An Adjoint-based Numerical Method for a class of nonlinear Fokker-Planck Equations

Handle URI:
http://hdl.handle.net/10754/626464
Title:
An Adjoint-based Numerical Method for a class of nonlinear Fokker-Planck Equations
Authors:
Festa, Adriano; Gomes, Diogo A. ( 0000-0002-3129-3956 ) ; Machado Velho, Roberto
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 the properties of schemes for HJ equations to the 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.
KAUST Department:
Center for Uncertainty Quantification in Computational Science and Engineering (SRI-UQ); Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Publisher:
arXiv
Issue Date:
22-Mar-2017
ARXIV:
arXiv:1703.07709
Type:
Preprint
Additional Links:
http://arxiv.org/abs/1703.07709v1; http://arxiv.org/pdf/1703.07709v1
Appears in Collections:
Other/General Submission; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorFesta, Adrianoen
dc.contributor.authorGomes, Diogo A.en
dc.contributor.authorMachado Velho, Robertoen
dc.date.accessioned2017-12-28T07:32:11Z-
dc.date.available2017-12-28T07:32:11Z-
dc.date.issued2017-03-22en
dc.identifier.urihttp://hdl.handle.net/10754/626464-
dc.description.abstractHere, 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 the properties of schemes for HJ equations to the 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.en
dc.publisherarXiven
dc.relation.urlhttp://arxiv.org/abs/1703.07709v1en
dc.relation.urlhttp://arxiv.org/pdf/1703.07709v1en
dc.rightsArchived with thanks to arXiven
dc.titleAn Adjoint-based Numerical Method for a class of nonlinear Fokker-Planck Equationsen
dc.typePreprinten
dc.contributor.departmentCenter for Uncertainty Quantification in Computational Science and Engineering (SRI-UQ)en
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.eprint.versionPre-printen
dc.contributor.institutionInstitut National de Sciences Appliquees, LMI lab Avenue de l'Universite, 76800 Saint-Etienne-du-Rouvray, Rouen, Franceen
dc.identifier.arxividarXiv:1703.07709en
kaust.authorGomes, Diogo A.en
kaust.authorMachado Velho, Robertoen
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