An Alternative Explicit and Unconditionally Stable Time-Domain Finite-Element Method for Analyzing General Lossy Electromagnetic Problems

A new method for making an explicit time-domain finite-element method unconditionally stable is developed for general electromagnetic analysis, where the dielectrics and conductors can be inhomogeneous, lossless, and lossy. In this method, for a given time step, we find the unstable modes that are the root cause of instability, and deduct them directly from the system matrix resulting from a time-domain finite-element based analysis. The resultant explicit time-domain simulation is absolutely stable for the given time step no matter how large it is, when the time step is chosen based on accuracy. Numerical experiments have demonstrated the accuracy, efficiency, and unconditional stability of the proposed new explicit method.