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Parameter Estimation of Si Diffusion in Fe Substrates After Hot Dipping and Diffusion Annealing

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Numerical Analysis and Its Applications (NAA 2004)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3401))

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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.

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References

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Author information

Authors and Affiliations

  1. Research Group for Numerical Functional Analysis and Mathematical, Modelling (NfaM2), Department of Mathematical Analysis, Ghent University, Galglaan 2, B-9000, Gent, Belgium

    B. Malengier

Authors
  1. B. Malengier
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Editor information

Editors and Affiliations

  1. Department of Land Surveying and Geo-Informatics, The Hong Kong Polytechnic University, Kowloon, P.O. Box, Hong Kong

    Zhilin Li

  2. Department of Mathematics, University of Rousse, 7017, Rousse, Bulgaria

    Lubin Vulkov

  3. Informatics & Mathematical Modeling, Technical University of Denmark, DK-2800, Lyngby, Denmark

    Jerzy Waśniewski

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© 2005 Springer-Verlag Berlin Heidelberg

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Malengier, B. (2005). Parameter Estimation of Si Diffusion in Fe Substrates After Hot Dipping and Diffusion Annealing. In: Li, Z., Vulkov, L., Waśniewski, J. (eds) Numerical Analysis and Its Applications. NAA 2004. Lecture Notes in Computer Science, vol 3401. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-31852-1_48

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  • DOI: https://doi.org/10.1007/978-3-540-31852-1_48

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-24937-5

  • Online ISBN: 978-3-540-31852-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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