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Numerical identification of a sparse Robin coefficient

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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 γ−γ 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.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Wuhan University, Wuhan, People’s Republic of China

    Zhiyuan Sun, Yuling Jiao & Xiliang Lu

  2. Department of Mathematics, University of California, Riverside, 900 University Ave., Riverside, CA, 92521, USA

    Bangti Jin

Authors
  1. Zhiyuan Sun
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  2. Yuling Jiao
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  3. Bangti Jin
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  4. Xiliang Lu
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Corresponding author

Correspondence to Xiliang Lu.

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Communicated by: Y. Xu

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Sun, Z., Jiao, Y., Jin, B. et al. Numerical identification of a sparse Robin coefficient. Adv Comput Math 41, 131–148 (2015). https://doi.org/10.1007/s10444-014-9352-5

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  • DOI: https://doi.org/10.1007/s10444-014-9352-5

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