Numerical identification of a sparse Robin coefficient
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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.
KeywordsInverse Robin problem Sparsity regularization Iteratively reweighted least squares method Semismooth Newton method
Mathematics Subject Classification (2010)65N21 49M15
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