Optimization of the Faber Polynomial based Propagator through Parallelization
Wladimir Plotnikov, Dirk Schulz · 2024
The Faber polynomial based approximation of the time dependent propagator enables the explicit solution of Maxwell’s equations. Compared to conventional solvers, the temporal propagation is not bound to the spatial approximation. This fact makes this approach particularly interesting for systems that require a fast computing time with a constant dense spatial resolution, particularly within the field of THz technology and photonics. If subgridding is applied within the computational domain to reduce the computational complexity, inhomogeneously discretized subareas are obtained, which can be evaluated with a lower order of the propagator expansion. Subsequently, local operators can be extracted from the global operator, used for the simultaneous evaluation of each subarea. Against this background, the main idea is to use both CPU and GPU for parallelization to further reduce the runtime of the computation since both global and local operators can benefit due to the explicit property.