An Explicit Time-Domain Finite-Element Method That Is Unconditionally Stable

The root cause of the instability is quantitatively identified for the explicit time-domain finite-element method that employs a time step beyond that allowed by the stability criterion. With the identification of the root cause, an unconditionally stable explicit time-domain finite-element method is successfully created. This method is unconditionally stable in the sense that it is stable for any time step no matter how large the time step is. The proposed method retains the strength of an explicit time-domain method in being matrix free while eliminating its shortcoming in time step. Numerical experiments have demonstrated the superior performance of the proposed method in computational efficiency as well as stability compared to the conditionally stable explicit method and the unconditionally stable implicit method. The essential idea of the proposed method for achieving unconditional stability in an explicit method is also applicable to other time domain methods