# Application of the Collocation Method for Solving the Problem of Diffraction of an Electromagnetic Wave by a Rectangular Metal Plate

TL;DR: In this paper, the problem of the electromagnetic wave diffraction by a rectangular perfectly conducting metal plate is considered and the solution of the problem is reduced to the integral equations for the tangential components of the magnetic intensity vector on the metal surface.

Abstract: The classical problem of the electromagnetic wave diffraction by a rectangular perfectly conducting metal plate is considered. The solution of the problem is reduced to the solving integral equations for the tangential components of the magnetic intensity vector on the metal surface. The collocation method is applied to the equation with the representation of the sought functions in the form of a series in the Chebyshev polynomials of the 1st and 2nd kind. Numerical experiments have been carried out for a different number of terms of the Fourier series of the sought functions and a different number of collocation points. Graphs comparing the results obtained for various parameters are presented. It is shown that an increase in the number of collocation points leads to a greater stability of the solution. It is concluded that there is no clear-cut convergence of the solution with this choice of collocation points.

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01 Jan 1968

TL;DR: This first book to explore the computation of electromagnetic fields by the most popular method for the numerical solution to electromagnetic field problems presents a unified approach to moment methods by employing the concepts of linear spaces and functional analysis.

Abstract: From the Publisher:
"An IEEE reprinting of this classic 1968 edition, FIELD COMPUTATION BY MOMENT METHODS is the first book to explore the computation of electromagnetic fields by the most popular method for the numerical solution to electromagnetic field problems. It presents a unified approach to moment methods by employing the concepts of linear spaces and functional analysis. Written especially for those who have a minimal amount of experience in electromagnetic theory, this book illustrates theoretical and mathematical concepts to prepare all readers with the skills they need to apply the method of moments to new, engineering-related problems.Written especially for those who have a minimal amount of experience in electromagnetic theory, theoretical and mathematical concepts are illustrated by examples that prepare all readers with the skills they need to apply the method of moments to new, engineering-related problems."

6,593 citations

01 Jan 2005

TL;DR: The most up-to-date resource available on antenna theory and design is the IEEE 802.11 as mentioned in this paper, which provides detailed coverage of ABET design procedures and equations, making meeting ABET requirements easy and preparing readers for authentic situations in industry.

Abstract: The most-up-to-date resource available on antenna theory and design. Expanded coverage of design procedures and equations makes meeting ABET design requirements easy and prepares readers for authentic situations in industry. New coverage of microstrip antennas exposes readers to information vital to a wide variety of practical applications.Computer programs at end of each chapter and the accompanying disk assist in problem solving, design projects and data plotting.-- Includes updated material on moment methods, radar cross section, mutual impedances, aperture and horn antennas, and antenna measurements.-- Outstanding 3-dimensional illustrations help readers visualize the entire antenna radiation pattern.

2,907 citations

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Toho University

^{1}TL;DR: In this article, the Kobayashi potential was used to solve the problem of diffraction of an electromagnetic plane wave by a perfectly conducting rectangular plate and its complementary problem-diffraction by a rectangular hole in an infinite conducting plate.

Abstract: The problems of diffraction of an electromagnetic plane wave by a perfectly conducting rectangular plate and its complementary problem-diffraction by a rectangular hole in an infinite conducting plate-are rigorously solved using the method of the Kobayashi (1931) potential. The mathematical formulation involves dual integral equations derived from the potential integrals and the boundary condition on the plane where a plate or hole is located. The weighting functions in the potential integrals are determined by applying the properties of the Weber-Schafheitlin's integrals and the solution is obtained in the form of a matrix equation. Illustrative computations are given for the far diffracted field pattern and the current densities induced on the plate. The results of the patterns are compared with the results obtained from physical optics (PO) and the physical theory of diffraction (PTD). The agreement is fairly good, particularly with the PTD solutions.

73 citations

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TL;DR: In this paper, the authors presented a solution for diffraction of plane electromagnetic waves by an infinitely thin, perfectly conducting, circular disk and by a circular hole in a plane conducting screen.

Abstract: Rigorous solutions are presented of the problems of diffraction of plane electromagnetic waves by an infinitely thin, perfectly conducting, circular disk and by a circular hole in a plane conducting screen. The unique solution satisfying the edge condition is obtained from the two component Hertz vector, by the method of expansion in the hypergeometric polynomial. Total scattering cross section, the transmission coefficient, electric current on the disk, electric field in the hole, and electric field at the distant place are shown in the figure as a function of k a =2π a /λ.

51 citations

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12 May 2014

44 citations