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Applied Math Colloquium

Friday, April 11, 2014, 11:30 AM
Cullimore Lecture Hall, Lecture Hall II
New Jersey Institute of Technology

A class of Cartesian methods: Augmented Immersed Interface Method and Applications

Zhilin Li

Center for Research in Scientific Computation and Mathematics, North Carolina State University

Abstract

In this talk, I will first introduce the Immersed Interface Method (IIM) and relations with other related Cartesian methods. The IIM is a sharp interface method that enforces jump conditions either exactly or approximately. Then the emphasis will focus on the Augmented Immersed Interface Method (AIIM) through various examples of interface problems, problems defined on irregular domain, and a recent work on fluid structure interaction between a fluid flow and a porous media, and other CFD applications. In the Augmented Immersed Interface Method, some intermediate variables are introduced so that we can get accurate discretization; decoupled problems, utilize fast solvers on rectangular domains. The augmented variable(s) has co-dimension one compared with the solution and thus can be solved by either a directly solver, or the GMRES method. In some sense, the AIIM is like a boundary integral method without the Green function, independent of source terms and boundary conditions. An efficient preconditioning technique has been developed. Various applications will also be presented during the talk.