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

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    Type
    Article
    Authors
    Sarmiento, Adel cc
    Espath, Luis cc
    Vignal, P.
    Dalcin, Lisandro cc
    Parsani, Matteo cc
    Calo, V.M.
    KAUST Department
    Applied Mathematics and Computational Science Program
    Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
    Extreme Computing Research Center
    Date
    2017-11-16
    Online Publication Date
    2017-11-16
    Print Publication Date
    2018-12
    Permanent link to this record
    http://hdl.handle.net/10754/626194
    
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    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.
    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.
    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.
    Publisher
    Elsevier BV
    Journal
    Journal of Computational and Applied Mathematics
    DOI
    10.1016/j.cam.2017.11.004
    Additional Links
    http://www.sciencedirect.com/science/article/pii/S0377042717305642
    ae974a485f413a2113503eed53cd6c53
    10.1016/j.cam.2017.11.004
    Scopus Count
    Collections
    Articles; Applied Mathematics and Computational Science Program; Extreme Computing Research Center; Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division

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