Semi-analytic Conjugate Gradient Method applied to a simple Inverse Heat Conduction Problem

Considering heat transfers in a one-dimensional domain, an academic identification problem is solved by the implementation of a conjugate gradient method (CGM). While temperature measurements are available on a domain boundary, inverse heat conduction problem (IHCP) is solved in order to estimate heat flux on the opposite boundary. Such problem has been widely investigated and the main novelty of our approach will be seen in the explicit formulation of CGM solution which is given into an approximation space split into a polynomial part and an exponential part. Then, a filtering property of the CGM is exhibited.