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.
- inverse problems
- method of fundamental solutions
- Electrical impedance tomography