## Abstract

We consider Maxwell’s equations where the conductivity contains fast random fluctuations in time. Using an Ornstein–Uhlenbeck process, we study the effects of correlations between the random fluctuations of two different different time scales, with one an order of magnitude smaller than the other. We show that this asymptotic regime gives rise to a limiting equation where the effects of the fluctuations in the conductivity are captured in additional terms containing deterministic and stochastic corrections. For deterministic dynamics, numerical solutions to the time dependent Maxwell’s equations using a new time stepping scheme are presented. This scheme, which is based on the leapfrog method and a fourth-order time filter, significantly reduces the short oscillations generated by numerical dispersion. It uses staggering in space only, allowing explicit treatment of the electric current density terms and application of numerical smoothers. Comparisons of simulation results where Maxwell’s equations are integrated in a presence of the scattering of an electromagnetic pulse by a perfectly conducting square and those obtained with the unfiltered leapfrog show that the developed method is robust and accurate.

Original language | English (US) |
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Title of host publication | Mathematics for Nonlinear Phenomena—Analysis and Computation - In Honor of Yoshikazu Giga’s 60th Birthday |

Publisher | Springer New York LLC |

Pages | 131-160 |

Number of pages | 30 |

Volume | 215 |

ISBN (Print) | 9783319667621 |

DOIs | |

State | Published - Jan 1 2017 |

Event | International Conference on Mathematics for Nonlinear Phenomena: Analysis and Computation in Honor of Professor Yoshikazu Giga on his 60th Birthday, MNP 2015 - Sapporo, Japan Duration: Aug 16 2015 → Aug 18 2015 |

### Other

Other | International Conference on Mathematics for Nonlinear Phenomena: Analysis and Computation in Honor of Professor Yoshikazu Giga on his 60th Birthday, MNP 2015 |
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Country | Japan |

City | Sapporo |

Period | 8/16/15 → 8/18/15 |

## Keywords

- Fast numerical schemes
- Maxwell equations
- Stochastic effects
- Wave propagation

## ASJC Scopus subject areas

- Mathematics(all)