Discrete and Continuous Models and Applied Computational ScienceDiscrete and Continuous Models and Applied Computational Science2658-46702658-7149Peoples' Friendship University of Russia named after Patrice Lumumba (RUDN University)1836710.22363/2312-9735-2018-26-2-129-139Research ArticleOn the Calculation of Electromagnetic Fields in Closed Waveguides with Inhomogeneous FillingTyutyunnikA A<p>assistant of Department of Applied Probability and Informatics of Peoples’ Friendship University of Russia (RUDN University) (</p>tyutyunnik_aa@rudn.universityPeoples’ Friendship University of Russia (RUDN University)1512201826212913921042018Copyright © 2018, Tyutyunnik A.A.2018<p>The paper investigates waveguides of constant cross-section with ideally conducting walls and arbitrary filling. The problem of finding the normal modes of a waveguide in a full vector formulation has been set and discretized. In the framework of numerical experiments, the guiding and evanescent modes of the waveguide are calculated for several variants of the fillings. The problem of diffraction of the normal waveguide mode incident on the joint of two waveguides, the cross-sections of which coincide, and the filling at the junction varies abruptly, is set and discretized. The results of numerical experiments for specific configurations of waveguide joints are presented, and the transmission and reflection coefficients of the guided modes are calculated. The solution of the Maxwell equations system is based on the decomposition of fields with the help of four potentials, and in the present work a symbolic-numerical method is realized that uses this approach. The numerical experiments presented in this paper show that the proposed approach and the method on its basis allow the effective calculation of various characteristics of waveguide systems. The adequacy of the approach used is also evidenced by comparing the results obtained with the results of V.V. Shevchenko for the diffraction problem at the junction of two open waveguides The symbolic-numerical method used in the work is implemented in the computer algebra system Maple, in particular, the calculations of matrix elements in the framework of the incomplete Galerkin method are carried out in symbolic form to accelerate further calculations using numerical methods.</p>MapleSageSagemathwaveguideMaxwell’s equationsnormal modespartial radiation conditionsincomplete Galerkin methodKantorovich methodSageSagemathволноводуравнения Максвелланормальные модыпарциальные условия излучениянеполный метод Галёркинаметод Канторовича[A. A. Samarskiy, A. N. Tikhonov, On the Representation of a Field in a Waveguide in the Form of a Sum of Fields TE and TM, Zhurnal tekhnicheskoy fiziki 18 (7) (1948) 959–970, in Russian.][I. E. Mogilevskii, A. G. Sveshnikov, Mathematical Problems of the Theory of Diffraction, Faculty of Physics MSU, Moscow, 2010, in Russian.][M. D. Malykh, L. A. Sevastianov, A. A. Tiutiunnik, N. E. Nikolaev, On the Representation of Electromagnetic Fields in Closed Waveguides Using Four Scalar Potentials, Journal of Electromagnetic Waves and Applications 32 (7) (2018) 886–898.][M. D. Malykh, A. L. Sevastianov, L. A. Sevastianov, A. A. Tyutyunnik, On the Reduction of Maxwell’s Equations in Waveguides to the System of Coupled Helmholtz Equations, RUDN Journal of Mathematics, Information Sciences and Physics 26 (1) (2018) 39–48, in Russian. doi:10.22363/2312-9735-2018-26-1-39-48.][D. V. Divakov, M. D. Malykh, A. L. Sevastianov, L. A. Sevastianov, Simulation of Polarized Light Propagation in the Thin-Film Waveguide Lens, RUDN Journal of Mathematics, Information Sciences and Physics 25 (1) (2017) 56–68, in Russian. doi:10.22363/2312-9735-2017-25-1-56-68.][D. V. Divakov, Numerical Solution of Waveguide Propagation Problem of Polarized Light in an Integrated Optical Waveguide, abstract of PhD thesis. Peoples’ Friendship University of Russia (RUDN University), Moscow. in Russian (2017).][А. А. Ivanov, V. V. Shevchenko, A Planar Transversal Junction of Two Planar Waveguides, Journal of Communications Technology and Electronics 54 (1) (2009) 63–72.][A. G. Sveshnikov, Incomplete Galerkin Method, DAN USSR 236 (5) (1977) 1076–1079, in Russian.][A. N. Bogolyubov, A. I. Erokhin, I. E. Mogilevsky, Vector Waveguide Model with Incoming Edges, Zhurnal radioelektroniki (electronic journal) (2), in Russian.][M. Bronstein, Symbolic Integration I, Springer-Verlag Berlin Heidelberg, Berlin, 1997.][B. Z. Katzenelenbaum, The Theory of Irregular Waveguides with Slowly Varying Parameters, AN USSR, Moscow, 1961, in Russian.][V. V. Shevchenko, Smooth Transitions in Open Waveguides, Nauka, Moscow, 1969, in Russian.]