Unconditionally stable finite-difference time-domain methods and their applications

The finite-difference time-domain (FDTD) method and its variations have been widely used in simulating electromagnetic structures that include RF/microwave/optical circuits. However, due to the use of explicit march-in-time schemes, their time steps are limited not only by the modeling accuracy but also by the Courant-Friedrich-Levy (CFL) stability condition. This CFL condition poses quite a significant restriction on the application of the FDTD methods to a number of problems, in particular those requiring highly non-uniform grids. In this talk, we present an overview of the two unconditionally stable FDTD schemes that have been developed in recent years. The first one is the alternating-direction-implicit (ADI) FDTD method and the second one is the FDTD method using Laguerre polynomials. We show the principles of these two methods and analyze the associated errors and the techniques to improve them. Finally, we demonstrate the advantages of the two methods by showing their applications such as computation of conducting loss and a PEC slot.