@article{c304b7f73b854f629f1a89d3dd58f902,
title = "Semi-analytical solutions for the problem of the electric potential set in a borehole with a highly conductive casing",
abstract = "Highly conductive thin casings pose a great challenge in the numerical simulation of well-logging instruments. Witty asymptotic models may replace the presence of casings by impedance transmission conditions in those numerical simulations. The accuracy of such numerical schemes can be tested against benchmark solutions computed semi-analytically in simple geometrical configurations. This paper provides a general approach to construct those benchmark solutions for three different models: one reference model that indeed considers the presence of the casing; one asymptotic model that avoids computations in the casing domain; and one asymptotic model that reduces the presence of the casing to an interface. Our technique uses a Fourier representation of the solutions, where special care has been taken in the analytical integration of singularities to avoid numerical instabilities.",
keywords = "Asymptotic models, Boreholes with casing, Electric potential, Semi-analytical solutions",
author = "Aralar Erdozain and Ignacio Muga and Victor P{\'e}ron and Gabriel Pinochet",
note = "Funding Information: This project has received funding from the European Union{\textquoteright}s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No 777778 (MATHROCKS). G. Pinochet has received funding from the National Agency for Research and Development (ANID), Scholarship Program, Beca de Mag{\'i}ster Nacional 2021 - 22210496. A. Erdozain, V. P{\'e}ron and I. Muga also have received funding from the European Union{\textquoteright}s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No 644602 (GEAGAM). I. Muga acknowledges support from the project DI INVESTIGACI{\'O}N INNOVADORA INTERDISCIPLINARIA PUCV 2021 N039.409/2021. Nanoi{\'o}nica: Un enfoque interdisciplinario. Publisher Copyright: {\textcopyright} 2022, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.",
year = "2022",
month = dec,
doi = "10.1007/s13137-022-00197-3",
language = "English",
volume = "13",
journal = "GEM - International Journal on Geomathematics",
issn = "1869-2672",
number = "1",
}