用于GPU计算的Eikonal方程的改进快速迭代算法
Improved Fast Iterative Algorithm for Eikonal Equation for GPU Computing
摘要：
本文提出了一种改进的快速迭代法来求解Eikonal方程，它可以并行实现。对Eikonal方程的快速迭代法进行了数值更新和误差修正两方面的改进。新值更新与快速迭代法非常相似，因为我们选择性地更新活动列表中由收敛度量选择的点。然而，为了减少运行时间，改进的算法不运行的窄带的相邻点的收敛性检查快速迭代法通常。附加的误差校正步骤是校正先前的值更新步骤可能引起的误差。错误校正步骤包括在一个单独的补救列表中查找和重新计算点值，这在GPU上很容易实现。与Eikonal方程的快速推进法和快速扫描法相比，本文的改进方法不需要计算在补救表和活动表中具有任何特殊排序的解。因此，我们的算法可以并行实现。在我们的实验中，我们实现了我们的新算法在GPU上并行和比较的运行时间与其他当前的算法。通过数值计算，在大多数情况下，改进的快速迭代法比其它算法运行速度快。
英文摘要：
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.
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