Novel Adaptive Steady-State Criteria for Finite-Difference Time-Domain Method

Two novel adaptive steady-state criteria are proposed to adaptively determine whether the steady state has been achieved in finite-difference time-domain (FDTD) method. The proposed criteria are established by the total electromagnetic energy in the computational region. To reduce the computational burden of electromagnetic energy calculation, a new approach is presented to replace the volume integral of energy with a surface integral. In addition, after newly defined attenuation coefficient and stability coefficient, novel adaptive steady-state criteria are proposed to overcome the premature convergence, nonmonotonicity, and nonconvergence challenges, which are serious in traditional adaptive steady-state criteria. At the end of this paper, numerical examples are given to demonstrate the effectiveness and superiority of our proposed criteria.