An Adjoint-Based Approach for a Class of Nonlinear Fokker-Planck Equations and Related Systems

Adriano Festa; Diogo A. Gomes; Roberto Machado Velho

doi:10.1007/978-3-030-01947-1_4

An Adjoint-Based Approach for a Class of Nonlinear Fokker-Planck Equations and Related Systems

Adriano Festa, Diogo A. Gomes, Roberto Machado Velho

Research output: Chapter in Book/Report/Conference proceeding › Chapter

1 Scopus citations

Abstract

Here, we introduce a numerical approach for a class of Fokker-Planck (FP) equations. These equations are the adjoint of the linearization of Hamilton-Jacobi (HJ) equations. Using this structure, we show how to transfer properties of schemes for HJ equations to FP equations. Hence, we get numerical schemes with desirable features such as positivity and mass-preservation. We illustrate this approach in examples that include mean-field games and a crowd motion model.

Original language	English (US)
Title of host publication	PDE Models for Multi-Agent Phenomena
Publisher	Springer Nature
Pages	73-92
Number of pages	20
ISBN (Print)	9783030019464
DOIs	https://doi.org/10.1007/978-3-030-01947-1_4
State	Published - Dec 23 2018

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): OSR-CRG2017-3452
Acknowledgements: The author “D. Gomes” was partially supported by KAUST baseline and start-up funds and by KAUST OSR-CRG2017-3452. The author “A. Festa” was partially supported by the Haute-Normandie Regional Council via the M2NUM project.

Access to Document

10.1007/978-3-030-01947-1_4

https://repository.kaust.edu.sa/bitstream/10754/631173/1/fpadjoint.pdf

Cite this

@inbook{cc229fb33a9d42c28a9ebb28f30c31ef,

title = "An Adjoint-Based Approach for a Class of Nonlinear Fokker-Planck Equations and Related Systems",

abstract = "Here, we introduce a numerical approach for a class of Fokker-Planck (FP) equations. These equations are the adjoint of the linearization of Hamilton-Jacobi (HJ) equations. Using this structure, we show how to transfer properties of schemes for HJ equations to FP equations. Hence, we get numerical schemes with desirable features such as positivity and mass-preservation. We illustrate this approach in examples that include mean-field games and a crowd motion model.",

author = "Adriano Festa and Gomes, {Diogo A.} and {Machado Velho}, Roberto",

note = "KAUST Repository Item: Exported on 2020-10-01 Acknowledged KAUST grant number(s): OSR-CRG2017-3452 Acknowledgements: The author “D. Gomes” was partially supported by KAUST baseline and start-up funds and by KAUST OSR-CRG2017-3452. The author “A. Festa” was partially supported by the Haute-Normandie Regional Council via the M2NUM project.",

year = "2018",

month = dec,

day = "23",

doi = "10.1007/978-3-030-01947-1_4",

language = "English (US)",

isbn = "9783030019464",

pages = "73--92",

booktitle = "PDE Models for Multi-Agent Phenomena",

publisher = "Springer Nature",

}

TY - CHAP

T1 - An Adjoint-Based Approach for a Class of Nonlinear Fokker-Planck Equations and Related Systems

AU - Festa, Adriano

AU - Gomes, Diogo A.

AU - Machado Velho, Roberto

N1 - KAUST Repository Item: Exported on 2020-10-01 Acknowledged KAUST grant number(s): OSR-CRG2017-3452 Acknowledgements: The author “D. Gomes” was partially supported by KAUST baseline and start-up funds and by KAUST OSR-CRG2017-3452. The author “A. Festa” was partially supported by the Haute-Normandie Regional Council via the M2NUM project.

PY - 2018/12/23

Y1 - 2018/12/23

N2 - Here, we introduce a numerical approach for a class of Fokker-Planck (FP) equations. These equations are the adjoint of the linearization of Hamilton-Jacobi (HJ) equations. Using this structure, we show how to transfer properties of schemes for HJ equations to FP equations. Hence, we get numerical schemes with desirable features such as positivity and mass-preservation. We illustrate this approach in examples that include mean-field games and a crowd motion model.

AB - Here, we introduce a numerical approach for a class of Fokker-Planck (FP) equations. These equations are the adjoint of the linearization of Hamilton-Jacobi (HJ) equations. Using this structure, we show how to transfer properties of schemes for HJ equations to FP equations. Hence, we get numerical schemes with desirable features such as positivity and mass-preservation. We illustrate this approach in examples that include mean-field games and a crowd motion model.

UR - http://hdl.handle.net/10754/631173

UR - https://link.springer.com/chapter/10.1007%2F978-3-030-01947-1_4

UR - http://www.scopus.com/inward/record.url?scp=85059091111&partnerID=8YFLogxK

U2 - 10.1007/978-3-030-01947-1_4

DO - 10.1007/978-3-030-01947-1_4

M3 - Chapter

SN - 9783030019464

SP - 73

EP - 92

BT - PDE Models for Multi-Agent Phenomena

PB - Springer Nature

ER -

An Adjoint-Based Approach for a Class of Nonlinear Fokker-Planck Equations and Related Systems

Abstract

Bibliographical note

Access to Document

Other files and links

Fingerprint

Cite this