A Rotating-Grid Upwind Fast Sweeping Scheme for a Class of Hamilton-Jacobi Equations
A Rotating-Grid Upwind Fast Sweeping Scheme for a Class of Hamilton-Jacobi Equations
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DOI：
10.1007/s10915-021-01531-x
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发表时间：
2020-05
影响因子：
2.5
通讯作者：
C. Parkinson
中科院分区：
文献类型：
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作者：
C. Parkinson
针对最优控制理论中一类与时间无关的Hamilton-Jacobi方程，提出了一种快速扫描方法。二维的基本方法使用四点模板，实现起来非常简单。我们测试我们的基本方法对Eikonal方程在不同的规范，然后提出了一个通用的方法旋转网格，并使用额外的近似在不同的方向上的衍生物，以更准确地捕捉特征流。我们显示我们的方法的实用性，将其应用到相关的问题，从工程。
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.