Symbolic Computation for inverse Boundary-Value Problems and its Application to impedance Tomography Reconstruction

An approach for solving inverse boundary-value problems is described using symbolic computation. Finite element or boundary element calculation of a given system is performed using the symbolic parameters which express its shape or material properties. Thus the calculated results such as potential distributions are explicitly provided as a function of the shape or material variables. The inverse problem can be solved directly by comparing the calculated distribution functions with desired or measured quantities. Applications include design optimization and identification or unknown internal system parameters. Experimental results regarding impedance topography reconstruction are shown.