An iterative method based on boundary integrals for elliptic Cauchy problems in semi-infinite domains

R. Chapko, B.T. Johansson

    Research output: Contribution to journalArticlepeer-review

    Abstract

    In this study, we investigate the problem of reconstruction of a stationary temperature field from given temperature and heat flux on a part of the boundary of a semi-infinite region containing an inclusion. This situation can be modelled as a Cauchy problem for the Laplace operator and it is an ill-posed problem in the sense of Hadamard. We propose and investigate a Landweber-Fridman type iterative method, which preserve the (stationary) heat operator, for the stable reconstruction of the temperature field on the boundary of the inclusion. In each iteration step, mixed boundary value problems for the Laplace operator are solved in the semi-infinite region. Well-posedness of these problems is investigated and convergence of the procedures is discussed. For the numerical implementation of these mixed problems an efficient boundary integral method is proposed which is based on the indirect variant of the boundary integral approach. Using this approach the mixed problems are reduced to integral equations over the (bounded) boundary of the inclusion. Numerical examples are included showing that stable and accurate reconstructions of the temperature field on the boundary of the inclusion can be obtained also in the case of noisy data. These results are compared with those obtained with the alternating iterative method.
    Original languageEnglish
    Pages (from-to)1-12
    Number of pages12
    JournalElectronic Journal of Boundary Elements
    Volume7
    Issue number1
    Publication statusPublished - 2009

    Bibliographical note

    Electronic Journal of Boundary Elements by http://ejbe.libraries.rutgers.edu is licensed under a Creative Commons Attribution-Noncommercial 3.0 United States License.

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