This report describes an application of relaxation technique to the alternating direction implicit finite-difference time-domain (ADI-FDTD) method. The ADI-FDTD method is quite stable even when the CFL condition is not satisfied. However, the ADI-FDTD method is computationally more complicate than the conventional FDTD method and this method requires to solving the tri-diagonal matrix equation. Thus, this method may require more computational cost than the standard FDTD method due to the large scale tri-diagonal matrix solution corresponding to a large number of meshes. In this report, relaxation-based solution technique is discussed for the matrix solution and a simple numerical example is shown. As a result, it is confirmed that ADI-FDTD method with the relaxation technique is useful for the acceleration of the electromagnetic field simulation.

For an efficient time-domain modeling of thin-film bulk acoustic wave resonators (TFBARs), a unconditionally stable finite-difference time-domain method based on the alternating direction implicit scheme (ADI-FDTD) is introduced to the analysis of a typical TFBAR structure. Because the time step size in ADI-FDTD is free from the stability constraint, this method is very useful to analyze electromechanical phenomena of TFBARs having fine geometrical variations, which is a challenging problem to conventional FDTD modeling. To validate the proposed scheme, the impedance characteristics are obtained by the proposed method and compared with the traditional FDTD results and the analytical solutions.