Spatial domain decomposition and model reduction for parabolic optimal control problems

Abstract

In this thesis, we propose a spatial domain decomposition method and model reduction techniques for the solution of linear-quadratic parabolic optimal control problems. Such problems arise directly from many applications such as the data assimilation, circuit design and oil reservoir modeling. The motivation for this work is threefold. First, we attempt to address the storage issue in numerically solving the parabolic optimal control problem. Secondly, spatial domain decomposition leads to parallelism. Therefore, data can be decomposed uniformly by assigning subdomains to each processor. Finally, for large-scale problems, the subproblems on the subdomains are still very large. Model reduction techniques applied to the subproblems are expected to dramatically reduce the size of the subproblems and save computational time.