Convergence of the Galerkin method in the problem of electromagnetic wave diffraction on a system of solids and curvilinear screens 

Aleksey A. Tsupak, Candidate of physical and mathematical sciences, associate professor, associate professor of the sub-department of mathematics and supercomputer modeling, Penza State University (40 Krasnaya street, Penza, Russia), altsupak@yandex.ru

Background. The purpose of this study is to prove the convergence of the projection method in the problem of diffraction of electromagnetic waves by scatterers of a complex shape. Material and methods. The Galerkin method is formulated for the vector integro-differential equation of the diffraction problem; basis vector functions are determined on volumetric bodies of arbitrary shape as well as on parametric curvilinear screens. Results. For volumetric solids and non-planar parameterized screens, basis functions satisfying the approximation condition are introduced; the convergence of the Galerkin method is proved. Conclusions: parameterization of screens makes it possible to significantly expand the applicability of the integral equations method for solving vector diffraction problems, as well as to justify the Galerkin method for their numerical solving.  

the problem of diffraction of electromagnetic waves, systems of solids and nonflat screens, integro-differential equations, basis functions, approximation condition, convergence of the Galerkin method

Tsupak A.A. Convergence of the Galerkin method in the problem of electromagnetic wave diffraction on a system of solids and curvilinear screens. Izvestiya vysshikh uchebnykh zavedeniy. Povolzhskiy region. Fiziko-matematicheskie nauki = University proceedings. Volga region. Physical and mathematical sciences. 2023;(4):14–25. (In Russ.). doi: 10.21685/2072-3040-2023-4-2