A method for partial estimation of electromagnetic wave diffraction by a longitudinal baffle in an endless waveguide 

Garnik V. Abgaryan, Assistant of the sub-department applied mathematics and artificial intelligence, Kazan (Volga region) Federal University (35 Kremlevskaya street, Kazan, Russia), E-mail: g.v.abgaryan@gmail.com
Almaz N. Khaybullin, Student, Kazan (Volga region) Federal University (35 Kremlevskaya street, Kazan, Russia), E-mail: almaz.khaybullin@mail.ru
Anna E. Shipilo, Student, Kazan (Volga region) Federal University (35 Kremlevskaya street, Kazan, Russia), E-mail: shadowfire-1@mail.ru 

Background. A 2D problem of diffraction of a TE-polarized electromagnetic wave in an infinite waveguide with a longitudinal baffle is studied. The mathematical formulation of this physical problem is equivalent to a boundary value problem for the Helmholtz equation with Dirichlet-type boundary conditions and matching conditions. To solve this problem, the method of partial regions is used. In accordance with this method, the solution of the problem in each subdomain is sought in the form of a series with unknown coefficients, which are found from the matching conditions at the media interface. Using the method of integral-summation identities, this boundary value problem is reduced to an infinite system of linear algebraic equations (SLAE) with respect to unknown coefficients. Results. An SLAE corresponding to the 2D problem of diffraction in an infinite waveguide with a longitudinal baffle is derived. Computational experiments have been carried out. Resonance effects are found, which are obtained in cases where the frequency of the incident wave is close to the natural frequencies of the subregions corresponding to the branched part of the waveguide. Diagrams of electromagnetic fields at resonant frequencies are constructed. The energy values of the electromagnetic field are calculated for various wave numbers. Conclusions. From the results of computational experiments, we can conclude that the accuracy of fulfillment of the boundary conditions of matching depends on the SLAE truncation parameter. To check the accuracy of fulfillment of the boundary conditions, the concept of the matching residual is introduced. It is shown that resonance phenomena are observed at frequencies of the incident wave close to the eigenvalues of the subregions corresponding to the branched part of the waveguide. 

diffraction problem, partial domain method, resonant frequency 

Abgaryan G.V., Khaybullin A.N., Shipilo A.E. A method for partial estimation of electromagnetic wave diffraction by a longitudinal baffle in an endless waveguide. Izvestiya vysshikh uchebnykh zavedeniy. Povolzhskiy region. Fiziko-matematicheskie nauki = University proceedings. Volga region. Physical and mathematical sciences. 2022;(4):3–16. (In Russ.). doi:10.21685/2072-3040-2022-4-1