Optimization of Faber Polynomial based Propagators via Proper Orthogonal Decomposition

Abstract The focus of this research lies on the extrapolation of the time dependent Faber polynomial based propagator applied on Maxwell’s equations with the Proper Orthogonal Decomposition 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 in order to enable large time stepsizes. To achieve a further acceleration of the computation time, the Proper Orthogonal Decomposition approach is used to enormously reduce the complexity of the evaluation. In this context, a hybrid model is examined to establish abalance between the calculation time by means of a reduced order model and the error accuracy via a full order model.