An Adjoint-Based Approach for a Class of Nonlinear Fokker-Planck Equations and Related Systems
KAUST DepartmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Applied Mathematics and Computational Science Program
KAUST Grant NumberOSR-CRG2017-3452
Online Publication Date2018-12-23
Print Publication Date2018
Permanent link to this recordhttp://hdl.handle.net/10754/631173
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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 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.
CitationFesta A, Gomes DA, Velho RM (2018) An Adjoint-Based Approach for a Class of Nonlinear Fokker-Planck Equations and Related Systems. PDE Models for Multi-Agent Phenomena: 73–92. Available: http://dx.doi.org/10.1007/978-3-030-01947-1_4.
SponsorsThe 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.