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    Numerical simulation of nonlinear continuity equations by evolving diffeomorphisms

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    Type
    Article
    Authors
    Carrillo, José A.
    Ranetbauer, Helene
    Wolfram, Marie-Therese
    Date
    2016-09-22
    Online Publication Date
    2016-09-22
    Print Publication Date
    2016-12
    Permanent link to this record
    http://hdl.handle.net/10754/623573
    
    Metadata
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    Abstract
    In this paper we present a numerical scheme for nonlinear continuity equations, which is based on the gradient flow formulation of an energy functional with respect to the quadratic transportation distance. It can be applied to a large class of nonlinear continuity equations, whose dynamics are driven by internal energies, given external potentials and/or interaction energies. The solver is based on its variational formulation as a gradient flow with respect to the Wasserstein distance. Positivity of solutions as well as energy decrease of the semi-discrete scheme are guaranteed by its construction. We illustrate this property with various examples in spatial dimension one and two.
    Citation
    Carrillo JA, Ranetbauer H, Wolfram M-T (2016) Numerical simulation of nonlinear continuity equations by evolving diffeomorphisms. Journal of Computational Physics 327: 186–202. Available: http://dx.doi.org/10.1016/j.jcp.2016.09.040.
    Sponsors
    JAC was partially supported by the Royal Society via a Wolfson Research Merit Award. HR and MTW acknowledge financial support from the Austrian Academy of Sciences ÖAW via the New Frontiers Group NSP-001. The authors would like to thank the King Abdullah University of Science and Technology for its hospitality and partial support while preparing the manuscript.
    Publisher
    Elsevier BV
    Journal
    Journal of Computational Physics
    DOI
    10.1016/j.jcp.2016.09.040
    ae974a485f413a2113503eed53cd6c53
    10.1016/j.jcp.2016.09.040
    Scopus Count
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