Parallelization of Faber Polynomial Based Propagators for Laser Applications

In order to simulate a laser system, the evaluation of a complex semilinear master equation is needed, including the description of the wave propagation by Maxwell's equations and appropriate rate equations. The denser the spatial discretization, the slower the computation time of the time‐dependent propagator. To counteract this restriction, the complexity is reduced by applying a nonuniform discretization and by using local operators, since it has already been shown that local operators are more efficient than a global operator. However, in practice, the main task is the management of the data transfer within the framework of local operators, as the necessary extraction and assembly processes represent an unintended overhead next to the actual expansion in terms of the Faber polynomial‐based approximation. Here, the use of a CPU and GPU is investigated to reduce the overhead through multiprocessing and to accelerate the expansion through multithreading, respectively. From the results obtained, the usefulness of the proposed approach is demonstrated. Also, an operator splitting approach onto the semilinear master equation is investigated to decrease the runtime, as the underlying matrix can be split into commutating matrices without splitting error.