Stability Analysis of the Two-Dimensional HIE-FDTD Method Including Lumped Resistors

Here, the stability analysis of the two-dimensional (2-D) hybrid implicit-explicit finite-difference time-domain (HIE-FDTD) algorithm with lumped resistors is discussed. Specially, there are three different difference schemes of lumped resistors are discussed: the explicit, semi-implicit, and implicit scheme. The stability analysis of the proposed method showed that the HIE-FDTD algorithm loaded with lumped elements is weakly conditionally stable and is not affected by the lumped resistor. In the end, a microstrip circuit loaded with lumped resistor is used to verify whether the analyzed numerical results are consistent with the experimental results.