Fronts propagating with curvature dependent speed: algorithms based on Hamilton-Jacobi formulations. Final report
Fronts propagating with curvature dependent speed: algorithms based on Hamilton-Jacobi formulations. Final report
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发表时间：
1987-09
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通讯作者：
S. Osher;J. Sethian
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作者：
S. Osher;J. Sethian
新的数值算法设计（PSC算法）以下的曲率相关的速度传播的前线。速度可以是曲率的任意函数，并且锋也可以由底层流被动平流。这些算法近似的运动方程，这类似于Hamilton-Jacobi方程的抛物右手边，通过使用技术从双曲守恒律。非振荡计划的各种订单的精度被用来解决方程，提供的方法，准确地捕捉形成的尖锐的梯度和尖点的移动前。该算法处理拓扑合并和打破自然，工作在任何数量的空间维度，并不需要将移动表面写为一个函数。该方法也可用于更一般的Hamilton-Jacobi型问题。通过计算各种表面运动问题的解决方案，证明了该算法。
New numerical algorithms are devised (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 used also for more general Hamilton-Jacobi-type problems. The algorithms are demonstrated by computing the solution to a variety of surface motion problems.