ETNA - Electronic Transactions on Numerical Analysis
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Verlag der Österreichischen Akademie der Wissenschaften Austrian Academy of Sciences Press
A-1011 Wien, Dr. Ignaz Seipel-Platz 2
Tel. +43-1-515 81/DW 3420, Fax +43-1-515 81/DW 3400 https://verlag.oeaw.ac.at, e-mail: verlag@oeaw.ac.at |
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DATUM, UNTERSCHRIFT / DATE, SIGNATURE
BANK AUSTRIA CREDITANSTALT, WIEN (IBAN AT04 1100 0006 2280 0100, BIC BKAUATWW), DEUTSCHE BANK MÜNCHEN (IBAN DE16 7007 0024 0238 8270 00, BIC DEUTDEDBMUC)
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ETNA - Electronic Transactions on Numerical Analysis ISBN 978-3-7001-8258-0 Online Edition Research Article
Patricia Díaz de Alba,
Federica Pes
S. 105 - 120 doi:10.1553/etna_vol61s105 Verlag der Österreichischen Akademie der Wissenschaften doi:10.1553/etna_vol61s105
Abstract: In this paper we introduce a two-dimensional first-kind integral model to describe the interaction between the soil and an electromagnetic device. This model is used to reconstruct the electrical conductivity of the soil from electromagnetic data. The definition of the two-dimensional model is derived, and a numerical study of the forward model based on Gauss–Legendre quadrature formulae is presented. To solve the inverse problem, a linear system obtained from the discretization of the integral equation in the model is considered. The main difficulty is the severe ill-conditioning of the system, so the Tikhonov regularization method is applied and different regularization matrices and choice-rules for the regularization parameter are proposed. Several numerical tests show the effectiveness of the proposed approach. Keywords: first-kind integral equations, Gauss–Legendre quadrature, Tikhonov regularization, electromagnetic data Published Online: 2024/09/18 08:45:45 Document Date: 2024/09/18 Object Identifier: 0xc1aa5572 0x003f5f86 Rights: . Electronic Transactions on Numerical Analysis (ETNA) is an electronic journal for the publication of significant new developments in numerical analysis and scientific computing. Papers of the highest quality that deal with the analysis of algorithms for the solution of continuous models and numerical linear algebra are appropriate for ETNA, as are papers of similar quality that discuss implementation and performance of such algorithms. New algorithms for current or new computer architectures are appropriate provided that they are numerically sound. However, the focus of the publication should be on the algorithm rather than on the architecture. The journal is published by the Kent State University Library in conjunction with the Institute of Computational Mathematics at Kent State University, and in cooperation with the Johann Radon Institute for Computational and Applied Mathematics of the Austrian Academy of Sciences (RICAM). Reviews of all ETNA papers appear in Mathematical Reviews and Zentralblatt für Mathematik. Reference information for ETNA papers also appears in the expanded Science Citation Index. ETNA is registered with the Library of Congress and has ISSN 1068-9613. …
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Verlag der Österreichischen Akademie der Wissenschaften Austrian Academy of Sciences Press
A-1011 Wien, Dr. Ignaz Seipel-Platz 2
Tel. +43-1-515 81/DW 3420, Fax +43-1-515 81/DW 3400 https://verlag.oeaw.ac.at, e-mail: verlag@oeaw.ac.at |