Abstract
This work deals with the simultaneous estimation of the spatially varying diffusion coefficient and of the source term distribution in a one-dimensional nonlinear diffusion problem. This work can be physically associated with the detection of material non-homogeneities such as inclusions, obstacles or cracks, heat conduction, groundwater flow detection, and tomography. Two solution techniques are applied in this paper to the inverse problem under consideration, namely: the conjugate gradient method with adjoint problem and a hybrid optimization algorithm. The hybrid optimization technique incorporates several of the most popular optimization modules; the Davidon-Fletcher-Powell (DFP) gradient method, a genetic algorithm (GA), the Nelder-Mead (NM) simplex method, quasi-Newton algorithm of Pshenichny-Danilin (LM), differential evolution (DE), and sequential quadratic programming (SQP). The accuracy of the two solution approaches was examined by using simulated transient measurements containing random errors in the inverse analysis.
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