# Permeability (1D FDTD)

**Permeability** $\mu$ describes the magnetic response of a material. In FDTD OpenMP's linear medium, magnetic flux density is proportional to the magnetic field:

$$
B_y=\mu H_y,\qquad \mu=\mu_r\mu_0
$$

Relative permeability $\mu_r$ compares a material with vacuum. The default is $\mu_r = 1$ throughout the grid. Increasing permeability while holding permittivity fixed reduces wave speed and increases wave impedance. A boundary between different impedances can produce a reflected wave.

`Fdtd_EzSimSetMu()` changes absolute permeability over a half-open cell range. The command-line driver accepts relative values instead. For example, `--set-mu-r=2,80,120` assigns twice the vacuum permeability to cells 80 through 119.

Permeability belongs to the magnetic samples on the [[fdtd-openmp-yee-grid|Yee grid]] and enters the coefficients used to update $H_y$. It also scales the magnetic conductivity used by the absorbing boundary.

The implementation stores a scalar permeability array and recomputes coefficients after changes through the simulation setter. It represents a fixed linear response, without magnetic hysteresis or frequency-dependent material behavior.