# Perfectly matched layer (PML) (1D FDTD)

A **perfectly matched layer (PML)** absorbs outgoing waves near the grid boundaries. FDTD OpenMP constructs a one-dimensional lossy layer at each end, with electric and magnetic damping chosen to preserve wave impedance:

$$
\frac{\sigma_m}{\mu}=\frac{\sigma_e}{\varepsilon}
$$

Conductivity increases cubically with normalized depth into the layer. A gradual increase reduces the abrupt change seen by an entering wave, while stronger losses near the outer edge attenuate it before it reaches the grid termination.

`Fdtd_EzSimSetPML()` accepts layer width in cells. The implementation uses polynomial order three and a target reflection parameter of $10^{-6}$ to calculate maximum conductivity. This parameter guides the profile; it does not guarantee the reflection measured on a discrete grid.

Electric conductivity is sampled at integer positions and magnetic conductivity at half-cell positions, matching the [[fdtd-openmp-yee-grid|Yee grid]]. Both enter the ordinary update coefficients.

This formulation needs only $E_z$ and $H_y$. Unlike two-dimensional FDTD CUDA, it does not split the electric field into directional components.