Convergence of a Generalized Fast-Marching Method for an Eikonal Equation with a Velocity-Changing Sign
Convergence of a Generalized Fast-Marching Method for an Eikonal Equation with a Velocity-Changing Sign
复制标题
具有速度变化符号的Ekonal方程的广义快进方法的收敛性
DOI：
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发表时间：
2008
影响因子：
2.9
通讯作者：
R. Monneau
中科院分区：
文献类型：
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作者：
E. Carlini;M. Falcone;N. Forcadel;R. Monneau
提出了一种新的变号速度程函方程的快速推进算法。该一阶方程对法向方向上的波前传播进行建模。该算法是快速推进法在两个方面的推广。首先，新格式可以处理速度随时间变化的情况，其次，对速度的符号变化没有限制。我们分析了该算法的性质，并证明了其在不连续粘性解类中的收敛性。最后，我们给出了波前在$mathbb{R}^2 $中传播的一些数值模拟。
We present a new fast-marching algorithm for an eikonal equation with a velocity-changing sign. This first order equation models a front propagation in the normal direction. The algorithm is an extension of the fast-marching method in two respects. The first is that the new scheme can deal with a time-dependent velocity, and the second is that there is no restriction on its change in sign. We analyze the properties of the algorithm, and we prove its convergence in the class of discontinuous viscosity solutions. Finally, we present some numerical simulations of fronts propagating in $mathbb{R}^2$.