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Numerical solution of a heat diffusion problem by boundary element methods using the Laplace transform

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Abstract

This paper is concerned with a heat diffusion problem in a half-space which is motivated by the detection of material defects using thermal measurements. This problem is solved by inverting the Laplace transform with respect to time on a contour in the complex plane using an exponentially convergent quadrature rule. This leads to a finite number of time-independent problems, which can be solved in parallel using boundary integral equation methods. We provide a full numerical analysis of this scheme on compact time intervals. Our results are formulated in a way that they can easily be used for other diffusion problems in exterior or interior domains.

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Authors and Affiliations

  1. Institut für Numerische und Angewandte Mathematik, Universität Göttingen, Lotzestrasse 16-18, 37083, Göttingen, Germany

    Thorsten Hohage

  2. Deparmento di Matemática Aplicada, C.P.S., Universidad de Zaragoza, 50018, Zaragoza, Spain

    Francisco–Javier Sayas

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  1. Thorsten Hohage
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  2. Francisco–Javier Sayas
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Correspondence to Thorsten Hohage.

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Hohage, T., Sayas, F. Numerical solution of a heat diffusion problem by boundary element methods using the Laplace transform. Numer. Math. 102, 67–92 (2005). https://doi.org/10.1007/s00211-005-0645-y

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  • DOI: https://doi.org/10.1007/s00211-005-0645-y

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