In this paper we propose an improved fast iterative method to solve the Eikonal equation, which can be implemented in parallel. We improve the fast iterative method for Eikonal equation in two novel ways, in the value update and in the error correction. The new value update is very similar to the fast iterative method in that we selectively update the points, chosen by a convergence measure, in the active list. However, in order to reduce running time, the improved algorithm does not run a convergence check of the neighboring points of the narrow band as the fast iterative method usually does. The additional error correction step is to correct the errors that the previous value update step may cause. The error correction step consists of finding and recalculating the point values in a separate remedy list which is quite easy to implement on a GPU. In contrast to the fast marching method and the fast sweeping method for the Eikonal equation, our improved method does not need to compute the solution with any special ordering in neither the remedy list nor the active list. Therefore, our algorithm can be implemented in parallel. In our experiments, we implemente our new algorithm in parallel on a GPU and compare the elapsed time with other current algorithms. The improved fast iterative method runs faster than the other algorithms in most cases through our numercal studies.
翻译：在本文中,我们提出了一个更好的快速迭接方法来解决 Eikonal 等式,可以平行实施。我们用两种新方式改进 Eikonal 等式的快速迭接方法,在数值更新和错误更正方面改进了 Eikonal 等式的快速迭接方法。新的值更新与快速迭接方法非常相似,因为我们有选择地更新了点,在活动列表中通过一种趋同措施选择了这些点。然而,为了缩短运行时间,改进的算法不会像快速迭接合方法通常那样对窄带的相邻点进行趋同检查。因此,额外的错误更正步骤是纠正前一个值更新步骤可能造成的错误。错误更正步骤包括查找和重新计算在另一个补救列表中的点值值,这很容易在 GPU 上执行。与快速行进的方法和 Eikonal 等式的快速扫描方法相比,我们改进的算法不需要在补救列表或活动列表中以任何特别命令来拼写解决方法。因此,我们的算法可以平行执行。在我们的实验中,我们将新的算法平行地平行地同时执行GPU 和将过去的时间比其他快速的变动法。
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