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Numerical simulation of continuity equations by evolving diffeomorphisms

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Carrillo, Jose A., Ranetbauer, Helene and Wolfram, Marie-Therese (2016) Numerical simulation of continuity equations by evolving diffeomorphisms. Journal of Computational Physics, 327 . pp. 186-202. doi:10.1016/j.jcp.2016.09.040

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Official URL: https://doi.org/10.1016/j.jcp.2016.09.040

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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 properties with various examples in spatial dimension one and two.

Item Type: Journal Article
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Science > Mathematics
Library of Congress Subject Headings (LCSH): Diffeomorphisms
Journal or Publication Title: Journal of Computational Physics
Publisher: Academic Press Inc. Elsevier Science
ISSN: 0021-9991
Official Date: 15 December 2016
Dates:
DateEvent
15 December 2016Published
22 September 2016Available
17 September 2016Accepted
Volume: 327
Page Range: pp. 186-202
DOI: 10.1016/j.jcp.2016.09.040
Status: Peer Reviewed
Publication Status: Published
Access rights to Published version: Restricted or Subscription Access
Funder: Royal Society (Great Britain). Wolfson Research Merit Award (RSWRMA), Österreichische Akademie der Wissenschaften [Austrian Academy of Sciences], King Abdullah University of Science and Technology (KAUST)

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