On the Infinite Particle Limit in Lagrangian Dynamics and Convergence of Optimal Transportation Meshfree Methods
On the Infinite Particle Limit in Lagrangian Dynamics and Convergence of Optimal Transportation Meshfree Methods
复制标题
拉格朗日动力学中的无限粒子极限与最优传输无网格方法的收敛性
DOI：
--
复制
发表时间：
2013
影响因子：
1.6
通讯作者：
B. Schmidt
中科院分区：
文献类型：
--
作者：
B. Schmidt
我们考虑无限多粒子极限下的拉格朗日系统。结果表明，相应的离散作用泛函伽玛收敛到一个连续的作用功能的粒子轨迹的概率措施。同时也证明了作用量的稳定点的收敛性。极小的限制功能，更一般地说，限制分布的驻点进行了调查，并集中在轨道上的欧拉-拉格朗日流。我们也考虑时间离散系统。这些结果，特别是提供了一个收敛性分析的最佳运输无网格方法近似的粒子流有限离散拉格朗日动力学。
We consider Lagrangian systems in the limit of infinitely many particles. It is shown that the corresponding discrete action functionals Gamma-converge to a continuum action functional acting on probability measures of particle trajectories. Also the convergence of stationary points of the action is established. Minimizers of the limiting functional and, more generally, limiting distributions of stationary points are investigated and shown to be concentrated on orbits of the Euler-Lagrange flow. We also consider time discretized systems. These results in particular provide a convergence analysis for optimal transportation meshfree methods for the approximation of particle flows by finite discrete Lagrangian dynamics.