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arXiv · 1305.1106

Discretized Tikhonov regularization for Robin boundaries localization

Hui Cao·Sergei V. Pereverzev·Eva Sincich
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Abstract

We deal with a boundary detection problem arising in nondestructive testing of materials. The problem consists in recovering an unknown portion of the boundary, where a Robin condition is satisfied, with the use of a Cauchy data pair collected on the accessible part of the boundary. We combine a linearization argument with a Tikhonov regularization approach for the local reconstruction of the unknown defect. Moreover, we discuss the regularization parameter choice by means of the so called balancing principle and we present some numerical tests that show the efficiency of our method.

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Hui Cao, Sergei V. Pereverzev, Eva Sincich. 2013-05-06. Discretized Tikhonov regularization for Robin boundaries localization. https://arxiv.org/abs/1305.1106

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