Conductivity introduces attenuation into the field equations. FDTD OpenMP stores electric conductivity $\sigma_e$ and fictitious magnetic conductivity $\sigma_m$ separately. Their loss terms are:
$$ \begin{aligned} \left.\frac{\partial E_z}{\partial t}\right|_{\mathrm{loss}} &=-\frac{\sigma_e}{\varepsilon}E_z \\ \left.\frac{\partial H_y}{\partial t}\right|_{\mathrm{loss}} &=-\frac{\sigma_m}{\mu}H_y \end{aligned} $$
Electric conductivity corresponds to current density produced by an electric field. Magnetic conductivity supplies a symmetric numerical loss term; it constructs an absorbing layer rather than ordinary electric conduction.
Both conductivities are zero in a new simulation. The PML assigns graded positive values near the grid ends, matching electric and magnetic loss rates to reduce reflection as a wave enters the layer.
The update coefficients incorporate conductivity before the time loop. Averages of old and new field values discretize the loss terms, producing a damping multiplier and a modified derivative multiplier.
Conductivity arrays are included in CSV output. The plotting tools can display their profiles alongside the fields, making the absorbing regions visible in the saved state.