An energy-stable generalized- α method for the Swift–Hohenberg equation

Handle URI:
http://hdl.handle.net/10754/626194
Title:
An energy-stable generalized- α method for the Swift–Hohenberg equation
Authors:
Sarmiento, Adel ( 0000-0003-0668-2084 ) ; Espath, L.F.R.; Vignal, P.; Dalcin, Lisandro ( 0000-0001-8086-0155 ) ; Parsani, Matteo ( 0000-0001-7300-1280 ) ; Calo, V.M.
Abstract:
We propose a second-order accurate energy-stable time-integration method that controls the evolution of numerical instabilities introducing numerical dissipation in the highest-resolved frequencies. Our algorithm further extends the generalized-α method and provides control over dissipation via the spectral radius. We derive the first and second laws of thermodynamics for the Swift–Hohenberg equation and provide a detailed proof of the unconditional energy stability of our algorithm. Finally, we present numerical results to verify the energy stability and its second-order accuracy in time.
KAUST Department:
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division; Applied Mathematics and Computational Science Program; Extreme Computing Research Center
Citation:
Sarmiento AF, Espath LFR, Vignal P, Dalcin L, Parsani M, et al. (2017) An energy-stable generalized- α method for the Swift–Hohenberg equation. Journal of Computational and Applied Mathematics. Available: http://dx.doi.org/10.1016/j.cam.2017.11.004.
Publisher:
Elsevier BV
Journal:
Journal of Computational and Applied Mathematics
Issue Date:
16-Nov-2017
DOI:
10.1016/j.cam.2017.11.004
Type:
Article
ISSN:
0377-0427
Sponsors:
This publication was made possible in part by the CSIRO Professorial Chair in Computational Geoscience at Curtin University and the Deep Earth Imaging Enterprise Future Science Platforms of the Commonwealth Scientific Industrial Research Organisation, CSIRO, of Australia. Additional support was provided by the European Union’s Horizon 2020 Research and Innovation Program of the Marie Skłodowska-Curie grant agreement No. 644602 and the Curtin Institute for Computation. The J. Tinsley Oden Faculty Fellowship Research Program at the Institute for Computational Engineering and Sciences (ICES) of the University of Texas at Austin has partially supported the visits of VMC to ICES.
Additional Links:
http://www.sciencedirect.com/science/article/pii/S0377042717305642
Appears in Collections:
Articles; Applied Mathematics and Computational Science Program; Extreme Computing Research Center; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorSarmiento, Adelen
dc.contributor.authorEspath, L.F.R.en
dc.contributor.authorVignal, P.en
dc.contributor.authorDalcin, Lisandroen
dc.contributor.authorParsani, Matteoen
dc.contributor.authorCalo, V.M.en
dc.date.accessioned2017-11-23T11:51:29Z-
dc.date.available2017-11-23T11:51:29Z-
dc.date.issued2017-11-16en
dc.identifier.citationSarmiento AF, Espath LFR, Vignal P, Dalcin L, Parsani M, et al. (2017) An energy-stable generalized- α method for the Swift–Hohenberg equation. Journal of Computational and Applied Mathematics. Available: http://dx.doi.org/10.1016/j.cam.2017.11.004.en
dc.identifier.issn0377-0427en
dc.identifier.doi10.1016/j.cam.2017.11.004en
dc.identifier.urihttp://hdl.handle.net/10754/626194-
dc.description.abstractWe propose a second-order accurate energy-stable time-integration method that controls the evolution of numerical instabilities introducing numerical dissipation in the highest-resolved frequencies. Our algorithm further extends the generalized-α method and provides control over dissipation via the spectral radius. We derive the first and second laws of thermodynamics for the Swift–Hohenberg equation and provide a detailed proof of the unconditional energy stability of our algorithm. Finally, we present numerical results to verify the energy stability and its second-order accuracy in time.en
dc.description.sponsorshipThis publication was made possible in part by the CSIRO Professorial Chair in Computational Geoscience at Curtin University and the Deep Earth Imaging Enterprise Future Science Platforms of the Commonwealth Scientific Industrial Research Organisation, CSIRO, of Australia. Additional support was provided by the European Union’s Horizon 2020 Research and Innovation Program of the Marie Skłodowska-Curie grant agreement No. 644602 and the Curtin Institute for Computation. The J. Tinsley Oden Faculty Fellowship Research Program at the Institute for Computational Engineering and Sciences (ICES) of the University of Texas at Austin has partially supported the visits of VMC to ICES.en
dc.publisherElsevier BVen
dc.relation.urlhttp://www.sciencedirect.com/science/article/pii/S0377042717305642en
dc.rightsNOTICE: this is the author’s version of a work that was accepted for publication in Journal of Computational and Applied Mathematics. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Journal of Computational and Applied Mathematics, [, , (2017-11-16)] DOI: 10.1016/j.cam.2017.11.004 . © 2017. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/en
dc.subjectSwift-Hohenberg equationen
dc.subjectEnergy stabilityen
dc.subjectTime integrationen
dc.subjectPattern formationen
dc.subjectNumerical instabilityen
dc.subjectNumerical dissipationen
dc.titleAn energy-stable generalized- α method for the Swift–Hohenberg equationen
dc.typeArticleen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.contributor.departmentApplied Mathematics and Computational Science Programen
dc.contributor.departmentExtreme Computing Research Centeren
dc.identifier.journalJournal of Computational and Applied Mathematicsen
dc.eprint.versionPost-printen
dc.contributor.institutionLeica Microsystems, Applied Microscopy, Dubai, United Arab Emiratesen
dc.contributor.institutionCurtin Institute for Computation, Curtin University, Perth, WA, 6845, Australiaen
dc.contributor.institutionMineral Resources, Commonwealth Scientific and Industrial Research Organization (CSIRO), Kensington, WA, 6152, Australiaen
dc.contributor.institutionApplied Geology, Western Australian School of Mines, Faculty of Science and Engineering, Curtin University, Perth, WA, 6845, Australiaen
kaust.authorSarmiento, Adelen
kaust.authorEspath, L.F.R.en
kaust.authorDalcin, Lisandroen
kaust.authorParsani, Matteoen
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