Stochastic FDTD for stochastic problems with axial symmetry

The random parameters remain hard to tackle for a long time in electromagnetic (EM) computations. Aiming at the time-dependent uncertainty in the axially symmetric structures, the formulations of the stochastic finite-difference time-domain (S-FDTD) method are derived, and the effectiveness is verified by a cylindrical ring structure. The simulation results indicate that the efficiency of S-FDTD method is much higher than that of the polynomial chaos (PC) method and the Monte Carlo (MC) method, that is, the S-FDTD method only takes about 3% of the computation time of the PC method and 0.03% of the computation time of the MC method with slightly lower accuracy. Thus the uncertainty in the EM calculation of axisymmetric cylindrical coordinates is possible to tackle, such as the uncertainties in the calculations of lightning electromagnetic pulse, high altitude electromagnetic pulse and so on.