Applications of Sharp Interface Method for Flow Dynamics, Scattering and Control Problems.

摘要

Our effort has been continued for developing and analyzing high order methods for the interface problems. Specifically, we have developed an adaptive mesh refinement for the Immersed Boundary and the Immersed Interface Method using the level set method for elliptic interface problems, the sensitivity calculation with respect to the parameter and shape for flow past obstacle and multi-moment immersed interface method for wave equation and Hamilton-Jacobi equation. Our approach uses the physical augmented variables and the domain embedding technique and allows us to develop fast and robust implementation of the immersed interface method for general interface problems.