Optimization of Faber Polynomial-Based Propagators via Proper Orthogonal Decomposition

Abstract The focus of this research lies in the extrapolation of the time-dependent Faber polynomial-based propagator applied to Maxwell’s equations with the Proper Orthogonal Decomposition (POD) approach. In particular, when investigating a system in the application area of THz-technology or nanophotonics, it is common to have geometries which require an extraordinary fine spatial resolution. Unfortunately, this is accompanied by the temporal resolution, which is restricted accordingly. For this reason, the explicit Faber approach is chosen to approximate the computationally intensive matrix exponential to enable large time step sizes. To achieve a further acceleration of the computation time, the POD approach is used to enormously reduce the complexity of the evaluation. In this context, a hybrid model is examined to establish a balance between the calculation time by means of a Reduced-Order Model (ROM) and the error accuracy via a Full-Order Model (FOM).