Fast-phase space computation of multiple arrivals
Fast-phase space computation of multiple arrivals
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DOI：
10.1073/pnas.102476599
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发表时间：
2002-05
影响因子：
11.1
通讯作者：
Sergey Fomel;J. Sethian
中科院分区：
文献类型：
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作者：
Sergey Fomel;J. Sethian
我们提出了一种计算静态Hamilton-Jacobi方程相空间解的快速、通用的计算技术。从特征方程的刘维尔公式开始，我们推导出静态的、与时间无关的欧拉偏微分方程的“逃逸方程”。它们表示从所有可能的起始构型到给定边界的所有到达点。在半拉格朗日方法、Eikonal方程的类dijkstra方法和有序逆风方法的思想基础上，通过“一次”公式在数值上构建了该解决方案。为了计算与所有可能的边界条件相对应的所有可能的轨迹，该技术的计算阶数为O(N log N)，其中N为计算相空间域中点的总数；然后通过快速后处理提取任何特定的边界条件集。在预先提供特定源分布的情况下，提出了加快算法速度的建议。作为一个应用，我们将该技术应用于计算Eikonal方程的优先、多重和最具能量到达的问题。
We present a fast, general computational technique for computing the phase-space solution of static Hamilton–Jacobi equations. Starting with the Liouville formulation of the characteristic equations, we derive “Escape Equations” which are static, time-independent Eulerian PDEs. They represent all arrivals to the given boundary from all possible starting configurations. The solution is numerically constructed through a “one-pass” formulation, building on ideas from semi-Lagrangian methods, Dijkstra-like methods for the Eikonal equation, and Ordered Upwind Methods. To compute all possible trajectories corresponding to all possible boundary conditions, the technique is of computational order O(N log N), where N is the total number of points in the computational phase-space domain; any particular set of boundary conditions then is extracted through rapid post-processing. Suggestions are made for speeding up the algorithm in the case when the particular distribution of sources is provided in advance. As an application, we apply the technique to the problem of computing first, multiple, and most energetic arrivals to the Eikonal equation.