Torsten Lüttich, Adel Mhamdi, Wolfgang Marquardt:
Design, formulation, and solution of multidimensional inverse heat conduction problems
Numerical Heat Transfer: Part B: Fundamentals, 2005, 47(2), 111-133
The solution of inverse heat conduction problems (IHCP) for the reconstruction of time-dependent, spatially unknown heat fluxes on the boundaries of two- and three-dimensional geometries from several temperature measurements is presented. The solution method is based on the interpretation of the IHCP in the frequency domain. We emphasize in detail the extension of the method to large-scale problems, i.e. the parameterization of the unknown heat fluxes with respect to the number of sensors and their positions, the reduction and stable inversion of the large linear state-space models obtained from semi-discretisation of the heat conduction equation.
The influence of each of the steps and the choice of their tuning parameters on the quality of the estimated heat flux are discussed. Two- and three-dimensional examples show the good performance of the method with regard to time- and space-resolution even in the presence of noisy measurements.
Inverse heat conduction, multi-dimensional, frequency domain, state-space, filtering, sensor placement, Hankel singular values, heat flux parameterization.