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Fast Algorithm for the Fourth-Order Elliptic Problem Based on Orthogonal Matrix Decomposition

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Parallel Processing and Applied Mathematics (PPAM 2015)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9573))

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Abstract

A fast algorithm for solving the first biharmonic boundary problem on a rectangular domain is presented. It is based on splitting the fourth-order problem into a coupled system of two-order problems, whose finite-difference approximations are solved iteratively with linear algebra routines. There, a crucial role plays the orthogonal eigenvalue decomposition of the iteration matrix, which leads to a reduction of the operational count for one iteration to the asymptotically optimal value. This approach is extensively tested from the point of view of the total computational time, number of iterations and the solution error. It is shown, that these values cope with the theoretical assumptions and scale convincingly up to a problem with 100 million grid points.

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References

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Acknowledgments

The second author was supported by the VEGA grant no. 2/0026/14.

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Authors and Affiliations

  1. Fachbereich Mathematik, Paris-Lodron-Universität Salzburg, Salzburg, Austria

    Paolo Di Stolfo

  2. Fachbereich Computerwissenschaften, Paris-Lodron-Universität Salzburg, Salzburg, Austria

    Marian Vajteršic

  3. Institute of Mathematics, Slovak Academy of Sciences, Bratislava, Slovakia

    Marian Vajteršic

Authors
  1. Paolo Di Stolfo
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  2. Marian Vajteršic
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Corresponding author

Correspondence to Paolo Di Stolfo .

Editor information

Editors and Affiliations

  1. Czestochowa University of Technolog, Czestochowa, Poland

    Roman Wyrzykowski

  2. Department of Computer Science, University of Southern California, Marina Del Rey, California, USA

    Ewa Deelman

  3. Electrical Engineering & Comput. Science, University of Tennessee, Knoxville, Tennessee, USA

    Jack Dongarra

  4. Czestochowa University of Technology, Institute of Computer & Information Sci., Czestochowa, Poland

    Konrad Karczewski

  5. Department of Computer Science, AGH University of Science and Technology, Krakow, Poland

    Jacek Kitowski

  6. Systèmes d’informations, Big Data et Rec, AGH University of Science and Technology, Krakow, Poland

    Kazimierz Wiatr

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Di Stolfo, P., Vajteršic, M. (2016). Fast Algorithm for the Fourth-Order Elliptic Problem Based on Orthogonal Matrix Decomposition. In: Wyrzykowski, R., Deelman, E., Dongarra, J., Karczewski, K., Kitowski, J., Wiatr, K. (eds) Parallel Processing and Applied Mathematics. PPAM 2015. Lecture Notes in Computer Science(), vol 9573. Springer, Cham. https://doi.org/10.1007/978-3-319-32149-3_54

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  • DOI: https://doi.org/10.1007/978-3-319-32149-3_54

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-32148-6

  • Online ISBN: 978-3-319-32149-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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