Geometric and Material Uncertainties Quantification of Electromagnetic-Thermal Simulation Using Stochastic Leapfrog ADI-FDTD Method

In this article, a stochastic leapfrog alternating implicit finite-difference time-domain (FDTD) method is proposed for solving problems involving electromagnetic and thermal fields. The proposed stochastic solver considers the random variations in not only material properties (primarily due to measurement limitations and material aging) but also geometry (mainly due to manufacturing errors and material deformation). The unconditional stability of the proposed stochastic method is further demonstrated with the von Neumann method. Finally, numerical examples of a microstrip bandpass filter, multilayered biological tissue model, and printed circuit board in a shielding enclosure with both geometric and material uncertainties are performed. Simulation results show good accuracy and efficiency of the proposed method when compared to the traditional stochastic FDTD and the Monte Carlo method for problems with fine structures in arbitrary directions.