Algorithms Based on Hamilton-Jacobi Formulations
Algorithms Based on Hamilton-Jacobi Formulations
复制标题
DOI：
--
复制
发表时间：
1988
期刊：
影响因子：
--
通讯作者：
S. Osher;J. Sethian
中科院分区：
文献类型：
--
作者：
S. Osher;J. Sethian
我们设计了一种新的数值算法，称为PSC算法，用于跟踪与曲率有关的速度传播的波前。速度可以是曲率的任意函数，锋面也可以被底层气流被动平流。这些算法利用双曲型守恒律的技巧逼近运动方程，类似于右侧抛物线的Hamilton-Jacobi方程。采用各种精度的非振荡格式来求解方程，提供了准确捕捉运动锋面中尖锐梯度和尖点形成的方法。该算法自然地处理拓扑合并和断开，在任意数量的空间维度中工作，并且不需要将移动曲面写成函数。该方法也可用于更一般的Hamilton-Jacobit型问题。我们通过计算各种表面运动问题的解来演示我们的算法。
We devise new numerical algorithms, called PSC algorithms, for following fronts propagating with curvature-dependent speed. The speed may be an arbitrary function of curvature, and the front can also be passively advected by an underlying flow. These algorithms approximate the equations of motion, which resemble Hamilton-Jacobi equations with parabolic right-hand-sides, by using techniques from the hyperbolic conservation laws. Non-oscillatory schemes of various orders of accuracy are used to solve the equations, providing methods that accurately capture the formation of sharp gradients and cusps in the moving fronts. The algorithms handle topological merging and breaking naturally, work in any number of space dimensions, and do not require that the moving surface be written as a function. The methods can be also used for more general Hamilton-Jacobitype problems. We demonstrate our algorithms by computing the solution to a variety of surface motion problems.