Tao Lin's Home Page

Tao Lin

Mathematics Department

Virginia Tech
Blacksburg, VA  24061-0123
E-mail: tlin (at) math (dot) vt (dot) edu
Phone:  (540) 231-2766
FAX:    (540) 231-5960
Office: McB 520


I will be teaching Math/CS 4414 in fall, 2018 and the course web pages are hosted on Canvas.

Research: Please go to my Research Web Page for more details

My research interests involve numerical methods for solving partial differential equations and integro-differential equations. My recent focus is the immersed finite element methods for interface problems and their applications.

A very brief introduction to the immersed finite elements (IFE): 

In many applications, we often need to simulate a procedure in a domain consisting of several materials separated from each other by curves or surfaces. This usually leads to the so called interface problem which is a boundary value problem of a PDE whose coefficients are discontinuous across the material interface.

The conventional finite element methods can be used to solve interface problems, but they usually require that the each element contains essentially one of the materials. Geometrically, this means that each element has to be on one side of a material interface.

The immersed finite elements are developed such that each element can contain multiple materials so that elements are allowed to sit on an interface. The basic features of the immersed finite elements are:

(a). Their meshes can be independent of the interface location; hence, if preferred, structured meshes can be used to solve a problem with non-trivial interface.

(b). The basis functions on an interface element are formed according the interface jump conditions.