Factorization Method for Finite Fine Structures

Abstract

Abstract-This paper deals with the development of the WienerHopf method for solving the diffraction of waves at fine strip-slotted structures. The classical problem for diffraction of plane wave at a strip is an important canonical problem. The boundary value problem is consecutively solved by a reduction to a system of singular boundary integral equations, and then to a system of Fredholm integral equations of the second kind, which effectively is solved by one of three presented methods: A reduction to a system of the linear algebraic equations with the help of the etalon integral and the saddle point method numerical discretization based on Gauss quadrature formulas the method of successive approximations. The solution to the problem in the first method contains a denominator that takes into account the resonance process. Moreover, the precision of the main contribution of the shortwave asymptotic solution is ensured down to the quasi-stationary limit. The paper presents also comparisons of with earlier known results.

Diffraction of Plane Wave by Strip With Arbitrary Orientation of Wave Vector

“…We will construct the solution of the system of the singular Equations (13) and (14) by a technique, developed in Ref. [10] as analytical sources, localized on the edges of the strip. Thus, the Fourier component of the current density is written as a sum of two analytical sources:…”

“…Really, each a summand of an integrand in (14) proves to be an analytical function in that half-plane where the integration contour is closed, according to the Jordan's lemma. Representing the B + (w) function in the form of a Cauchy type integral (16), taking a residue in the point w = u and compensating the branch point in the LHP [10], we obtain the required function from (13):…”

“…The classical diffraction problem of a plane wave, orthogonally impinged on a strip edge was considered in a closed-form [10]. In the present paper a generalization of the article [10] in case when the plane wave propagates in an arbitrary direction is carried out.…”

“…In the present paper a generalization of the article [10] in case when the plane wave propagates in an arbitrary direction is carried out. For convenience the boundary-value problem is divided into two independent ones which are named after Dirichlet and Neumann and then are solved separately by the Wiener-Hopf method [5,10].…”

“…In the present paper a generalization of the article [10] in case when the plane wave propagates in an arbitrary direction is carried out. For convenience the boundary-value problem is divided into two independent ones which are named after Dirichlet and Neumann and then are solved separately by the Wiener-Hopf method [5,10]. It is important to observe that the obtained solution automatically satisfies the boundary Meixner's condition [11] on the strip edge which determines the uniqueness of the solution of the boundary-value problem.…”