Unconditionally stable ADI-FDTD method including passive lumped elements

From the stability analysis for the conventional explicit finite-difference time-domain (FDTD) method including the passive lumped element, one can find that its stability is related either to the mesh size or to both the mesh size and the values of the elements. This paper presents a three-dimensional (3-D) alternating-direction-implicit FDTD (ADI-FDTD) method, including various lumped elements, such as resistors, capacitors, and inductors. The stability of these schemes is proved to be neither related to the mesh size, nor to the values of the elements. This unconditional stability is different from that of the previous explicit schemes including lumped elements and is therefore a distinct advantage. These 3-D schemes can be justified to achieve improved computation efficiency. Some numerical experiments are performed for the demonstration of the higher efficiency and validation of these schemes.