Electromagnetic scattering from arbitrary flat plates: Analysis of the problem by using method of moments with different sinc type basis functions (original) (raw)
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Turkish Journal of Electrical Engineering and Computer Sciences
Electromagnetic scattering from strips of layers is analyzed using the method of moments (MoM) for both polarizations in spatial domain with the sinc-type orthogonal sets as basis and testing functions. We exploited the sinc function's properties of exponential convergence, the orthogonality, easy convolution and better handling of singular kernels in MoM procedure resulting in fast performance and reasonable accuracy even in ordinary MoM treatment. We transferred the integral of the Hankel function multiplied by sinc functions to Hankel function introducing a slight error with large band width. We proved that this relative error during the generation of the main matrix elements is smaller than that of the free space error, i.e., 1%-0.5% for considerably large matrix sizes. Our approach is readily applicable to a singular kernel problem due to properties of the sinc functions in particular 2D geometry. The procedure undertaken here is proven to be very efficient as regard to similar treatments in the literature developed mainly for regular kernels. Various numerical results are calculated such as the surface induced current and normalized far field radiation pattern. We compared them with the results available in the literature.
Microwave and Optical Technology Letters, 2008
In this work, we present an alternate set of basis functions, each defined over a pair of planar triangular patches, for the method of moments solution of electromagnetic scattering and radiation problems associated with arbitrarily shaped, closed, conducting surfaces. The present basis functions are point-wise orthogonal to the pulse basis functions previously defined. The prime motivation to develop the present set of basis functions is to utilize them for the electromagnetic solution of dielectric bodies using a surface integral equation formulation which involves both electric and magnetic currents. However, in the present work, only the conducting body solution is presented and compared with other data.
Singular Edge and Corner Basis Functions for Scattering from Conducting Plates
2018 48th European Microwave Conference (EuMC), 2018
The Method of Moments (MoM) is an efficient way of obtaining solutions of integral equations for 2D and 3D electromagnetic structures by subdividing them into simple shapes such as triangles and rectangles and using suitable polynomial basis functions to describe fields or currents. In the presence of sharp edges and corners, the currents may be unbounded and the accuracy of the solution may be poor due to the inappropriate model provided by a polynomial basis. Attempts to improve the accuracy by increasing the number of cells or the polynomial order of the basis functions may fail as a result. In this paper new basis functions are proposed with unbounded behavior, to more efficiently model edge and corner singularities for quadrilateral cells.
Progress In Electromagnetics Research, 2010
This paper presents an extension over a novel, three dimensional high frequency method for the calculation of the scattered electromagnetic (EM) field from a Perfect Electric Conductor (PEC) plate, which is based on the Physical Optics (PO) approximation and the Stationary Phase Method (SPM). This extension defines a new analytical method which is proved to be very efficient in computer execution time and enhances the accuracy of its predecessor around the area of the main scattering lobe. This new analytical method accomplishes high accuracy through the use of higher order approximation terms, which imply the use of Fresnel functions (SPM-F method). By using higher order Fresnel approximation terms, no impact on the time efficiency of the SPM method appears to
Electromagnetic scattering by surfaces of arbitrary shape
Antennas and Propagation, IEEE …, 1982
The electric field integral equation (EFIE) is used with the moment method to develop a simple and efficient numerical procedure for treating problems of scattering by arbitrarily shaped objects. For numerical purposes, the objects are modeled using planar triangular surfaces patches. Because the EFIE formulation is used, the procedure is applicable to both open and closed surfaces. Crucial to the numerical formulation is the development of a set of special subdomain-type basis functions which are defined on pairs of adjacent triangular patches and yield a current representation free of line or point charges at subdomain boundaries. The method is applied to the scattering problems of a plane wave illuminated flat square plate, bent square plate, circular disk, and sphere. Excellent correspondence between the surface current computed via the present method and that obtained via earlier approaches or exact formulations is demonstrated in each case. E [ 1 1. Not only is the connectivity of a wire-grid model easily specified for computer input, but the approach also has the advantage that all numerically computed integrals in the moment matrix are one dimensional.
Radio Science, 2003
1] The physical optics approximation is employed in the derivation of a closed form expression for the radar cross section (RCS) of a flat, perfectly conducting plate of various shapes, located over a dielectric, possibly lossy half-space. The half-space is assumed to lie in the far field region of the plate. The well-known "four-path model" is invoked in a firstorder approximation of the half-space contribution to the scattering mechanisms. Numerical results are compared to a reference, Moment Method solution, and the agreement is investigated, to assess the accuracy of the approximations used. The analytical expressions derived can facilitate very fast RCS calculations for realistic scatterers, such as ships in a sea environment, or aircraft flying low over the ground.
Progress In Electromagnetics Research, 2011
We present new implementations in Method of Moments of two types of second kind integral equations: (i) the recently proposed Electric-Magnetic Field Integral Equation (EMFIE), for perfectly conducting objects, and (ii) the Müller formulation, for homogeneous or piecewise homogeneous dielectric objects. We adopt the Taylororthogonal basis functions, a recently presented set of facet-oriented basis functions, which, as we show in this paper, arise from the Taylor's expansion of the current at the centroid of the discretization triangles. We show that the Taylor-orthogonal discretization of the EMFIE mitigates the discrepancy in the computed Radar Cross Section observed in conventional divergence-conforming implementations for moderately small, perfectly conducting, sharp-edged objects. Furthermore, we show that the Taylor-discretization of the Müllerformulation represents a valid option for the analysis of sharpedged homogenous dielectrics, especially with low dielectric contrasts, when compared with other RWG-discretized implementations for dielectrics. Since the divergence-Taylor Orthogonal basis functions are facet-oriented, they appear better suited than other, edge-oriented, discretization schemes for the analysis of piecewise homogenous objects since they simplify notably the discretization at the junctions arising from the intersection of several dielectric regions.
A fast analysis of electromagnetic scattering by arbitrarily shaped homogeneous dielectric objects
Microwave and Optical Technology Letters, 2003
In this paper, we present a fast analysis of electromagnetic scattering by arbitrarily shaped 3D homogeneous dielectric objects. The solution is based on the PMCHW integral equation formulation. The method of moments (MoM) is used to solve the integral equations and the precorrected fast Fourier transform (P-FFT) method is used to eliminate the need to generate and store the square impedance matrix and to speed up the matrix–vector product. Several numerical examples are included, which illustrate the accuracy and capability of the present method. © 2003 Wiley Periodicals, Inc. Microwave Opt Technol Lett 38: 30–35, 2003
Journal of scientific computing, 2000
The problem of electromagnetic scattering by a homogeneous dielectric object is usually formulated as a pair of coupled integral equations involving two unknown currents on the surface S of the object. In this paper, however, the problem is formulated as a single integral equation involving one unknown current on S. Unique solution at resonance is obtained by using a combined field integral equation. The single integral equation is solved by the method of moments using a Galerkin test procedure. Numerical results for a dielectric sphere are in good agreement with the exact results. Furthermore, the single integral equation method is shown to have superior convergence speed of iterative solution compared with the coupled integral equations method.