An Efficient Stochastic HIE-FDTD Algorithm for Uncertainty Quantification of Electromagnetic Fields

The stochastic hybrid implicit-explicit FDTD (S-HIE-FDTD) is proposed to quantificationally calculate the statistical variations of the electromagnetic fields. To come up with the update equations of the S-HIE-FDTD, we re-formulate the update equations of the deterministic HIE-FDTD to take the mean and the variance of the conductivity and the permittivity as inputs. The CFL condition of the proposed method only depends on the space sizes along two directions, and it uses a time step size that is larger than that of fully explicit schemes for computation domains with fine structures only in the rest of direction.