Boundary estimation problems arising in thermal tomography

Problems on the identification of two-dimensional spatial domains arising in the detection and characterization of structural flaws in materials are considered. For a thermal diffusion system with external boundary input, observations of the temperature on the surface are used in a output least-squares approach. Parameter estimation techniques based on the 'method of mappings' are discussed and approximation schemes are developed based on a finite-element Galerkin approach. Theoretical convergence results for computational techniques are given and the results are applied to experimental data for the identification of flaws in thermal testing of materials.