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Adaptive wavelet methods and sparsity reconstruction for inverse heat conduction problems

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Abstract

This paper is concerned with the numerical treatment of inverse heat conduction problems. In particular, we combine recent results on the regularization of ill-posed problems by iterated soft shrinkage with adaptive wavelet algorithms for the forward problem. The analysis is applied to an inverse parabolic problem that stems from the industrial process of melting iron ore in a steel furnace. Some numerical experiments that confirm the applicability of our approach are presented.

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Authors and Affiliations

  1. Center for Industrial Mathematics/Fachbereich 3, University of Bremen, Postfach 33 04 40, 28334, Bremen, Germany

    Thomas Bonesky & Peter Maass

  2. Philipps-Universität Marburg, Fachbereich 12, Hans-Meerwein-Str., 35032, Marburg, Germany

    Stephan Dahlke

  3. Institut für Mathematik, Johannes Gutenberg-Universität Mainz, Staudingerweg 9, 55099, Mainz, Germany

    Thorsten Raasch

Authors
  1. Thomas Bonesky
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  2. Stephan Dahlke
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  3. Peter Maass
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  4. Thorsten Raasch
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Corresponding author

Correspondence to Stephan Dahlke.

Additional information

Communicated by guest editors Jin Cheng, Benny Y. C. Hon and Masahiro Yamamoto.

Thomas Bonesky was supported by Deutsche Forschungsgemeinschaft, grant number MA 1657/15-1

Peter Maass was supported by Deutsche Forschungsgemeinschaft, SPP 1180, grant number MA 1657/17-1

Stephan Dahlke and Thorsten Raasch were supported by Deutsche Forschungsgemeinschaft, grants number DA 360/12-1, DA 360/7-1

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Bonesky, T., Dahlke, S., Maass, P. et al. Adaptive wavelet methods and sparsity reconstruction for inverse heat conduction problems. Adv Comput Math 33, 385–411 (2010). https://doi.org/10.1007/s10444-010-9147-2

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