A highly scalable massively parallel fast marching method for the Eikonal equation

TL;DR

This paper introduces a highly scalable parallel implementation of the fast marching method for solving the Eikonal equation, enabling efficient large-scale computations through a novel domain decomposition and restart approach.

Contribution

It presents a new massively parallel fast marching algorithm with a restart scheme and domain decomposition, significantly improving scalability and performance for large problems.

Findings

Achieved significant parallel speedups on up to 65,536 processes.

Successfully solved problems with up to 1 billion grid points.

Demonstrated efficiency and flexibility across various test cases.

Abstract

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.