A New Parareal Algorithm for Time-Periodic Problems with Discontinuous Inputs
This work addresses the need for efficient time-parallel solvers in power engineering applications involving pulse-width-modulated signals.
The paper presents a new Parareal algorithm for solving time-periodic problems with discontinuous inputs, achieving faster convergence than standard methods, as demonstrated on an induction machine simulation.
The Parareal algorithm, which is related to multiple shooting, was introduced for solving evolution problems in a time-parallel manner. The algorithm was then extended to solve time-periodic problems. We are interested here in time-periodic systems which are forced with quickly-switching discontinuous inputs. Such situations occur, e.g., in power engineering when electric devices are excited with a pulse-width-modulated signal. In order to solve those problems numerically we consider a recently introduced modified Parareal method with reduced coarse dynamics. Its main idea is to use a low-frequency smooth input for the coarse problem, which can be obtained, e.g., from Fourier analysis. Based on this approach, we present and analyze a new Parareal algorithm for time-periodic problems with highly-oscillatory discontinuous sources. We illustrate the performance of the method via its application to the simulation of an induction machine.