A New Parareal Algorithm for Problems with Discontinuous Sources
Abstract
The Parareal algorithm allows one to solve evolution problems exploiting parallelization in time. Its convergence and stability have been proved under the assumption of regular (smooth) inputs. We present and analyze here a new Parareal algorithm for ordinary differential equations which involve discontinuous right-hand sides. Such situations occur in various applications, e.g., when an electric device is supplied with a pulse-width-modulated signal. Our new Parareal algorithm uses a smooth input for the coarse problem with reduced dynamics. We derive error estimates that show how the input reduction influences the overall convergence rate of the algorithm. We support our theoretical results by numerical experiments, and also test our new Parareal algorithm in an eddy current simulation of an induction machine.
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Information & Authors
Information
Published In
SIAM Journal on Scientific Computing
Pages: B375 - B395
DOI: 10.1137/18M1175653
ISSN (online): 1095-7197
Copyright
© 2019, Society for Industrial and Applied Mathematics.
History
Submitted: 15 March 2018
Accepted: 14 February 2019
Published online: 2 April 2019
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Funding Information
Bundesministerium für Bildung und Forschung https://doi.org/10.13039/501100002347 : 05M2018RDA (PASIROM)
Funding Information
Deutsche Forschungsgemeinschaft https://doi.org/10.13039/501100001659 : SCHO1562/1-2
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