Symbolic-numeric implementation of the four potential method for calculating normal modes of square electromagnetic waveguide with rectangular insert

Abstract

In this paper, the Maple computer algebra system is used to construct a symbolic-numeric implementation of the method for calculating normal modes of square closed waveguides in a vector formulation. The method earlier proposed by Malykh et al. [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), 886-898 (2018)] will be referred to as the method of four potentials. The Maple system is used at all stages of treating the system of differential equations for four potentials: the generation of the Galerkin basis, the substitution of approximate solution into the system under study, the formulation of a computational problem, and its approximate solution.The paper presents the results of the verification method.In this paper, the Maple computer algebra system is used to construct a symbolic-numeric implementation of the method for calculating normal modes of square closed waveguides in a vector formulation. The method earlier proposed by Malykh et al. [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), 886-898 (2018)] will be referred to as the method of four potentials. The Maple system is used at all stages of treating the system of differential equations for four potentials: the generation of the Galerkin basis, the substitution of approximate solution into the system under study, the formulation of a computational problem, and its approximate solution.The paper presents the results of the verification method.