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An introduction to the parabolic equation method for electromagnetic wave propagation in tunnels

An introduction to the parabolic equation method for electromagnetic wave propagation in tunnels The purpose of this paper is to provide a brief introduction of the finite difference based parabolic equation (PE) modeling to the advanced engineering students and academic researchers.Design/methodology/approachA three-dimensional parabolic equation (3DPE) model is developed from the ground up for modeling wave propagation in the tunnel via a rectangular waveguide structure. A discussion of vector wave equations from Maxwell’s equations followed by the paraxial approximations and finite difference implementation is presented for the beginners. The obtained simulation results are compared with the analytical solution.FindingsIt is shown that the alternating direction implicit finite difference method (FDM) is more efficient in terms of accuracy, computational time and memory than the explicit FDM. The reader interested in maximum details of individual contributions such as the latest achievements in PE modeling until 2021, basic PE derivation, PE formulation’s approximations, finite difference discretization and implementation of 3DPE, can learn from this paper.Research limitations/implicationsFor the purpose of this paper, a simple 3DPE formulation is presented. For simplicity, a rectangular waveguide structure is discretized with the finite difference approach as a design problem. Future work could use the PE based FDM to study the possibility of utilization of meteorological techniques, including the effects of backward traveling waves as well as making comparisons with the experimental data.Originality/valueThe proposed work is directly applicable to typical problems in the field of tunnel propagation modeling for both national commercial and military applications. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png COMPEL: Theinternational Journal for Computation and Mathematics in Electrical and Electronic Engineering Emerald Publishing

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Publisher
Emerald Publishing
Copyright
© Emerald Publishing Limited
ISSN
0332-1649
eISSN
0332-1649
DOI
10.1108/compel-07-2021-0245
Publisher site
See Article on Publisher Site

Abstract

The purpose of this paper is to provide a brief introduction of the finite difference based parabolic equation (PE) modeling to the advanced engineering students and academic researchers.Design/methodology/approachA three-dimensional parabolic equation (3DPE) model is developed from the ground up for modeling wave propagation in the tunnel via a rectangular waveguide structure. A discussion of vector wave equations from Maxwell’s equations followed by the paraxial approximations and finite difference implementation is presented for the beginners. The obtained simulation results are compared with the analytical solution.FindingsIt is shown that the alternating direction implicit finite difference method (FDM) is more efficient in terms of accuracy, computational time and memory than the explicit FDM. The reader interested in maximum details of individual contributions such as the latest achievements in PE modeling until 2021, basic PE derivation, PE formulation’s approximations, finite difference discretization and implementation of 3DPE, can learn from this paper.Research limitations/implicationsFor the purpose of this paper, a simple 3DPE formulation is presented. For simplicity, a rectangular waveguide structure is discretized with the finite difference approach as a design problem. Future work could use the PE based FDM to study the possibility of utilization of meteorological techniques, including the effects of backward traveling waves as well as making comparisons with the experimental data.Originality/valueThe proposed work is directly applicable to typical problems in the field of tunnel propagation modeling for both national commercial and military applications.

Journal

COMPEL: Theinternational Journal for Computation and Mathematics in Electrical and Electronic EngineeringEmerald Publishing

Published: Aug 26, 2022

Keywords: Wave propagation; Parabolic equation method; Alternative direction implicit method; Electromagnetic waves; Finite difference method; Computational electromagnetics

References