Computational Electromagnetics Textbook Experiments

Computational electromagnetics is a discipline focused on numerical methods for electromagnetic field calculations, with the Finite-Difference Time-Domain (FDTD) method standing as one of its core algorithms widely applied in electromagnetic simulations and engineering design. The experimental programs in textbooks typically implement FDTD's fundamental principles to help learners understand electromagnetic wave propagation, reflection, scattering, and other phenomena in space.

A typical FDTD experimental program may include these key components: Grid Discretization: The computational domain is discretized using Yee cells, ensuring electric and magnetic field components alternate in space and time. In code implementation, this involves defining 3D arrays for E and H fields with staggered indexing. Update Equations: Maxwell's equations are solved iteratively using finite-difference approximations. The core code implements leapfrog time-stepping where electric fields update using curl-H terms, followed by magnetic field updates using curl-E terms. Boundary Conditions: Absorption boundary conditions like Perfectly Matched Layers (PML) are implemented to simulate infinite space and prevent unphysical reflections. This requires additional field components and update equations at domain boundaries. Source Excitation: Gaussian pulses or sinusoidal waves are commonly coded as soft/hard sources to observe propagation characteristics. Source implementation involves injecting specific field values at designated grid points during time stepping. Post-processing Analysis: Visualization tools plot field distributions or frequency-domain responses to validate results. This typically involves Fourier transforms of time-domain data and contour/vector field plotting routines.

These experimental programs serve as bridges between theory and practice, helping learners master optimization of computational parameters (like grid size and time step) for improved simulation accuracy and efficiency. For advanced applications, programs can be extended to model complex media (e.g., dispersive materials) using auxiliary differential equations, or coupled with other numerical methods like Method of Moments (MoM).