Entire-domain Basis Functions Research Articles

Pyramidal and Entire Domain Basis Functions in the Method of Moments

New basis functions are used for the problem of solving the surface current on a conducting plate by the method of moments. Pyramidal functions adopted from the finite element method are geometrically flexible. Entire domain trigonometrical functions offer the advantage of computing the tangential electric field everywhere on the surface of the plate, because the surface charge densities are continuous. In this way the error can be estimated in the domain of the operator.

Analysis off waveguide-fed thick radiating rectangular windows in a ground plane

A moment method analysis of a radiating window in an infinite conducting plane excited by a rectangular waveguide is presented. The boundary conditions at the two interfaces are derived taking the effect of window thickness into account. The application of the moment method, using entire domain basis functions, transforms the integral equations representing the boundary conditions into matrix equations. The reflection coefficient seen by the feed waveguide is evaluated from amplitude coefficients determined from matrix inversion. Excellent agreement between theoretical and experimental values of complex reflection coefficient is obtained.

Analysis of Gaussian cavity-backed slot radiators

The problem of a slot radiator backed by a Gaussian cavity is analyzed. The fields in the cavity are expressed in terms of Gauss–Hermite functions whose orthogonality property is used to obtain the expansion coefficients. An integral equation is derived for the tangential electric field in the slot aperture and entire-domain basis and testing functions are utilized in its numerical evaluation. The restrictions imposed on the cavity dimensions by the wave beam assumptions are discussed and the equation for the surface of the cavity backwall is given. Finally, typical numerical results for the voltage distribution along the slot aperture are presented for the cases of symmetric and skew-symmetric excitations.

A numerical solution for conducting bodies of arbitrary shape

An efficient numerical technique based on a Fourier expansion of the surface current is developed to study the electromagnetic scattering from three-dimensional geometries of arbitrary shape. In this method, the discrete domain representing the structure surface is geometrically represented by two orthogonal contours. One is selected along the intersection of the x–z plane with the object's surface, and the other along the corresponding one in the x–y plane. Entire domain basis functions are selected for the current component in the x–y plane, and subdomain linear basis functions are used to represent the other current component. The method of moments is used to solve the problem numerically. The technique is then applied to study the scattering from discrete surfaces such as squares and rectangles, to compare them with those of the coordinate-transformation technique developed earlier. The behavior of the solutions with the number of modes is investigated to determine their coupling.

Modal analysis method for bodies of arbitrary cross-section for numerical computation

A modal analysis method is used to investigate scattering from conducting objects of rectangular cross-section, and to determine the variation of the radar cross-section due to the polarisation or direction of the incident wave and the effect of the mode coupling resulting from crosssectional perturbation from a circular cylinder. The traditional approach of surface integral equations in conjunction with a moment method is used to solve the problem numerically. A geometric transformation is used to select entire domain basis functions for the surface current along the cross-section. Subdomain basis functions are used to represent the current component in the plane orthogonal to the cross-section. Owing to the geometric structure of the object the current modes are coupled. The degree of coupling and convergence of the modes are investigated. Representative results for objects of square and rectangular cross-sections are presented and discussed.

On entire-domain basis functions with square-root edge singularity (EM scattering)

The surface current density generated on thin conducting scatterers or radiations has a well-known singular edge behaviour. Using an explicit transformation between certain regular and singular basis functions, the author compares the convergences of the current expansions of both sets. Also studied are the complementary expansions of the scattered field which result from integrating the current. The discussion is extended to periodic strip structures where the phenomenon of relative convergence is demonstrated. >