Interface Problems and Level Set Method
Student No.:50
Time:Mon/Wed 15:10-17:00, 2014-9-1~2014-9-24
Instructor:Li-Tien Cheng  [University of California, San Diego]
Place:Conference Room 3, Floor 2, jin Chun Yuan West Building
Starting Date:2014-9-1
Ending Date:2014-9-24



Interfaces appear in a variety of problems across multiple scientific fields. They play the role of surfaces separating water and air in fluid flow; the inside and outside of cells in biology; a molecule from surrounding solvent in chemistry; and areas of wave arrival in wave propagation. Mathematical techniques for simulating the dynamics of such interfaces fit in large part in two categories: Lagrangian and Eulerian methods. The level-set method is an important example of an Eulerian method. Its advantage is in its ability to automatically handle topological changes in the interface while representing the interface, and resolving it, implicitly over a fixed, possibly uniform grid. The mathematics involved makes heavy use of partial differential equations and finite difference schemes. We aim to introduce the level-set method, and its complementary tools such as Hamilton-Jacobi Equations and their numerics, and reveal its intricacies through examples and applications such as Image Processing Applications.