Annals of Mathematical Sciences and Applications
Volume 8 (2023)
Special Issue Dedicated to the Memory of Professor Roland Glowinski
Guest Editors: Annalisa Quaini, Xiaolong Qin, Xuecheng Tai, and Enrique Zuazua
A least-squares method for the numerical solution of a 2D optimal transportation problem
Pages: 547 – 563
Optimal transportation of raw material from suppliers to customers is an issue in supply chain that we address here with a continuous model. A least-squares method is designed to solve the prescribed Jacobian problem that arises in optimal transportation in two dimensions of space. An iterative algorithm allows to decouple the variational aspects of the problem from the nonlinearities and from the weak treatment of the boundary conditions. Numerical experiments illustrate the transport of material in several configurations.
optimal transport, prescribed Jacobian equation, Monge–Ampère equation, least-squares method, mixed finite element method
2010 Mathematics Subject Classification
35F30, 49M20, 65K10, 65N30
In memory of Prof. Roland Glowinski
The authors were partially supported by HES-SO RCSO E&M project #118745.
Received 31 July 2023
Accepted 24 August 2023
Published 14 November 2023