MATLAB Implementation of 2D FDTD with Mur Boundary Conditions for Rectangular Scatterer Analysis

This documentation provides an overview of 2D FDTD methodology, Mur absorbing boundary conditions implementation, and rectangular scatterer simulation. Below we expand these concepts with technical implementation specifics.

The Finite-Difference Time-Domain (FDTD) method represents a numerical approach for solving Maxwell's equations in two-dimensional space. The implementation involves discretizing both spatial domains (using Yee cell structure) and temporal progression through leapfrog time-stepping. Core algorithmic components include electric field updates via curl-H equations and magnetic field updates through curl-E equations, typically implemented using central difference approximations. Code implementation requires careful management of field arrays (Ez for TM modes, Hx/Hy components) and time-stepping loops where each iteration updates field values across the computational grid.

To simulate unbounded domains efficiently, Mur absorbing boundary conditions are implemented at grid edges to minimize artificial reflections. The first-order Mur condition applies wave equation approximations at boundaries through field value corrections using adjacent nodes' historical data. Implementation involves creating specialized update functions for boundary nodes that incorporate propagation direction factors, typically requiring additional arrays to store previous time step values at boundaries. Proper implementation ensures wave energy dissipation with minimal numerical dispersion.

The rectangular scatterer simulation involves defining a dielectric or conducting rectangle within the computational domain. Code implementation requires material property matrices (epsilon_r, mu_r) and obstacle masking functions that modify update equations within the object region. Scattering analysis implements field monitors around the object to capture near-field patterns, with far-field transformation possible through near-to-far-field conversion algorithms. Post-processing includes radar cross-section calculations and field visualization techniques using MATLAB's contourf or pcolor functions for electromagnetic pattern analysis.