论文标题
半碎屑的半缘最佳传输方法
Semi-discrete optimal transport methods for the semi-geostrophic equations
论文作者
论文摘要
我们给出了一个新的建设性证明，证明了3维不可压缩的半地球形方程（SG）在地球形坐标中的存在，以进行紧凑的支持，以进行任意初始措施。该新的证明基于半污垢最佳运输技术，它通过以满足普通微分方程的轨迹来表征地球坐标中SG的离散解。它的简单性和与欧拉坐标的明确关系是有利的。使用我们的方法，我们可以为大量的离散初始度量获得改进的时间正常，并明确计算两个离散解决方案。该方法自然产生了一种有效的数值方法，我们通过对使用数值求解器进行半污染物最佳运输问题产生的二维半晶状体流动进行模拟来说明，该模拟与普通的微分方程求解器相结合。
We give a new and constructive proof of the existence of global-in-time weak solutions of the 3-dimensional incompressible semi-geostrophic equations (SG) in geostrophic coordinates, for arbitrary initial measures with compact support. This new proof, based on semi-discrete optimal transport techniques, works by characterising discrete solutions of SG in geostrophic coordinates in terms of trajectories satisfying an ordinary differential equation. It is advantageous in its simplicity and its explicit relation to Eulerian coordinates through the use of Laguerre tessellations. Using our method, we obtain improved time-regularity for a large class of discrete initial measures, and we compute explicitly two discrete solutions. The method naturally gives rise to an efficient numerical method, which we illustrate by presenting simulations of a 2-dimensional semi-geostrophic flow in geostrophic coordinates generated using a numerical solver for the semi-discrete optimal transport problem coupled with an ordinary differential equation solver.
