Computational Aspects of Solving Inverse Problems for Elliptic PDEs on Perforated Domains Using the Collage Method

Abstract

The treatment of an inverse problem on a perforated domain is complicated heavily by the presence of the perforations or holes. We present several theoretical results that provide relationships between the problem on the perforated domain and the same problem on the corresponding unperforated/solid domain. The results establish that we can approximate the solution of the inverse problem on the perforated domain by instead solving the inverse problem on the associated solid domain. Examples are provided.