Abstract
A time domain numerical procedure is presented for a simulation of electromagnetic wave phenomena. The technique is an adaptation of the finite-difference time domain (FDTD) approach usually applied to model electromagnetic wave propagation. In this paper a simple 2D implementation of FDTD algorithm in mathematica environment is presented. Source implementation and the effect of conductivity on the incident field are investigated. Simple illustrations of propagation in a non-conducting, partial conducting and conducting medium are provided. For the computational space, Cartesian grids of fixed size were used as it makes grid generation to be relatively easy. The numerical data generated by the program code were sampled at various time steps from t0=1 to 90 along the computational space. The simulation results show the advancement of the pulse into the medium at various time stepping, shift in the peak of the amplitude was observed on the pulse for all the time steps. An attempt to further show the attenuation as the wave propagates into the stratified medium is made. The amplitude of the pulse falls sharply from 0.006 to 1x10-11 for t0=1 and t0=50. The results indicate the working of the model and it could be used to study the behavior of the wave as it does propagate across the medium.Keywords: Stratified Medium, Finite Difference Time Domain (FDTD), mathematica, Maxwell’s Equations, Electromagnetic Waves (EM)
Highlights
Maxwell’s equations provide a description of electromagnetic phenomenon often mathematical difficulties are usually encountered while trying to solve the equations in the circumstances of practical applications
This can be simplified to state that the change in the electric field (E field) is dependent on the change in the H field across space; these result in the finite difference time domain (FDTD) equation
Wolfram Mathematica environment version 7.0 was used for implementation of the algorithm
Summary
Maxwell’s equations provide a description of electromagnetic phenomenon often mathematical difficulties are usually encountered while trying to solve the equations in the circumstances of practical applications. The technique is one of the key simulation tools in study of electromagnetic propagation [2]. It is a popular electromagnetic modelling technique in the general class of differential time domain numerical modelling methods. When Maxwell’s differential form equations are examined, it can be seen that the time derivative of the electric field (E field) is dependent on the curl of the magnetic field (H field) This can be simplified to state that the change in the E field (time derivative) is dependent on the change in the H field across space (the curl); these result in the FDTD equation.
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