A Stochastic FDTD Algorithm for Uncertainty Quantification of Electromagnetic-Thermal Simulation

This article introduces a computational approach that utilizes the stochastic finite-difference time-domain (S-FDTD) method to solve problems involving both electromagnetic and thermal fields with uncertainty parameters. This stochastic solver not only considers electrical parameters such as permittivity and permeability as random variables, but also takes into account thermal parameters such as specific heat capacity and thermal conductivity. In addition, two different simulation strategies were proposed for the specific implementation of electromagnetic-thermal coupling. As a result, the proposed algorithm achieves statistical estimation of uncertainty in the multiphysical co-simulation of electromagnetic fields and thermal fields. This article presents the procedure and intricacies of formula derivation for the proposed method. Furthermore, the precision and feasibility of the proposed method are verified through simulations of layered tissue models with reference to Monte Carlo results. The simulation of a complex human head model demonstrates that the proposed method is capable of handling complex objects and meeting practical application requirements. This method has wide applications in biomedical applications and electromagnetic protection and provides theoretical and technical support for statistical estimation in these areas.