The Method of Fundamental Solutions for Detection of Cavities in Eit

In this paper, the method of fundamental solutions (MFS) is used to solve numerically an inverse problem which consists of finding an unknown cavity within a region of interest based on given boundary Cauchy data. A range of examples are used to demonstrate that this technique is very effective at locating cavities in both two- and three-dimensional geometries for exact input data. The MFS is then developed to include a regularisation parameter that enables cavities to be located accurately and stably even for noisy input data.