一种求解Eikonal方程的高可扩展大规模并行快速推进方法
A highly scalable massively parallel fast marching method for the Eikonal equation
摘要：
快速推进法是求解Eikonal方程的一种广泛应用的数值方法，它产生于各种科学和工程领域。长期以来，它被认为是固有的顺序和一个有效的并行算法适用于大规模的实际应用是在文献中没有。在这项研究中，我们提出了一个高度可扩展的大规模并行实现的快速行军方法，使用区域分解的方法。该算法的核心是一种新的重新启动的窄带方法，该方法协调通信频率和顺序运行额外的计算量，以实现前所未有的并行性能。在每次重启过程中，采用窄带快速行进法，通过简单的同步局部交换和全局归约，分别实现相邻子域重叠区域的更新数据通信和最新前沿状态的获取.通过特殊的数据结构和增强的状态标记，利用前端特征的独立性来提取快速行进方法中的掩蔽并行性。并行算法的效率，灵活性和适用性通过几个例子证明。这些问题进行了广泛的测试，六个网格多达10亿点，使用不同数量的过程，从1到65536。使用成千上万的进程实现了显着的并行加速。详细的伪代码的顺序和并行算法提供说明并行实现的简单性和它的相似性顺序窄带快速行进算法。
英文摘要：
The fast marching method is a widely used numerical method for solving the Eikonal equation arising from a variety of scientific and engineering fields. It is long deemed inherently sequential and an efficient parallel algorithm applicable to large-scale practical applications is not available in the literature. In this study, we present a highly scalable massively parallel implementation of the fast marching method using a domain decomposition approach. Central to this algorithm is a novel restarted narrow band approach that coordinates the frequency of communications and the amount of computations extra to a sequential run for achieving an unprecedented parallel performance. Within each restart, the narrow band fast marching method is executed; simple synchronous local exchanges and global reductions are adopted for communicating updated data in the overlapping regions between neighboring subdomains and getting the latest front status, respectively. The independence of front characteristics is exploited through special data structures and augmented status tags to extract the masked parallelism within the fast marching method. The efficiency, flexibility, and applicability of the parallel algorithm are demonstrated through several examples. These problems are extensively tested on six grids with up to 1 billion points using different numbers of processes ranging from 1 to 65536. Remarkable parallel speedups are achieved using tens of thousands of processes. Detailed pseudo-codes for both the sequential and parallel algorithms are provided to illustrate the simplicity of the parallel implementation and its similarity to the sequential narrow band fast marching algorithm.
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