Abstract
A new hybrid finite element method (HFEM) was developed, using basis functions of first and second order, to analyse the electromagnetic wave propagation in three types of waveguides: disk waveguides, ring waveguides and cylindrical waveguides. For validation purposes, results obtained with the HFEM method were compared with those obtained with a recursive finite element method (RFEM) and with two different analytical methods. The domain discretization effect on the results of the new HFEM method was examined using either a uniform distribution of nodes or a Delaunay distribution method. The results show that the Delaunay method, used in the mesh definition, is important, not only to assure the reliability of the method but also to significantly reduce the computation time and memory consumption. Also, the influence of the distance between the fictitious boundary and the waveguide core was analysed showing an important effect on the result numerical accuracy. In conclusion, results show that the new hybrid finite element method presented has a significant advantage on calculation time over the recursive finite element method.
Highlights
The finite element method (FEM) arose due to the need to solve complex problems [1]
The main objective of this section is the validation of the new hybrid finite element method (HFEM) method
This section is divided into three subsections: in the first one, the electromagnetic wave propagation in a disk waveguide was considered, and the results were compared with recursive finite element method (RFEM) method results [18]; in the second and third ones the electromagnetic wave propagation in an infinite height ring waveguide and in a finite height ring waveguide was considered, and the results were compared with the results of an analytical model presented by Marcatili [22] and, in the third case, with an analytical model presented by Torres [23].The HFEM and the RFEM were implemented using a set of routines encoded in the "Mathematica" language
Summary
The finite element method (FEM) arose due to the need to solve complex problems [1]. The FEM is, in our days, one of the most important numerical methods used in simulation in different areas [4], namely in biomedical applications [5], [6], in the optimization [7], design and simulation of electrical, electronic and optical devices [8]. The importance of the method is mainly due to its ability to handle problems with complicated geometries and irregular boundaries. The FEM needs adequate space-time discretization, in order to obtain accurate results. Large dimension field problems have to be solved, demanding powerful computers and consuming great amounts of computational time
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