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Discretized Tikhonov regularization for Robin boundaries localization

Authors
Journal
Applied Mathematics and Computation
0096-3003
Publisher
Elsevier
Publication Date
Identifiers
DOI: 10.1016/j.amc.2013.10.036
Keywords
  • Tikhonov Regularization
  • Robin Boundary Condition
  • Free Boundary Problem
  • Balancing Principle
  • Local Identification

Abstract

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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