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Computational Aspects of Solving Inverse Problems for Elliptic PDEs on Perforated Domains Using the Collage Method

In: Mathematical and Computational Approaches in Advancing Modern Science and Engineering

Author

Listed:
  • H. Kunze

    (University of Guelph, Department of Mathematics and Statistics)

  • D. La Torre

    (University of Milan, Department of Economics, Management, and Quantitative Methods
    Khalifa University, Department of Applied Mathematics and Sciences)

Abstract

The treatment of an inverse problem on a perforated domain is complicated heavily by the presence of the perforations or holes. We present several theoretical results that provide relationships between the problem on the perforated domain and the same problem on the corresponding unperforated/solid domain. The results establish that we can approximate the solution of the inverse problem on the perforated domain by instead solving the inverse problem on the associated solid domain. Examples are provided.

Suggested Citation

  • H. Kunze & D. La Torre, 2016. "Computational Aspects of Solving Inverse Problems for Elliptic PDEs on Perforated Domains Using the Collage Method," Springer Books, in: Jacques Bélair & Ian A. Frigaard & Herb Kunze & Roman Makarov & Roderick Melnik & Raymond J. Spiteri (ed.), Mathematical and Computational Approaches in Advancing Modern Science and Engineering, pages 113-120, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-30379-6_11
    DOI: 10.1007/978-3-319-30379-6_11
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