论文标题
用有限体积的最佳运输计算
Computation of Optimal Transport with Finite Volumes
论文作者
论文摘要
我们构建了两点通量近似（TPFA）有限体积方案，以以其动态形式解决二次最佳传输问题，即Benamou和Brenier最初引入的问题。我们从数字上表明，这些类型的离散化很容易在其更自然的实施中形成不稳定性，并且我们提出了基于嵌套网格的变体，以克服这些问题。尽管问题缺乏严格的凸度，但至少出于离散的潜力和离散成本，我们还得出了有关该方法收敛性的定量估计。最后，我们介绍了基于障碍方法的策略，以解决离散优化问题。
We construct Two-Point Flux Approximation (TPFA) finite volume schemes to solve the quadratic optimal transport problem in its dynamic form, namely the problem originally introduced by Benamou and Brenier. We show numerically that these type of discretizations are prone to form instabilities in their more natural implementation, and we propose a variation based on nested meshes in order to overcome these issues. Despite the lack of strict convexity of the problem, we also derive quantitative estimates on the convergence of the method, at least for the discrete potential and the discrete cost. Finally, we introduce a strategy based on the barrier method to solve the discrete optimization problem.
