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Next: Acknowledgments Up: Fomel: Fast marching Previous: Solving the eikonal equation

Conclusions

Variational principles have played an exceptionally important role in the foundations of mathematical physics. Their potential in numerical algorithms should not be underestimated.

In this paper, I interpret the fast marching eikonal solver with the help of Fermat's principle. Two important generalizations follow immediately from that interpretation. First, it allows us to obtain a fast method of first-arrival traveltime computation on triangulated grids. Furthermore, we can obtain a general principle, which extends the fast marching algorithm to other Hamilton-type equations and their variational principles. More research is required to confirm these promises.

In addition, future research should focus on 3-D implementations and on increasing the approximation order of the method.




2013-03-03