A parallel fast sweeping method for the Eikonal equation

Authors:
Miles Detrixhe;FréDéRic Gibou;Chohong Min
Affiliations:
Mechanical Engineering Department, University of California, Santa Barbara, CA 93106, United States;Mechanical Engineering Department, University of California, Santa Barbara, CA 93106, United States and Computer Science Department, University of California, Santa Barbara, CA 93106, United State ...;Mathematics Department, Ewha Womans University, Seoul 120-750, Republic of Korea
Venue:
Journal of Computational Physics
Year:
2013

Citing 8
Cited 0

Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations

Journal of Computational Physics
A viscosity solutions approach to shape-from-shading

SIAM Journal on Numerical Analysis
Fast Marching Methods

SIAM Review
Optimal Algorithm for Shape from Shading and Path Planning

Journal of Mathematical Imaging and Vision
Some Improvements of the Fast Marching Method

SIAM Journal on Scientific Computing
Iterative Methods for Sparse Linear Systems

Iterative Methods for Sparse Linear Systems
A Fast Iterative Method for Eikonal Equations

SIAM Journal on Scientific Computing
A unified approach to noise removal, image enhancement, and shape recovery

IEEE Transactions on Image Processing

Quantified Score

Hi-index	31.45

Visualization

Abstract

We present an algorithm for solving in parallel the Eikonal equation. The efficiency of our approach is rooted in the ordering and distribution of the grid points on the available processors; we utilize a Cuthill-McKee ordering. The advantages of our approach is that (1) the efficiency does not plateau for a large number of threads; we compare our approach to the current state-of-the-art parallel implementation of Zhao (2007) [14] and (2) the total number of iterations needed for convergence is the same as that of a sequential implementation, i.e. our parallel implementation does not increase the complexity of the underlying sequential algorithm. Numerical examples are used to illustrate the efficiency of our approach.