Monograph•

# Scattering and Diffraction by Wedges 1: The Wiener-Hopf Solution - Theory

21 Sep 2020-

About: The article was published on 2020-09-21. It has received 6 citations till now. The article focuses on the topics: Scattering & Diffraction.

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TL;DR: In this paper, the authors present the modern state of the WienerHopf factorization method and its generalizations, and the main constructive results for matrix WFH problems are presented, approximate methods a...

Abstract: This paper reviews the modern state of the WienerHopf factorization method and its generalizations. The main constructive results for matrix WienerHopf problems are presented, approximate methods a...

6 citations

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TL;DR: In this article, the generalized WienerHopf equations (GWHEs) for wave motion in angular regions filled by arbitrary linear grids are derived for spectral functional equations, and a general method to deduce spectral functional equation and GWHE is introduced.

Abstract: In this work, we introduce a general method to deduce spectral functional equations and, thus, the generalized WienerHopf equations (GWHEs) for wave motion in angular regions filled by arbitrary li...

4 citations

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TL;DR: In this paper , an explicit algorithm for solving the Wiener-hopf factorization problem for matrix polynomials is presented, where the exact solution of the problem is constructed by a symbolic computation and a level of confidence in the final result in the case of an unstable set of partial indices is discussed.

Abstract: We discuss an explicit algorithm for solving the Wiener–Hopf factorization problem for matrix polynomials. By an exact solution of the problem, we understand the one constructed by a symbolic computation. Since the problem is, generally speaking, unstable, this requirement is crucial to guarantee that the result following from the explicit algorithm is indeed a solution of the original factorization problem. We prove that a matrix polynomial over the field of Gaussian rational numbers admits the exact Wiener–Hopf factorization if and only if its determinant is exactly factorable. Under such a condition, we adapt the explicit algorithm to the exact calculations and develop the ExactMPF package realized within the Maple Software. The package has been extensively tested. Some examples are presented in the paper, while the listing is provided in the electronic supplementary material. If, however, a matrix polynomial does not admit the exact factorization, we clarify a notion of the numerical (or approximate) factorization that can be constructed by following the explicit factorization algorithm. We highlight possible obstacles on the way and discuss a level of confidence in the final result in the case of an unstable set of partial indices. The full listing of the package ExactMPF is given in the electronic supplementary material.

2 citations

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10 Jul 2022TL;DR: In this paper , the authors present a general method based on the application of an extended version of the Wiener-Hopf (WH) technique for the analysis of the electromagnetic scattering and diffraction.

Abstract: The study of electromagnetic wave in interaction of Perfect Electrically Conducting (PEC) wedge in anisotropic media is of great interest in propagation models, GPR technologies and aerospace applications. In this work we present a general method based on the application of an extended version of the Wiener-Hopf (WH) technique for the analysis of the electromagnetic scattering and diffraction. This method is part of the semi-analytical spectral methods that allow physical interpretation of the solution in terms of field components.