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International Conference on High Performance Computing in Science and Engineering

HPCSE 2015: High Performance Computing in Science and Engineering pp 60–67Cite as

An Equation Error Approach for the Identification of Elastic Parameters in Beams and Plates with \(H_1\) Regularization

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9611))

Abstract

In this short note deals with the nonlinear inverse problem of identifying a variable parameter in fourth-order partial differential equations using an equation error approach. These equations arise in several important applications such as car windscreen modeling, deformation of plates, etc. To counter the highly ill-posed nature of the considered inverse problem, a regularization must be performed. The main contribution of this work is to show that the equation error approach permits the use of \(H^1\) regularization whereas other optimization-based formulations commonly use \(H_2\) regularization. We give the existence and convergence results for the equation error formulation. An illustrative numerical example is given to show the feasibility of the approach.

Dedicated to Prof. Alemdar Hasanoglu (Hasanov) on his 60th birthday

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Acknowledgments

The work of A.A. Khan is supported by a grant from the Simons Foundation (#210443 to Akhtar Khan). The work of B. Jadamba is supported by RITs COS Faculty Development Grant (FEAD) for 2014.

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Authors and Affiliations

  1. Center for Applied and Computational Mathematics, School of Mathematical Sciences, Rochester Institute of Technology, 85 Lomb Memorial Drive, Rochester, NY, 14623, USA

    P. Caya, B. Jadamba & A. A. Khan

  2. Department of Mathematics and Computer Science, University of Catania, 95125, Catania, Italy

    F. Raciti

  3. Institute of Mathematics, Martin-Luther-University Halle-Wittenberg, Halle (Saale), Germany

    B. Winkler

Authors
  1. P. Caya
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  2. B. Jadamba
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  3. A. A. Khan
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  4. F. Raciti
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  5. B. Winkler
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Corresponding author

Correspondence to A. A. Khan .

Editor information

Editors and Affiliations

  1. VSB - Technical University of Ostrava, Ostrava, Czech Republic

    Tomáš Kozubek

  2. Institute of Geonics of the CAS, Ostrava, Czech Republic

    Radim Blaheta

  3. Institute of Mathematics of the CAS, Prague, Czech Republic

    Jakub Šístek

  4. Institute of Computer Science of the CAS, Prague, Czech Republic

    Miroslav Rozložník

  5. VSB - Technical University of Ostrava, Ostrava, Czech Republic

    Martin Čermák

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Caya, P., Jadamba, B., Khan, A.A., Raciti, F., Winkler, B. (2016). An Equation Error Approach for the Identification of Elastic Parameters in Beams and Plates with \(H_1\) Regularization. In: Kozubek, T., Blaheta, R., Šístek, J., Rozložník, M., Čermák, M. (eds) High Performance Computing in Science and Engineering. HPCSE 2015. Lecture Notes in Computer Science(), vol 9611. Springer, Cham. https://doi.org/10.1007/978-3-319-40361-8_4

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  • DOI: https://doi.org/10.1007/978-3-319-40361-8_4

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-40360-1

  • Online ISBN: 978-3-319-40361-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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