An introduction to the Level Set method and its applications

"An introduction to the Level Set method and its applications", organizado por CITMAga. Será impartido por Alejandro López Núñez (Departamento de Económicas, Universidade da Coruña)

Data: luns, 17 de marzo

Hora: 12:30 h.

Duración: 45 min

Lugar: Aula de Graos, Facultade de Informática e en liña: (MS Teams)

Abstract:

Moving interfaces appear in a wide range of scientific problems, usually adding a layer of complexity that needs to be addressed. Thus, several numerical methods have been developed recently to tackle this issue. One of the most popular methods is the Level Set method [1], a mathematical tool used to track the movement of free boundaries under a certain velocity field. This method consists in representing the free boundary as the zero level set of a higher dimensional function, Φ(x, t), called the level set function. This function is time-dependent and tracks not only the zero level set, but also every other level set, which can be useful in problems with multiple moving interfaces.

Another moving interface method is the Fast-Marching Method [2,3]. It is, in fact, a stand-alone method, significantly faster than many other methods when applicable, but it is commonly paired with the Level Set method in modern Level Set implementations. It consists in considering the interface to be represented implicitly by the so-called time of crossing map, Φ(x), so that the isocontour t = Φ(x) marks the position of the moving interface at time t. In this seminar, a brief explanation of both methods will be presented, as well as the algorithmic strategies to implement them. After that, several classical examples will be solved, as well as more advanced applications of the Level Set implementation.

[1] S. Osher, J. A. Sethian, Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulations, Journal of Computational Physics 79 (1) (1988) 12–49.
[2] D. L. Chopp, Some improvements of the fast-marching method, SIAM Journal on Scientific Computing 23 (1) (2001) 230–244.
[3] J. A. Sethian, A fast marching level set method for monotonically advancing fronts., Proceedings of the National Academy of Sciences 93 (4) (1996) 1591–1595.