Structure preserving schemes for mean-field equations of collective behavior

Lorenzo Pareschi; Mattia Zanella

doi:10.1007/978-3-319-91548-7_31

Structure preserving schemes for mean-field equations of collective behavior

Lorenzo Pareschi, Mattia Zanella

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

7 Scopus citations

Abstract

In this paper, we consider the development of numerical schemes for mean-field equations describing the collective behavior of a large group of interacting agents. The schemes are based on a generalization of the classical Chang–Cooper approach and are capable to preserve the main structural properties of the systems, namely nonnegativity of the solution, physical conservation laws, entropy dissipation, and stationary solutions. In particular, the methods here derived are second order accurate in transient regimes, whereas they can reach arbitrary accuracy asymptotically for large times. Several examples are reported to show the generality of the approach.

Original language	English
Title of host publication	Theory, Numerics and Applications of Hyperbolic Problems II
Editors	Michael Westdickenberg, Christian Klingenberg
Publisher	Springer New York LLC
Pages	405-421
Number of pages	17
ISBN (Print)	9783319915470
DOIs	https://doi.org/10.1007/978-3-319-91548-7_31
State	Published - 2018
Externally published	Yes
Event	16th International Conference on Hyperbolic Problems: Theory, Numerics and Applications, 2016 - Aachen, Germany Duration: 1 Aug 2016 → 5 Aug 2016

Publication series

Name	Springer Proceedings in Mathematics and Statistics
Volume	237
ISSN (Print)	2194-1009
ISSN (Electronic)	2194-1017

Conference

Conference	16th International Conference on Hyperbolic Problems: Theory, Numerics and Applications, 2016
Country/Territory	Germany
City	Aachen
Period	1/08/16 → 5/08/16

Keywords

Collective behavior
Fokker-Planck equations Mean-field equations
Structure preserving methods

Access to Document

10.1007/978-3-319-91548-7_31

Cite this

@inproceedings{12e9761733a2417a8334595bf797ba57,

title = "Structure preserving schemes for mean-field equations of collective behavior",

abstract = "In this paper, we consider the development of numerical schemes for mean-field equations describing the collective behavior of a large group of interacting agents. The schemes are based on a generalization of the classical Chang–Cooper approach and are capable to preserve the main structural properties of the systems, namely nonnegativity of the solution, physical conservation laws, entropy dissipation, and stationary solutions. In particular, the methods here derived are second order accurate in transient regimes, whereas they can reach arbitrary accuracy asymptotically for large times. Several examples are reported to show the generality of the approach.",

keywords = "Collective behavior, Fokker-Planck equations Mean-field equations, Structure preserving methods",

author = "Lorenzo Pareschi and Mattia Zanella",

note = "Publisher Copyright: {\textcopyright} Springer International Publishing AG, part of Springer Nature 2018.; 16th International Conference on Hyperbolic Problems: Theory, Numerics and Applications, 2016 ; Conference date: 01-08-2016 Through 05-08-2016",

year = "2018",

doi = "10.1007/978-3-319-91548-7_31",

language = "English",

isbn = "9783319915470",

series = "Springer Proceedings in Mathematics and Statistics",

publisher = "Springer New York LLC",

pages = "405--421",

editor = "Michael Westdickenberg and Christian Klingenberg",

booktitle = "Theory, Numerics and Applications of Hyperbolic Problems II",

}

Pareschi, L & Zanella, M 2018, Structure preserving schemes for mean-field equations of collective behavior. in M Westdickenberg & C Klingenberg (eds), Theory, Numerics and Applications of Hyperbolic Problems II. Springer Proceedings in Mathematics and Statistics, vol. 237, Springer New York LLC, pp. 405-421, 16th International Conference on Hyperbolic Problems: Theory, Numerics and Applications, 2016, Aachen, Germany, 1/08/16. https://doi.org/10.1007/978-3-319-91548-7_31

Structure preserving schemes for mean-field equations of collective behavior. / Pareschi, Lorenzo; Zanella, Mattia.
Theory, Numerics and Applications of Hyperbolic Problems II. ed. / Michael Westdickenberg; Christian Klingenberg. Springer New York LLC, 2018. p. 405-421 (Springer Proceedings in Mathematics and Statistics; Vol. 237).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

TY - GEN

T1 - Structure preserving schemes for mean-field equations of collective behavior

AU - Pareschi, Lorenzo

AU - Zanella, Mattia

N1 - Publisher Copyright: © Springer International Publishing AG, part of Springer Nature 2018.

PY - 2018

Y1 - 2018

N2 - In this paper, we consider the development of numerical schemes for mean-field equations describing the collective behavior of a large group of interacting agents. The schemes are based on a generalization of the classical Chang–Cooper approach and are capable to preserve the main structural properties of the systems, namely nonnegativity of the solution, physical conservation laws, entropy dissipation, and stationary solutions. In particular, the methods here derived are second order accurate in transient regimes, whereas they can reach arbitrary accuracy asymptotically for large times. Several examples are reported to show the generality of the approach.

AB - In this paper, we consider the development of numerical schemes for mean-field equations describing the collective behavior of a large group of interacting agents. The schemes are based on a generalization of the classical Chang–Cooper approach and are capable to preserve the main structural properties of the systems, namely nonnegativity of the solution, physical conservation laws, entropy dissipation, and stationary solutions. In particular, the methods here derived are second order accurate in transient regimes, whereas they can reach arbitrary accuracy asymptotically for large times. Several examples are reported to show the generality of the approach.

KW - Collective behavior

KW - Fokker-Planck equations Mean-field equations

KW - Structure preserving methods

UR - http://www.scopus.com/inward/record.url?scp=85049441989&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-91548-7_31

DO - 10.1007/978-3-319-91548-7_31

M3 - Conference contribution

AN - SCOPUS:85049441989

SN - 9783319915470

T3 - Springer Proceedings in Mathematics and Statistics

SP - 405

EP - 421

BT - Theory, Numerics and Applications of Hyperbolic Problems II

A2 - Westdickenberg, Michael

A2 - Klingenberg, Christian

PB - Springer New York LLC

T2 - 16th International Conference on Hyperbolic Problems: Theory, Numerics and Applications, 2016

Y2 - 1 August 2016 through 5 August 2016

ER -

Structure preserving schemes for mean-field equations of collective behavior

Abstract

Publication series

Conference

Keywords

Access to Document

Other files and links

Fingerprint

Cite this