FDTD Method Implementation with Graphical Visualization

This example demonstrates the Finite-Difference Time-Domain (FDTD) method, a widely-used computational electromagnetics technique. FDTD numerically solves electromagnetic wave equations by discretizing fields in both time and space on a computational grid, enabling simulation of wave propagation and interactions. As one of the most prevalent methods in computational electromagnetics, FDTD can model diverse phenomena including reflection, refraction, transmission, and dispersion. Its applications span antenna design, optical device simulation, and electromagnetic compatibility analysis. Our Python implementation employs key algorithmic components: Yee's grid for spatial discretization, central-difference approximations for derivative calculations, and perfectly matched layer (PML) boundary conditions. The code structure includes field update equations for electric and magnetic components using leapfrog time stepping, with matplotlib/pyplot libraries generating dynamic visualizations of field distributions. The graphical output displays real-time evolution of electromagnetic waves through color-mapped 2D plots, providing intuitive understanding of simulation results.