Wave diffraction from the PEC finite wedge

• Published in: Journal of engineering mathematics Vol. 134; no. 1
• Main Author: Kuryliak, Dozyslav B.
• Format: Journal Article
• Language: English
• Published: Dordrecht Springer Netherlands 01.06.2022; Springer Nature B.V
• Subjects: Applications of Mathematics; Computational Mathematics and Numerical Analysis; Eigenvectors; Linear algebra; Mathematical and Computational Engineering; Mathematical Modeling and Industrial Mathematics; Mathematics; Mathematics and Statistics; Operators; Regularization; Theoretical and Applied Mechanics; Wave diffraction; Wave scattering; Wave diffraction; Principal value integrals; Analytical regularization; Integral equations; Kontorovich–Lebedev integrals; Wedge; Mode-matching
• ISSN: 0022-0833; 1573-2703
• DOI: 10.1007/s10665-022-10222-x

The aim of this paper is to discuss the problem of wave diffraction from the finite wedge on a rigorous level using the method of analytical regularization. We apply the Kontorovich–Lebedev integrals that are considered in principal value sense and the eigenfunctions series for this purpose. The problem is reduced to a couple of the independent infinite systems of linear algebraic equations (ISLAE) of the first kind. The convolution type operators are singled out from them and the inverse operators are represented in analytical form. These two couples of operators are called the regularizing operators. They are used to reduce the initial ISLAE of the first kind to the ISLAE of the second kind. The numerical examples of wave scattering from the wedge are analysed.