Non-overlapping domain decomposition and heterogeneous modeling used in solving free boundary problems

Non-overlapping domain decomposition techniques for free boundary problems are extensively considered in this dissertation. We use a model problem to test the effectiveness of various kinds of DDM schemes.; The problem of fluid flow past a truncated concave shaped profile between walls is solved using conformal mapping techniques. An open wake is formed behind the profile. The problem formulated in a hodograph plane is decomposed into two non-overlapping domains. We use different modeling techniques to describe the problems. First, a heterogeneous model is used, i.e., we use different functions in different subdomains to describe the problem. In one of these domains, a Baiocchi type transformation is used to obtain a fixed domain formulation for the part of the transformed problem containing an unknown boundary. The second method is a heterogeneous modeled problem where the Baiocchi type transformation is extended into the second domain. Next, a parallel version of the latter model is considered. Numerical results show all the methods have good Agreement with a published solution. Furthermore, the parallel version of the DDM method is extended to solve other free boundary problems.; Finally, the convergence issue from a mathematical point of view is considered. The existence and convergence properties of the free boundary problems considered in this dissertation, (including the problem of flow past a concave shaped profile, the rectangular dam problem and the problem of flow through a porous dam with a toe drain), are proved.