Symbolic computation for inverse boundary-value problems and its application to impedance tomography reconstruction

A symbolic approach to inverse boundary-value problems is described. Finite-element or boundary-element calculation of a given system is performed using symbolic parameters expressing its material or shape properties. The calculated results such as potential distributions are explicitly provided as a function of the material or shape variables. The inverse problem can be solved directly by comparing the calculated distribution functions with measured or desired quantities. Applications include identification of unknown internal system parameters as well as design optimization. Preliminary experimental results aimed at impedance tomography reconstruction are shown