# Update coefficients (1D FDTD)

**Update coefficients** combine material properties, conductivities, and grid steps into factors reused by the field kernels. FDTD OpenMP stores four arrays: `ce1`, `ce2`, `ch1`, and `ch2`.

For either field, let $p$ denote permittivity $\varepsilon$ or permeability $\mu$, and let $\sigma$ denote the corresponding conductivity. The coefficient pair is:

$$
a=\frac{\sigma\Delta t}{2p},\qquad
C_1=\frac{1-a}{1+a},\qquad
C_2=\frac{\Delta t}{p\Delta x(1+a)}
$$

$C_1$ multiplies the previous field value. $C_2$ multiplies the difference between its two neighboring samples of the other field. Spatial division is already included in $C_2$, so the kernels need only subtraction, multiplication, and addition.

In a lossless cell, $\sigma = 0$, giving $C_1 = 1$ and $C_2 = \Delta t/(p\Delta x)$. Nonzero conductivity changes both coefficients to include damping.

`Fdtd_EzCoeffsUpdate()` prepares these arrays. Simulation setters for materials, boundaries, and grid steps call it again after changing their inputs. The [[fdtd-openmp-pml|PML]] therefore uses the ordinary field loops with coefficients derived from its graded losses.