The comparison of the stability on the extended 3D LOD-FDTD and ADI-FDTD methods including lumped elements

The stability comparison of the extended three-dimensional locally one-dimensional finite difference time domain (3-D LOD-FDTD) and alternating-direction implicit finite-difference time-domain (ADI-FDTD) including lumped elements is analyzed, and three common elements are investigated: resistor, capacitor, and inductor. The elements are inserted into the LOD-FDTD and ADI-FDTD in the explicit, semi-implicit and implicit schemes. Stability analysis shows that the extended LOD-FDTD and ADI-FDTD methods are unconditionally stable in the semi-implicit and implicit schemes while conditionally stable in the explicit scheme, and its stability criterion depends on both the values of the element and the mesh sizes. Finally, a simple microstrip circuit including an inductor is simulated in the extended methods to demonstrate the validity of the stability analysis, and the extended LOD-FDTD method is shown to consume less CPU time.