A Group-Ordered Fast Iterative Method for Eikonal Equations

Abstract

In the past decade, many numerical algorithms for the Eikonal equation have been proposed. Recently, the research of Eikonal equation solver has focused more on developing efficient parallel algorithms in order to leverage the computing power of parallel systems, such as multi-core CPUs and GPUs (Graphics Processing Units). In this paper, we introduce an efficient parallel algorithm that extends Jeong et al . ’s FIM (Fast Iterative Method, [1] ), originally developed for the GPU, for multi-core shared memory systems. First, we propose a parallel implementation of FIM using a lock-free local queue approach and provide an in-depth analysis of the parallel performance of the method. Second, we propose a new parallel algorithm, Group-Ordered Fast Iterative Method (GO-FIM) , that exploits causality of grid blocks to reduce redundant computations, which was the main drawback of the original FIM. In addition, the proposed GO-FIM method employs clustering of blocks based on the updating order where each cluster can be updated in parallel using multi-core parallel architectures. We discuss the performance of GO-FIM and compare with the state-of-the-art parallel Eikonal equation solvers.