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arXiv · 1810.12372

A New Parareal Algorithm for Time-Periodic Problems with Discontinuous Inputs

Martin J. Gander·Iryna Kulchytska-Ruchka·Sebastian Schöps
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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.

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Martin J. Gander, Iryna Kulchytska-Ruchka, Sebastian Schöps. 2018-10-29. A New Parareal Algorithm for Time-Periodic Problems with Discontinuous Inputs. https://doi.org/10.1007/978-3-030-56750-7_27

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