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Geometrically exact time-integration mesh-free schemes for advection-diffusion problems derived from optimal transportation theory and their connection with particle methods

Fedeli, L. and Pandolfi, A. and Ortiz, M. (2017) Geometrically exact time-integration mesh-free schemes for advection-diffusion problems derived from optimal transportation theory and their connection with particle methods. International Journal for Numerical Methods in Engineering, 112 (9). pp. 1175-1193. ISSN 0029-5981. http://resolver.caltech.edu/CaltechAUTHORS:20171106-141823774

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Abstract

We develop an optimal transportation mesh-free particle method for advection-diffusion in which the concentration or density of the diffusive species is approximated by Dirac measures. We resort to an incremental variational principle for purposes of time discretization of the diffusive step. This principle characterizes the evolution of the density as a competition between the Wasserstein distance between two consecutive densities and entropy. Exploiting the structure of the Euler–Lagrange equations, we approximate the density as a collection of Diracs. The interpolation of the incremental transport map is effected through mesh-free max-ent interpolation. Remarkably, the resulting update is geometrically exact with respect to advection and volume. We present three-dimensional examples of application that illustrate the scope and robustness of the method.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://dx.doi.org/10.1002/nme.5552DOIArticle
http://onlinelibrary.wiley.com/doi/10.1002/nme.5552/fullPublisherArticle
https://arxiv.org/abs/1703.02165arXivDiscussion Paper
ORCID:
AuthorORCID
Pandolfi, A.0000-0002-7084-7456
Additional Information:© 2017 John Wiley & Sons, Ltd. LF and MO gratefully acknowledge the support of the U.S. National Science Foundation through the Partnership for International Research and Education (PIRE) on Science at the Triple Point Between Mathematics, Mechanics and Materials Science, Award Number 0967140.
Group:GALCIT
Funders:
Funding AgencyGrant Number
NSFOISE-0967140
Subject Keywords:optimal transportation, diffusion problems, time integrators, approximation theory
Record Number:CaltechAUTHORS:20171106-141823774
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20171106-141823774
Official Citation:Fedeli, L., Pandolfi, A., and Ortiz, M. (2017) Geometrically exact time-integration mesh-free schemes for advection-diffusion problems derived from optimal transportation theory and their connection with particle methods. Int. J. Numer. Meth. Engng, 112: 1175–1193. doi: 10.1002/nme.5552.
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:82995
Collection:CaltechAUTHORS
Deposited By: Lydia Suarez
Deposited On:06 Nov 2017 23:01
Last Modified:12 Dec 2017 22:20

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