Aplicação do Método das Diferenças Finitas no Domínio do Tempo na Simulação de Ondas Eletromagnéticas em Meios com Perfis Variáveis

Abstract

The modeling of electromagnetic wave propagation is essential in applications related to communications, energy transmission, and medical imaging. Classical Electromagnetism describes this phenomenon through partial differential equations, whose analytical solutions become complex or unfeasible in realistic scenarios. In this context, numerical methods such as the Finite-Difference Time-Domain (FDTD) method arise as efficient alternatives, especially with the advancement of computational capabilities. This work aims to apply the FDTD method to simulate the one-dimensional propagation of electromagnetic waves. An algorithm was developed in the SciLab software to model different electrical conductivity profiles. Validation was performed by comparing the numerical results with the analytical solution of a sinusoidal plane wave propagating in free space. Additionally, Gaussian pulse simulations were conducted to evaluate wave behavior in media with constant, linear, and exponential conductivity. The influence of spatial resolution on the algorithm’s execution time was also analyzed. The results showed excellent agreement with the analytical solution, demonstrating the accuracy of the FDTD method. It was also observed that increasing spatial resolution leads to higher computational cost, and that conductivity profiles directly affect reflection and absorption phenomena. It is concluded that the FDTD method is a robust and reliable tool for the numerical study of electromagnetic wave propagation in one dimension.