Journal
SIAM JOURNAL ON SCIENTIFIC COMPUTING
Volume 34, Issue 2, Pages A547-A578Publisher
SIAM PUBLICATIONS
DOI: 10.1137/10080909X
Keywords
Fast Marching Method; Fast Sweeping Method; eikonal PDEs; cell-decomposition; label-setting; label-correcting
Categories
Funding
- National Science Foundation [DMS-0514487, DMS-1016150]
- Alfred P. Sloan Foundation
- Direct For Mathematical & Physical Scien
- Division Of Mathematical Sciences [1016150] Funding Source: National Science Foundation
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Fast Marching and Fast Sweeping are the two most commonly used methods for solving the eikonal equation. Each of these methods performs best on a different set of problems. Fast Sweeping, for example, will outperform Fast Marching on problems where the characteristics are largely straight lines. Fast Marching, on the other hand, is usually more efficient than Fast Sweeping on problems where characteristics frequently change their directions and on domains with complicated geometry. In this paper we explore the possibility of combining the best features of both approaches by using Marching on a coarser scale and sweeping on a finer scale. We present three new hybrid methods based on this idea and illustrate their properties in several numerical examples with continuous and piecewise-constant speed functions in R-2.
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