C++ Implementation of FDTD Method for Electromagnetic Wave Radiation Simulation

The Finite-Difference Time-Domain (FDTD) method is a classical numerical technique for calculating electromagnetic wave propagation, particularly suitable for simulating radiation field behavior in complex media. The C++ implementation effectively leverages object-oriented programming features to construct efficient simulation systems, allowing for modular design and code reusability.

The core computational logic typically revolves around time-stepping solutions of Maxwell's equations. The program maintains three-dimensional arrays for electric and magnetic fields, alternately updating these field quantities using central difference schemes. Each time step calculation consists of two phases: magnetic field update and electric field update, requiring handling of boundary conditions (such as PML absorbing boundaries) and excitation source injection between these phases. Code implementation would typically involve nested loops iterating through spatial grid points with carefully optimized update equations.

A typical class structure includes several key modules: a grid discretization class responsible for spatial step size configuration; a material properties class managing permittivity and permeability distributions; a field update class encapsulating the Yee algorithm implementation; and a source excitation class handling radiation sources like Gaussian pulses or sinusoidal waves. Performance optimization techniques often employ pointer operations instead of array indexing and loop unrolling to enhance computational efficiency. The field update methods would implement the standard FDTD update equations with proper indexing following the Yee cell arrangement.

Such programs require special attention to numerical stability issues, where the time step must satisfy the CFL condition. Parallel computing versions typically utilize MPI or OpenMP to accelerate large-scale simulations, involving special handling of data exchange boundaries during field updates. The parallel implementation would require domain decomposition strategies and careful synchronization at processor boundaries to maintain algorithm correctness.