Course title: Introduction to the Immersed Boundary and Interface Methods
Instructor: Prof. Zhilin Li
(Center for Research in Scientific Computation & Mathematics North Carolina State University Raleigh, NC 27695)
Room and Time: Room 210, 9:00am-11:30am, July 9 (Monday), July 11 (Wednesday), July 13 (Friday).
Content of the course:
Peskin's Immersed Boundary (IB) Method is a popular mathematical model and numerical method developed for simulating blood flow in human's heart in 1980's. Since then, it has been applied to problems in mathematical biology, material science, fluid mechanics, and many others. In this course, Prof. Li will introduce the IB method through some examples and describe mathematical formulations, theory, and related numerical methods.
The Immersed Interface Method (IIM) was motivated by the Peskin's Immersed Boundary Method. The IIM shares many characteristics of the IB method. Both methods use simple grid structure. The original motivation of IIM is to improve the accuracy of the IB method from first order to second order. This has been achieved by incorporating the jump conditions into numerical schemes near or on the interface. Prof. Li will also explain how the IB/IIM methods can be coupled with evolution schemes such as front tracking and the level set methods for free boundary and moving interface problems.
Reference: The Immersed Interface Method -- Numerical Solutions of PDEs Involving Interfaces and Irregular Domains, Zhilin Li and Kazufumi Ito, SIAM Frontiers in Applied mathematics, 33.
Schedule of the course: Three lectures will be presented by Prof. Zhilin Li on June 9, 11, 13, respectively.
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