Numerical solutions to the Eikonal equation are computed using variants of the fast marching method, the fast sweeping method, and the fast iterative method. In this paper, we provide a unified view of these algorithms that highlights their similarities and suggests a wider class of Eikonal solvers. We then use this framework to justify applying concurrent priority scheduling techniques to Eikonal solvers. We demonstrate that doing so results in good parallel performance for a problem from seismology. We explain why existing Eikonal solvers may produce different results despite using the same differencing scheme and demonstrate techniques to address these discrepancies. These techniques allow us to obtain deterministic output from our asynchronous fine-grained parallel Eikonal solver.

翻译：Eikonal等式的数字解决方案是使用快速进化法、快速扫描法和快速迭接法等变量计算出来的。 在本文中,我们对这些算法提供了统一的观点,这些算法突出其相似之处,并提出了一系列更广泛的Eikonal求解器。 然后我们用这个框架来为同时对Eikonal求解器应用优先排期技术提供理由。 我们证明这样做对地震学的问题产生良好的平行性能。 我们解释为什么现有的Eikonal求解器尽管使用同样的差异化方法并展示了解决这些差异的方法,却可能产生不同的结果。 这些方法使我们能够从我们无共性、细细的平行Eikonal求解器中获得确定性输出。