Analysis of numerical-analytical methods of solving an electrodynamic problem for longitudinal-regular waveguides with complex curved transverse contour

Background. The paper analyses numerical grid methods, based on difference schemes and finite elements, and numerical-analytical methods, based on a series of analytical solutions of Maxwell's equations. These methods are used in practice to describe electromagnetic fields longitudinal-regular waveguides with complex curved transverse contours. Materials and methods. It is shown that the numerical grid methods have high work content, because any changes in configuration of a transverse contour of a waveguide requires construction of the entire chain of labor-intensive computational procedures. However, there are restrictions on the ratio of the geometric dimensions, acceptable for calculation, and the configuration of transverse contours of waveguides. It is caused by complexity of building a grid analogue of a computational domain and selection of an efficient algorithm for solving the problem. In addition, application of these methods is inefficient in calculation of dielectric waveguides, as it does not ensure the required accuracy of calculation of electrodynamic parameters due to approximate setting of external boundary conditions. The analysis of the known numerical and analytical methods showed that their application for approximate solution of the electrodynamic problem is limited to a small set of waveguide models. Thus, expressions for microwave fields, calculated using the Galerkin-Ritz numerical-analytical method, satisfy the Maxwell equations approximately, and boundary conditions for them are strictly met only on those sections of transverse contours of research-precut waveguides, that correspond to the contour of the “auxiliary” waveguide of a rectangular shape. Therefore, constant propagations are calculated with accuracy from 5$\%$ to 25$\%$ (the accuracy of calculations depends on the configuration of transverse contours of waveguides), and the spatial distribution of microwave fields is calculated only qualitatively. Results and conclusions. The method on the basis of fractional areas solves the internal electromagnetic problem for longitudinal-regular metal waveguides with dielectric and gyromagnetic filling. The method allows to take into strict account boundary conditions taking into consideration the conduct of UHF fields near the edges of transverse contours of waveguides. However, its use is limited by the cases where the cross-section of waveguides can be represented as a grid of rectangular cells (partial regions). The Method on the basis of non-orthogonal eigenfunction auxiliary radiation sources allows to solve internal and external electrodynamic tasks. However, boundary conditions are not strict enough, leading to errors of calculation of electrodynamic parameters being $10^{-2}-10^{-4}$. There are also restrictions on configurations of transverse contours of waveguides, acceptable for calculation, due to complexity of constructing an auxiliary circuit from linear sources of radiation, and difficulty of choosing among them.