:<math> \breve{s}_{mi}(t) = \frac{\delta(t)}{\kappa_{mi}} - \frac{\sigma_{mi}}{\kappa_{mi}^2} u(t)\exp \left[-\left(\frac{\sigma_{mi}}{\kappa_{mi}} + \alpha_{mi} \right)\frac{t}{\mu_0} \right] </math>
<!--[[Image:FDTD97(1).png]]-->
where d(t) and u(t) denote the Dirac delta and unit step functions, respectively. The convolutions on the right hand side of the time domain equations can be accelerated by the use of the recursive convolution (RC) method.
The CPML parameters are chosen to be an increasing function of the distance from the boundaries of the computational domain. EM.Cube uses a polynomial profile of degree n<sub>PML</sub>. Given the interrelationships among these parameters, one can write:
[[Image:FDTD100<math> \sigma_{ei}(1r).png]]= \frac{\varepsilon_0}{\mu_0}\sigma_{mi}(r) = \sigma_{max}\left( \dfrac{r}{\delta} \right)^{n_{PML}} </math>
:<math> \kappa_{ei}(r) = \kappa_{mi}(r) = 1 + \left( \kappa_{max} - 1 \right) \left( \dfrac{r}{\delta} \right)^{n_{PML} } </math>
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:<math> \alpha_{ei}(r) = \frac{\varepsilon_0}{\mu_0} \alpha_{mi}(r) = \alpha _{min} + \left(\alpha_{max } - \alpha_{min } \right) \left( \frac{r}{\delta} \right)^{n_{PML}} </math>
<!--[[Image:FDTD100(1).png]]-->
where r is the distance of field observation point inside the CPML layer from the edge of the computational domain. The parameters σ<sub>max</sub>, κ<sub>max</sub>, α<sub>min</sub> and α<sub>max</sub> as well as n<sub>PML</sub> can be modified by the user.