Fast two-scale methods for Eikonal equations
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. Fas...
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Zusammenfassung: | 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 of these 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 on several numerical
examples with continuous and piecewise-constant speed functions in $R^2$. |
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DOI: | 10.48550/arxiv.1110.6220 |