#### ABSTRACT

We consider a domain decomposition method for a
fluid-structure interaction problem. The fluid-structure interaction
problem involves two mathematical models, each posed on a different
domain, so that domain decomposition occurs naturally. Our approach to
a domain decomposition method is based on a strategy in which unknown
data at the interface is determined through an optimization
process. We prove that the solution of the optimization problem
exists. And we show that the Lagrange multiplier rule may be used to
transform the constrained optimization problem into an unconstrained
one and that rule is applied to derive an optimality system from which
optimal solutions may be obtained. We then study a gradient method for
solving optimization problem.

*TUESDAY, November 27, 2001*

**Time:** 1:30 P.M.

**Location:** Physical Plant Building 300