Abstract
Article introduces an extension of the approximating functions method, a particular case of the finite element method (FEM) with interpolating functions in the form of Lagrange polynomials of a special form, to solve electrodynamics problems in a planar waveguide with constant polarization in the spatial-temporal domain using the Volterra integral equation method. The main goal of the article is to expand the area of applicability of this method to three-dimensional problems in a planar waveguide with constant polarization, as well as to obtain general interpolation expressions in analytical form, which will be used to construct a system of nonlinear equations for solving specific problems.
Highlights
The Volterra integral equation method is an approach based on integral equations equivalent to the Maxwell’s equations [1,2] to solve electrodynamics problems in 1-3 dimensional space and time domain
The present work continues to develop the approximating functions method for the planar waveguides with non-magnetic media with losses for the case of constant polarization inside it
PROBLEM STATEMENT As it was shown in work [15], the equation for the problem with planar waveguide with non-magnetic media with
Summary
The Volterra integral equation method is an approach based on integral equations equivalent to the Maxwell’s equations [1,2] to solve electrodynamics problems in 1-3 dimensional space and time domain. Its key features are natural description of non-stationary and nonlinear features, unified definition of the inner and outer problems, and inclusion of initial and boundary conditions in the same equations – the equations form is Volterra integral equation of the second kind and it is the same for various media and does not depend on the initial signal expression. These advantages of the Volterra integral equation method significantly simplify the problem statement and its solution process, based on the universal modeling algorithms for a wide range of electrodynamics problems [3,4]. The present work continues to develop the approximating functions method for the planar waveguides with non-magnetic media with losses for the case of constant polarization inside it
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