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An Alternative Explicit and Unconditionally Stable Time-Domain Finite-Element Method for Electromagnetic Analysis

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, or 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, and irrespective of the space step. The accuracy of the method is also guaranteed when the time step is chosen based on accuracy. In addition to a formulation for lossless problems, formulations for general lossy problems are also presented in detail. Numerical experiments have demonstrated the accuracy, efficiency, and unconditional stability of the proposed new explicit method.