We present a fast sweeping method for a class of Hamilton-Jacobi equations that arise from time-independent problems in optimal control theory. The basic method in two dimensions uses a four point stencil and is extremely simple to implement. We test our basic method against Eikonal equations in different norms, and then suggest a general method for rotating the grid and using additional approximations to the derivatives in different directions in order to more accurately capture characteristic flow. We display the utility of our method by applying it to relevant problems from engineering.

中文翻译：

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一类Hamilton-Jacobi方程的旋转网格迎风快速扫掠方案

我们为一类由最优控制理论中与时间无关的问题引起的汉密尔顿-雅各比方程组提供了一种快速清扫方法。二维的基本方法使用四点模具，实现起来非常简单。我们针对不同范式中的Eikonal方程测试了基本方法，然后提出了旋转网格并在不同方向上对导数使用其他逼近的通用方法，以便更准确地捕获特征流。通过将其应用于工程中的相关问题，我们展示了该方法的实用性。