FDTD (finite-difference time-domain) replaces the derivatives in Maxwell's equations with differences between nearby field samples. In FDTD OpenMP, the magnetic update reads the electric field on either side of its staggered position:
for (size_t k = 0; k < width - 1; k++) { Hy[k] = Ch1[k] * Hy[k] + Ch2[k] * (Ez[k + 1] - Ez[k]); }
Hy[k] is the magnetic sample between Ez[k] and Ez[k + 1]. Their difference approximates the spatial derivative, and the precomputed coefficients include material properties and the grid steps.
The next loop updates $E_z$ from differences in the new $H_y$. Repeating these two local phases propagates waves across the grid. The Yee grid determines the sample positions; the CFL condition limits a stable time step.
Source: fdtd_ez_kernels.c.