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Solving Uncertainly Defined Curvilinear Potential 2D BVPs by the IFPIES

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Computational Science – ICCS 2023 (ICCS 2023)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14074))

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Abstract

The paper presents the interval fast parametric integral equations system (IFPIES) applied to model and solve uncertainly defined curvilinear potential 2D boundary value problems with complex shapes. Contrary to previous research, the IFPIES is used to model the uncertainty of both boundary shape and boundary conditions. The IFPIES uses interval numbers and directed interval arithmetic with some modifications previously developed by the authors. Curvilinear segments in the form of Bézier curves of the third degree are used to model the boundary shape. However, the curves also required some modifications connected with applied directed interval arithmetic. It should be noted that simultaneous modelling of boundary shape and boundary conditions allows for a comprehensive approach to considered problems. The reliability and efficiency of the IFPIES solutions are verified on 2D complex potential problems with curvilinear domains. The solutions were compared with the interval solutions obtained by the interval PIES. All performed tests indicated the high efficiency of the IFPIES method.

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Authors and Affiliations

  1. Institute of Computer Science, University of Bialystok, Ciolkowskiego 1M, 15-245, Bialystok, Poland

    Andrzej Kużelewski, Eugeniusz Zieniuk & Marta Czupryna

Authors
  1. Andrzej Kużelewski
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  2. Eugeniusz Zieniuk
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  3. Marta Czupryna
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Corresponding author

Correspondence to Andrzej Kużelewski .

Editor information

Editors and Affiliations

  1. Czech Technical University in Prague, Prague, Czech Republic

    Jiří Mikyška

  2. University of Amsterdam, Amsterdam, The Netherlands

    Clélia de Mulatier

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

    Maciej Paszynski

  4. University of Amsterdam, Amsterdam, The Netherlands

    Valeria V. Krzhizhanovskaya

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

    Jack J. Dongarra

  6. University of Amsterdam, Amsterdam, The Netherlands

    Peter M.A. Sloot

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Kużelewski, A., Zieniuk, E., Czupryna, M. (2023). Solving Uncertainly Defined Curvilinear Potential 2D BVPs by the IFPIES. In: Mikyška, J., de Mulatier, C., Paszynski, M., Krzhizhanovskaya, V.V., Dongarra, J.J., Sloot, P.M. (eds) Computational Science – ICCS 2023. ICCS 2023. Lecture Notes in Computer Science, vol 14074. Springer, Cham. https://doi.org/10.1007/978-3-031-36021-3_12

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  • DOI: https://doi.org/10.1007/978-3-031-36021-3_12

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-36020-6

  • Online ISBN: 978-3-031-36021-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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