Parareal Convergence for Oscillatory PDEs with Finite Time-scale Separation
dc.contributor.author | Peddle, A | |
dc.contributor.author | Haut, T | |
dc.contributor.author | Wingate, B | |
dc.date.accessioned | 2019-08-01T10:43:23Z | |
dc.date.issued | 2019-11-12 | |
dc.description.abstract | A variant of the Parareal method for highly oscillatory systems of PDEs was proposed by Haut and Wingate (2014). In that work they proved superlinear conver- gence of the method in the limit of infinite time scale separation. Their coarse solver features a coordinate transformation and a fast-wave averag- ing method inspired by analysis of multiple scales PDEs and is integrated using an HMM-type method. However, for many physical applications the timescale separation is finite, not infinite. In this paper we prove con- vergence for finite timescale separaration by extending the error bound on the coarse propagator to this case. We show that convergence requires the solution of an optimization problem that involves the averaging win- dow interval, the time step, and the parameters in the problem. We also propose a method for choosing the averaging window relative to the time step based as a function of the finite frequencies inherent in the problem. | en_GB |
dc.description.sponsorship | University of Exeter | en_GB |
dc.identifier.citation | Vol. 41 (6), pp. A3476–A3497 | en_GB |
dc.identifier.doi | 10.1137/17M1131611 | |
dc.identifier.uri | http://hdl.handle.net/10871/38184 | |
dc.language.iso | en | en_GB |
dc.publisher | Society for Industrial and Applied Mathematics | en_GB |
dc.rights | © 2019 SIAM. Open access. Published by SIAM under the terms of the Creative Commons 4.0 license | |
dc.subject | parareal | en_GB |
dc.subject | Parallel in Time | en_GB |
dc.subject | Wave Averaging | en_GB |
dc.subject | Oscillatory Stiffness | en_GB |
dc.subject | Time-scale separation | en_GB |
dc.title | Parareal Convergence for Oscillatory PDEs with Finite Time-scale Separation | en_GB |
dc.type | Article | en_GB |
dc.date.available | 2019-08-01T10:43:23Z | |
dc.description | This is the final version. Available on open access from the Society for Industrial and Applied Mathematics via the DOI in this record | en_GB |
dc.identifier.eissn | 1095-7197 | |
dc.identifier.journal | SIAM Journal on Scientific Computing | en_GB |
dc.rights.uri | https://creativecommons.org/licenses/by/4.0/ | en_GB |
dcterms.dateAccepted | 2019-07-05 | |
rioxxterms.version | VoR | en_GB |
rioxxterms.licenseref.startdate | 2019-07-05 | |
rioxxterms.type | Journal Article/Review | en_GB |
refterms.dateFCD | 2019-08-01T10:40:06Z | |
refterms.versionFCD | AM | |
refterms.dateFOA | 2020-01-20T11:21:23Z | |
refterms.panel | B | en_GB |
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Except where otherwise noted, this item's licence is described as © 2019 SIAM. Open access. Published by SIAM under the terms of the Creative Commons 4.0 license