An Unconditionally Stable 2-D Stochastic WLP-FDTD Method for Geometric Uncertainty in Superconducting Transmission Lines

In this article, a compact unconditionally stable two-dimensional (2-D) stochastic weighted Laguerre polynomial finite-difference time-domain (S-WLP-FDTD) method for geometric uncertainty in superconducting transmission lines is proposed. It calculates both the Maxwell equations and the London equations and uses a weighted Laguerre polynomial (WLP) scheme to eliminate the stability constraint. The mean and the standard deviation of electromagnetic fields, voltages, and currents are calculated. Compared with the Monte Carlo method and 2-D S-FDTD method, the proposed method has the same accuracy but much higher efficiency. The runtime of the proposed S-WLP-FDTD method is only 2.4% of that of the S-FDTD method. Thus, the proposed method is suitable for predicting the influence of geometric uncertainty on superconducting transmission lines.