Short Course: Mathematical Foundations for Numerical Treatments of Problems in Domains Extended to Infinity

Lecturer: Prof. George C. Hsiao (University of Delaware)

Problems in domains extended to infinity are generally treated by either boundary integral equation

methods or boundary-field equation methods. The essential ideas here is to reformulate the problem under consideration to either an equivalent boundary integral equation on compact boundary

manifold or to an equivalent boundary-field equation in a bounded region. Both reformulated problems can then be treated by standard variational methods including their numerical approximations. In this series of six lectures, the following selected topic will be included:

1. Boundary integral equations--- an overview

2. Boundary-field equation mathods

3. A dual-mixed formulation for an exterior Stokes problem

4. Fluid-structure interaction

5. Time-dependent boundary integral equations

6. Time-dependent fluid-structure interaction

These topics also serve the purposes for introducing boundary-field equation methods from their original developments to the recent advances in theory as well as in applications. These lectures are expository and aim particularly at audiences in applied and numerical mathematics, sciences, and engineerings.

The specific shedule is to be determined.