A New Parareal Algorithm for Problems with Discontinuous Sources

We recently proposed a new Parareal algorithm for problems with discontinuous sources which are common in electrical engineering, e.g., when an electric device is supplied with a pulse-width-modulated signal. Our algorithm uses a smooth input for the coarse problem with reduced dynamics. In the new arXiv preprint 1803.05503 preprint an error estimates is derived that shows how the input reduction influences the overall convergence rate of the algorithm. The theoretical results are supported by numerical experiments, including an eddy current simulation of an induction machine.