V.V. Akhiyarov - Ph. D. (Eng.), Leading Research Scientist, SRI of Radioelectronic Technics of Bauman Moscow State Technical University E-mail: vakhiyarov@gmail.com

Electromagnetic and acoustic wave scattering from a wedge is one of the key problems in the diffraction theory. Classical method of its solution is the field representation as Summerfeld integral. For the Dirichlet and Neumann boundary condition this problem has well known solution, in this case diffraction coefficient is calculated using simple trigonometric function. For the impedance boundary condition this problem have been solved by G.D. Maliuzhinets with the use of special function, which known as Maliuzhinets function. In this article the simple approximations of Maliuzhinets function Θ(z) is discussed. It is shown that these approximations can-t provide high accuracy and it leads to diffraction coefficient error. A new method for function Θ(z) approximation based on double exponential transformation is suggested. The proposed formula is presented in the form of converges series. The relative estimation error for various approximations of Maliuzhinets function is produced. It is shown that the obtained in this work formula provides a much higher accuracy than known methods. The diffraction coefficient for impedance wedge obtained using proposed approximation is calculated and the relative estimation error is done.

 

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