In the last decade, there have been dramatic advances in our knowledge
of solving coupled processes characterized by solid mechanics, fluid
dynamics as well as fluid-structure interaction. Often such solution
methodologies require sophisticated computational techniques to be
carried out over complex domains.  Such analysis may be accomplished by
partitioning the global domain into several local sub-domains each of
which may be constructed separately by different analysts and the global
solution can then be constructed by piecing together local solutions
obtained from the individually modeled sub-domains. In this talk, a
multilevel computational technique to accomplish this will be described.
Stability and convergence results for the solution methodology will be
discussed.  Computational results that show the optimality of the
technique will be presented for various benchmark applications involving
coupled processes.