Yee lattice

Remarks

Check that the curl of $E$ is a central difference at the points of $H$. At the point $(i + \frac12, j + \frac12, k)$ of $H_z$, the Maxwell equation for $\partial_t H_z$ needs $(\nabla \times E)_z = \partial_x E_y - \partial_y E_x$. The values $E_y$ at $(i, j + \frac12, k)$ and $(i + 1, j + \frac12, k)$ give a difference in $x$ centred at $i + \frac12$. The values $E_x$ at $(i + \frac12, j, k)$ and $(i + \frac12, j + 1, k)$ give a difference in $y$ centred at $j + \frac12$. So both differences are centred at the point of $H_z$, and the approximation is second order.

Non-example: a collocated grid, which stores all six components at the points $(i, j, k)$, is not a Yee lattice. There a centred first difference must use the points $i - 1$ and $i + 1$, and the grid splits into decoupled sublattices that carry spurious modes.

The cubes may be replaced by rectangular boxes, and in two dimensions the lattice splits into a TE and a TM arrangement.