Biomedical Engineering Reference
In-Depth Information
practitioner to consider alternative numerical methods. It may or may not be
the case that the level set method is still the best choice.
For a more comprehensive discussion on the level set method, the interested
reader is directed to the topics by Sethian [104] (which also includes the fast
marching method) and Osher and Fedkiw [84].
Questions
1. What are the main advantages of the level set method?
2. What is the importance of the connection between the level set method and
hyperbolic conservation laws?
3. What is the difference between the level set method and the fast marching
method?
4. Why are triple junctions a problem for the level set method?
5. What is the primary purpose of reinitialization, and why is it important
to do it as accurately as possible?
6. What is the alternative to using repeated reinitializations?
7. What kinds of problems can be solved by the general ordered upwind
method that could not be solved by the fast marching method?
8. What is the difference between the original velocity extension and the new
velocity extension methods?
9. Can the level set method be implemented using the finite element method?
10. What is the advantage of using the X-FEM over a standard finite element
formulation?
11. Is the level set method appropriate for all interface propagation problems?
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