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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
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 | ||||||||
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| 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: |
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| 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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