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Automatic Algorithms for the Construction of Element Partition Trees for Isogeometric Finite Element Method

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Man-Machine Interactions 5 (ICMMI 2017)

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 659))

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Abstract

The IGA-FEM is a modern method for simulation of different engineering and biomedical problems by using B-spline basis functions. To allow for real time interaction between human and computer while performing numerical simulations, there is a need for extremely fast solvers solving systems of linear equations generated while performing simulations. In this paper, an algorithm for construction of the ordering that controls the execution of the multi-frontal direct solver algorithm is presented. The ordering prescribes the permutation of the computational matrix in order to minimize the computational cost of the direct solver. We show that execution of our algorithm generating the recursive partitions of the h-adaptive grids with B-spline basis functions allows reducing the computational cost of the IGA-FEM simulations.

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Author information

Authors and Affiliations

  1. Department of Computer Science, AGH University of Science and Technology, Kraków, Poland

    Bartosz Janota

  2. The Faculty of Physics, Astronomy and Applied Computer Science, Jagiellonian University, Kraków, Poland

    Anna Paszyńska

Authors
  1. Bartosz Janota
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  2. Anna Paszyńska
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Corresponding author

Correspondence to Anna Paszyńska .

Editor information

Editors and Affiliations

  1. Institute of Informatics, Silesian University of Technology, Gliwice, Poland

    Aleksandra Gruca

  2. Institute of Informatics, Silesian University of Technology, Gliwice, Poland

    Tadeusz Czachórski

  3. Institute of Informatics, Silesian University of Technology, Gliwice, Poland

    Katarzyna Harezlak

  4. Institute of Informatics, Silesian University of Technology, Gliwice, Poland

    Stanisław Kozielski

  5. Institute of Informatics, Silesian University of Technology, Gliwice, Poland

    Agnieszka Piotrowska

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Janota, B., Paszyńska, A. (2018). Automatic Algorithms for the Construction of Element Partition Trees for Isogeometric Finite Element Method. In: Gruca, A., Czachórski, T., Harezlak, K., Kozielski, S., Piotrowska, A. (eds) Man-Machine Interactions 5. ICMMI 2017. Advances in Intelligent Systems and Computing, vol 659. Springer, Cham. https://doi.org/10.1007/978-3-319-67792-7_28

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  • DOI: https://doi.org/10.1007/978-3-319-67792-7_28

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-67791-0

  • Online ISBN: 978-3-319-67792-7

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