Wave diffraction from the truncated hollow wedge: analytical regularization and Wiener–Hopf analysis

• Published in: Zeitschrift für angewandte Mathematik und Physik 2022-10, Vol.73 (5), Article 208
• Main Authors: Kuryliak, Dozyslav B., Lysechko, Victor O.
• Format: Article
• Language: English
• Subjects: Cylindrical coordinates; Eigenvectors; Electromagnetic radiation; Engineering; Linear algebra; Mathematical Methods in Physics; Operators (mathematics); Regularization; Regularization methods; Theoretical and Applied Mechanics; Wave diffraction; Wave scattering; Wiener-Hopf method
• ISSN: 0044-2275; 1420-9039
• DOI: 10.1007/s00033-022-01841-6

The electromagnetic wave diffraction from perfectly conducting truncated wedges is considered on the rigorous level in cylindrical coordinates. An analytical regularization method is developed to obtain mathematically accurate problem solutions. The solution method is based on the unknown field representation through the principal value Kontorovich–Lebedev integral and the eigenfunctions series. We analyze the scattering from the semi-infinite truncated wedge, which consists of two non-parallel and non-intersecting perfectly conducting and infinitely thin half-planes, and develop this technique for analysis of more complicated problems of wave diffraction from the truncated wedge of finite length. The problems are reduced to the infinite systems of linear algebraic equations (ISLAE) of the first kind. The convolution type operators and their inverse ones are used to reduce them to the ISLAE of the second kind applied to the analytical regularization procedure. Two versions of the procedure, such as left- and right-sides regularization, are considered. The developed technique is compared with the Wiener–Hopf method. The numerical examples of wave scattering from the truncated wedge, including its well-known geometries as the semi-plane and the slit in the infinite plane, are analyzed.