Parameter estimation of si diffusion in fe substrates after hot dipping and diffusion annealing

  • Authors:

  • B. Malengier

  • Affiliations:

  • Research Group for Numerical Functional Analysis and Mathematical, Modelling (NfaM2), Department of Mathematical Analysis, Ghent University, Gent, Belgium

  • Venue:
  • NAA'04 Proceedings of the Third international conference on Numerical Analysis and its Applications
  • Year:
  • 2004

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Abstract

In this paper a general model is developed for the simulation of one dimensional diffusion annealing. Our main interest is the determination of the diffusion coefficient from measured values at discrete space-time points within the sample. The method is based on a suitable reduction of the pde to a system of odes by a second order finite difference space discretization. The inverse problem is solved by implementation of the Levenberg-Marquardt method. This allows the estimation of the parameters and the determination of Cramér-Rao lower bounds.