论文标题
1-D抛物线最佳运输问题的数值分析
Numerical Analysis of the 1-D Parabolic Optimal Transport Problem
论文作者
论文摘要
最佳运输问题的数值方法是研究的积极领域。 Kitagawa和abedin的最新工作表明，随着时间的流逝，时间依赖方程的解会成倍地收敛，以至于无穷大与最佳运输问题的解决方案相关。这提出了用于计算最佳图的快速数值算法；我们在1维情况下研究了这种算法。具体而言，我们使用有限差方案来解决时间依赖性的最佳运输问题并对该方案进行误差分析。还提供和讨论了数字示例的集合。
Numerical methods for the optimal transport problem is an active area of research. Recent work of Kitagawa and Abedin shows that the solution of a time-dependent equation converges exponentially fast as time goes to infinity to the solution of the optimal transport problem. This suggests a fast numerical algorithm for computing optimal maps; we investigate such an algorithm here in the 1-dimensional case. Specifically, we use a finite difference scheme to solve the time-dependent optimal transport problem and carry out an error analysis of the scheme. A collection of numerical examples is also presented and discussed.
