Annals of Mathematical Sciences and Applications

Volume 8 (2023)

Number 3

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

DOI: https://dx.doi.org/10.4310/AMSA.2023.v8.n3.a5

Authors

Alexandre Caboussat (Geneva School of Business Administration, University of Applied Sciences Western Switzerland, Carouge, Switzerland)

Dimitrios Gourzoulidis (Geneva School of Business Administration, University of Applied Sciences Western Switzerland, Carouge, Switzerland)

Abstract

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.

Keywords

optimal transport, prescribed Jacobian equation, Monge–Ampère equation, least-squares method, mixed finite element method

2010 Mathematics Subject Classification

35F30, 49M20, 65K10, 65N30

Full Text (PDF format)

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