeni Electrical Engineering Department, University of Mississippi, University Abstract. The scatteringof an electromagnetic plane wave from an arbitrary configuration of parallel circular cylinders is investigated usingfour different techniques. The cylinders are made of perfectly conducting or homogeneous dielectric material. These techniquesare a boundary value type of solution, an iterative scattering procedure, a hybrid approachbased on a combination of exact and method of moments solution, and a high-frequencyasymptotic approximation. The analysis is given in detail for the transversemagnetic(TM) polarization, and that for the transverseelectric (TE) polarization is outlined. Numerical results are provided to show the major differencesbetween these techniquesand the validity of using circular cylindersin modelingcomposite two-dimensional scatterers. 1. Introduction Numerous electromagneticand antenna applica- tionsrequireaccurate analysis for predicting the scat- tering or radar cross-section characteristics of multi- ple objects. Among these applications is the modeling of reflecting and/or absorbing surfaces by an array of circularcylinders or stripsof finite width. The prob- lem of the scattering by many cylinders has been under continuous investigation for decades usingdif- ferent techniques[Row, 1955; Millar, 1960; Zitron and Karp, 1961; Twersky, 1962; Andreasen, 1964; Mullin et al., 1965; Olaofe, 1970a, b; Howarth and Pavlasek, 1973; Howarth, 1973; Young and Ber- trand, 1975; Hongo, 1978; Ragheb and Hamid, 1985; Elsherbeni and Hamid, 1987a, b]. However, efficientapplicationof thesetechniques for simulat- ing continuous surfaces is rather recent [Ragheb and Hamid, 1987; Ragheb, 1987; Ludwig, 1987; Elsherbeni and Kishk, 1989; Elsherbeni and Hamid, 1991; Paknys, 1991; Elsherbeni and Kishk, 1992; Chew and Wang, 1990; Wang and Chew, 1991; Chew et al., 1992]. Although reflecting surfaces can also be modeled by fiat strips, previous investiga- tions have not shown any significant improvement in obtaining accurate scattering data due to the use of strips instead of circular cylinders [Ragheb, 1987; Ludwig, 1987; Elsherbeni and Kishk, 1989; Elsherbeni and Hamid, 1991;Paknys, 1991;Elsher- Copyright 1994 by the American GeophysicalUnion. Paper number 94RS00327. 0048-6604/94/94RS-00327508.00 beni and Kishk, 1992; Chew and Wang, 1990; Wang and Chew, 1991; Chew et al., 1992; Ragheb and Hamid, 1988]. On the contrary, it became very obvious that the complexity of the analysis for the scattering from a large number of strips relative to that of cylinders makes the computationalcost very high. This is basically related to the simple canon- ical solutionfor the scattering from a singlecylinder in terms of Bessel and Hankel functions compared to that of the scattering from a single strip which involves odd and even Mathieu functions. In this regard, the analysis of four different tech- niques for the scattering from multiple circular cylinders will be outlined in this paper along with illustrative numerical examples for the far fields of an array of circular cylinders. These techniques include a boundary value point matching type of solution, an iterative scattering algorithm, a hybrid approach which combinesan eigenfunctionexpan- sion solution with the method of moments, and an asymptotic high-frequency method. The geometry of the analyzed problems consistsof a plane wave incident on parallel cylinders that are arbitrarily positionedas shown in Figure 1. The cylinders are made of perfectly conducting,homogeneous dielec- tric materials or combinations. In all subsequent analysis we will considerthat all cylinders are dielectric, M is the total number of cylinders, and ri is the radiusof the ith cylinderand the center of the ith cylinder is representedby the cylindrical coordinates (p•, qb•). For a conducting cylinder the relative intrinsic impedancel/r of the dielectric cylinder is set to zero. The transverse 1023