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International Conference on Computational Science

ICCS 2021: Computational Science – ICCS 2021 pp 465–479Cite as

Comprehensive Regularization of PIES for Problems Modeled by 2D Laplace’s Equation

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12742))

Abstract

The paper proposes the concept of eliminating the explicit computation of singular integrals appearing in the parametric integral equation system (PIES) used to simulate the steady-state temperature field distribution. These singularities can be eliminated by regularizing the PIES formula with the auxiliary regularization function. Contrary to existing regularization methods that only eliminate strong singularities, the proposed approach is definitely more comprehensive due to the fact that it eliminates all strong and weak singularities. As a result, all singularities associated with PIES's integral functions can be removed. A practical aspect of the proposed regularization is the fact that all integrals appearing in the resulting formula can be evaluated numerically with a standard Gauss-Legendre quadrature rule. Simulation results indicate the high accuracy of the proposed algorithm.

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Authors and Affiliations

  1. Institute of Computer Science, University of Bialystok, Konstantego Ciołkowskiego 1M, 15-245, Białystok, Poland

    Krzysztof Szerszeń, Eugeniusz Zieniuk, Agnieszka Bołtuć & Andrzej Kużelewski

Authors
  1. Krzysztof Szerszeń
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  2. Eugeniusz Zieniuk
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  3. Agnieszka Bołtuć
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  4. Andrzej Kużelewski
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Correspondence to Krzysztof Szerszeń .

Editor information

Editors and Affiliations

  1. AGH University of Science and Technology, Krakow, Poland

    Maciej Paszynski

  2. Ludwig-Maximilians-Universität München, Munich, Germany

    Dieter Kranzlmüller

  3. University of Amsterdam, Amsterdam, The Netherlands

    Valeria V. Krzhizhanovskaya

  4. University of Tennessee at Knoxville, Knoxville, TN, USA

    Jack J. Dongarra

  5. University of Amsterdam, Amsterdam, The Netherlands

    Peter M. A. Sloot

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Szerszeń, K., Zieniuk, E., Bołtuć, A., Kużelewski, A. (2021). Comprehensive Regularization of PIES for Problems Modeled by 2D Laplace’s Equation. In: Paszynski, M., Kranzlmüller, D., Krzhizhanovskaya, V.V., Dongarra, J.J., Sloot, P.M.A. (eds) Computational Science – ICCS 2021. ICCS 2021. Lecture Notes in Computer Science(), vol 12742. Springer, Cham. https://doi.org/10.1007/978-3-030-77961-0_38

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  • DOI: https://doi.org/10.1007/978-3-030-77961-0_38

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-77960-3

  • Online ISBN: 978-3-030-77961-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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