FDTD MATLAB GUI Programming with 1D, 2D, and 3D Implementation Featuring MUR Absorbing Boundary

This article provides a comprehensive discussion of FDTD (Finite-Difference Time-Domain) method implementation using MATLAB GUI programming, covering 1D, 2D, and 3D simulation suites. We focus particularly on the 1D implementation featuring MUR (Mur's Absorbing Boundary Condition) - a second-order accurate boundary condition that minimizes wave reflections at computational domain edges. The implementation typically involves updating boundary field components using specialized difference equations that absorb outgoing waves. For 2D and 3D extensions, we explore how FDTD algorithms handle electromagnetic wave propagation through Yee's grid discretization, where electric and magnetic fields are staggered in space and time. Key MATLAB functions include mesh generation using meshgrid(), field updating via finite difference equations, and boundary condition implementation through specific coefficient matrices. We demonstrate practical applications for solving various electromagnetic problems including waveguide analysis, antenna radiation, and scattering phenomena, accompanied by actual case studies showing code structure and visualization techniques using MATLAB's plotting capabilities.