A New Parareal Algorithm for Time-Periodic Problems with Discontinuous Inputs
Abstract
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.
Cite
@article{arxiv.1810.12372,
title = {A New Parareal Algorithm for Time-Periodic Problems with Discontinuous Inputs},
author = {Martin J. Gander and Iryna Kulchytska-Ruchka and Sebastian Schöps},
journal= {arXiv preprint arXiv:1810.12372},
year = {2021}
}