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Advances in Computational Mathematics

, Volume 41, Issue 1, pp 131–148 | Cite as

Numerical identification of a sparse Robin coefficient

  • Zhiyuan Sun
  • Yuling Jiao
  • Bangti Jin
  • Xiliang LuEmail author
Article

Abstract

We investigate an inverse problem of identifying a Robin coefficient with a sparse structure in the Laplace equation from noisy boundary measurements. The sparse structure of the Robin coefficient γ is understood as a small perturbation of a reference profile γ 0 in the sense that their difference γγ 0 has a small support. This problem is formulated as an optimal control problem with an L 1-regularization term. An iteratively reweighted least-squares algorithm with an inner semismooth Newton iteration is employed to solve the resulting optimization problem, and the convergence of the iteratively weighted least-squares algorithm is established. Numerical results for two-dimensional problems are presented to illustrate the efficiency of the proposed method.

Keywords

Inverse Robin problem Sparsity regularization Iteratively reweighted least squares method Semismooth Newton method 

Mathematics Subject Classification (2010)

65N21 49M15 

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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • Zhiyuan Sun
    • 1
  • Yuling Jiao
    • 1
  • Bangti Jin
    • 2
  • Xiliang Lu
    • 1
    Email author
  1. 1.School of Mathematics and StatisticsWuhan UniversityWuhanPeople’s Republic of China
  2. 2.Department of MathematicsUniversity of California, RiversideRiversideUSA

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