There have been several methods developed to simulate optical systems of the interferometers used to detect gravitational wave signals. Each has unique features suited to study specific behaviors and all work is complementary to each other.
The time domain simulation model is a method which can handle non-stationary and non-linear responses of systems, like the locking process of interferometers. The frequency domain model is suited to study the stationary state with a linear response, like the analysis of control systems with full optical interactions. The FFT model is a special kind of frequency domain model, which is dedicated to study the details of optical systems, although it is much slower than the normal frequency domain model.
This talk explains common underlying dynamics of these models and clarifies the differences between each implementation and the limitations of applications.