A Comparison of Nonlinear Programming Approaches to an Ellipticinverse Problem and a New Domain Decomposition Approach

We compare three nonlinear programming approaches to a well-known elliptic inverse problem in three spatial dimensions. Two of these approaches may be viewed as conventional; the third approach is new and is based on a domain decomposition technique for the solution of the governing elliptic equation. We discuss the beneets that may be obtained from treating the governing diierential equation in an inverse problem as equality constraints in the optimization problem. We present numerical results and discuss the relative eecacy of the three approaches.