Electromagnetic Wave Propagation Equations in 2D by Finite Difference Method

Authors: N. Fusun Oyman Serteller

Abstract:

In this paper, the techniques to solve time dependent electromagnetic wave propagation equations based on the Finite Difference Method (FDM) are proposed by comparing the results with Finite Element Method (FEM) in 2D while discussing some special simulation examples.  Here, 2D dynamical wave equations for lossy media, even with a constant source, are discussed for establishing symbolic manipulation of wave propagation problems. The main objective of this contribution is to introduce a comparative study of two suitable numerical methods and to show that both methods can be applied effectively and efficiently to all types of wave propagation problems, both linear and nonlinear cases, by using symbolic computation. However, the results show that the FDM is more appropriate for solving the nonlinear cases in the symbolic solution. Furthermore, some specific complex domain examples of the comparison of electromagnetic waves equations are considered. Calculations are performed through Mathematica software by making some useful contribution to the programme and leveraging symbolic evaluations of FEM and FDM.

Keywords: Finite difference method, finite element method, linear-nonlinear PDEs, symbolic computation, wave propagation equations.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.3455621

References:

[1] J. C Bancroft, Simple wave modelling, Crewes Research Report,Volume 14-2002.
[2] Hanhui Xu, Chunguang Xu, Shiyuan Zhou, Study of Lamb Wave Propagation in Plate for UNDE by 2-D FEM Model, 2010 International Conference on Measuring Technology and Mechatronics Automation, pp.556-560. 2010.
[3] Marek Michalik, Simulation and Analysis of Power System Transients, Lecture Notes, e-mail: michalik @ pwr.wroc.pl Wrocław, February, 2008.
[4] Lu R. W., G., A reduced Computational Method about Wave Equation for Radio wave Propagation Predications, IEEE International Conferences on Microwave and millimeter wave Technology (ICMMT), (1), pp: 470 – 472,2016.
[5] M., Fraray, Mathematica Tutarial, Boise State University, version I, november, 2008.
[6] M. A. Nasser, How to solve basic engineering and mathematics problems using Mathematica, Matlab and Maple, January 28, 2015.
[7] Leitao, V. M. A., Generalized finite differences using fundamental solutions". Int J Numer Meth Eng, 81, 5, pp. 564-583.2010.
[8] Shabnam Ladan, and M. S. Abrishamian, Simulation and Measurement the Radiation of an Antenna inside a Metallic Case using FDTD,” WASET” World Academy of Science, Engineering and Technology International Journal of Electronics and Communication Engineering Vol:2, No:6, pp. 1236-1242, 2008.
[9] K. Vneet, Srivatava, Mukesh K. Awasthi, R. K. Charasia, M. Tamsir. The telegraph Equation and Its solution by reduced differential transform method, Hindawi modelling and simulation, Agust. pp. 1-6, 2013.
[10] N. F Oyman Serteller., D. Ustundag., Numerical Solution of Energy Transmission Lines Equivalent Circuit Equations with Adomian Decompositon method, Journal of Applied Nonlinear Dynamics,5(1), pp.65-71, 2016.
[11] E. A. Gevorkyan, Propagation of Electromagnetic Waves in a Regular Waveguide with Multiperiodically Modulated Media, 2017 XXIInd International Seminar/Workshop on Direct and Inverse Problems of Electromagnetic and Acoustic Wave Theory (DIPED), pp.100-103, 2017.
[12] Sha Xiao, Z. Yang, Cheng Sun, Bai-tao Sun, Pei-lei Yan, Yong Yang, Simulation of wave propagation in Cracked Elastic Medium Using FDM-FEM, 2017 Symposium on Piezoelectricity, Acoustic Waves, and Device Applications, China, pp.174-178,2017.
[13] Uber Richard P., Wood Aihua W., Communication Finite Element Boundary Integral Simulation of Transient Electromagnetic Scattering from Multiple Cavities, IEEE Transaction on Antennas and Propagation, vol.65, (6), pp: Pages: 3267 - 3272, 2017.
[14] G. Cerri, F. Moglie., R. Montesi, P. Russo., E Vecchioni., FDTD Solution of the Maxwell Boltzman System for Electromagnetic Wave Propogation in Plasma, IEEE Transaction on Antennas and Propagation 56(8), pp. 2584-2588, 2008.
[15] E Treeby, Jiri Jaros, Rohrbac Daniel, B. T Cox, Modelling Elastic Wave Propagation Using the k-Wave MATLAB Toolbox Bradley, IEEE International Ultrasonics Symposium Proceedings, pp.146-149, 2014.
[16] S. Maci, Guidance and radiation of metasurface waves, Plenary Talk, 2017.
[17] Stefan Wolfram, Wolfram Mathematica book, www.stephenwolfram.com/publications/mathematica-book, 2018.