Temperature distribution reconstruction by eigenfunction interpolation of boundary measurement data

This paper treats the inverse problem of evaluating the temperature distribution over time in a composite solid material which unlike most of the other publications can have an arbitrary geometry. This approach is capable of evaluating the temperature over all the points within the domain of a non-homogeneous object at every time instance. The method utilizes measurements in just few points of the peripheral surface of the geometry. The collected data are applied to estimate the weight coefficients of the numerically computed eigenfunctions of the problem which in turn leads to reconstruction of the temperature distribution everywhere.