Approximation of Monge-Kantorovich Problems

Description

Optimal transportation of substances, goods, or information is a classical mathematical problem with applications in economics, meteorology, and computer science. It can be formulated as a high-dimensional linear program whose direct solution is difficult. More efficient approaches are based on equivalent continuous formulations via partial differential equations or variational problems. These are nonlinear and nondifferentiable mathematical problems that require a suitable discretization and iterative solution. The project focuses on the development and numerical analysis of finite element discretizations, the automatic efficient mesh refinement based on rigorous a posteriori error estimates, and the fast iterative solution. Special emphasis is on the avoidance of regularizations and use of unjustified smoothness assumptions on solutions.

Publications

No publications from this project yet.

Preprints

Sören Bartels, Giuseppe Buttazzo: Numerical Solution of a Nonlinear Eigenvalue Problem Arising in Optimal Insulation (SPP1962-032, 08/2017, [bib])

Research Area

Members

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    Prof. Sören Bartels

    Albert-Ludwigs-Universität Freiburg
    Principal Investigator
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    Zhangxian Wang

    Albert-Ludwigs-Universität Freiburg
    Research Assistant
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    Dr. Andrea Bonito

    Texas A&M University
    Cooperation Partner
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    Dr. Max Jensen

    University of Sussex
    Cooperation Partner
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    Prof. Ricardo H. Nochetto

    University of Maryland
    Cooperation Partner

Project Related News

  • 10. 10. 2016 : Welcome to our new project member

    Zhangxian Wang joins project 1.