Efficient inverse solvers for thermal tomography

Abstract

Thermal tomography is a method for recovering heterogeneous thermal properties employing only boundary measurements. This paper focuses on the development of efficient inverse solvers for scenarios where the evolution of boundary conditions can vary in time. A transient heat model with two material parameters – volumetric capacity and a coefficient of thermal conductivity – is introduced for the description of the underlying physical phenomena. All proposed identification algorithms are deterministic methods based on a regularised Gauss-Newton method. A basic framework, implementation details, and the modification of general constraints initially derived for a standard setup of the Calderón problem are discussed here. Moreover, the algorithms are numerically verified for numerous examples, and results obtained show that the inverse problem exhibits a certain degree of ambiguity for a particular measurement-loading scenario. In other words, the important material property minimising the magnitude of error of the objective function seems to be the effusivity field rather than accurate identification of the individual thermal fields.