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A Comparison of Accuracy and Efficiency of Parallel Solvers for Fractional Power Diffusion Problems

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Parallel Processing and Applied Mathematics (PPAM 2017)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10777))

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Abstract

In this paper, we construct and investigate parallel solvers for three dimensional problems described by fractional powers of elliptic operators. The main aim is to make a scalability analysis of parallel versions of several state of the art solvers. The originality of this work is that we also consider the accuracy of the selected numerical algorithms. For comparison of accuracy, we use solutions obtained solving the test problem by the Fourier algorithm. Such analysis enables to compare the efficiency of the proposed parallel algorithms depending on the required accuracy of solution and on a number of processes used in computations.

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Acknowledgment

The work of authors was supported by EU under the COST programme Action IC1305, “Network for Sustainable Ultrascale Computing (NESUS)”. The third author has been partially supported by the Bulgarian National Science Fund under Grant BNSF-DN12/1.

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Authors and Affiliations

  1. Vilnius Gediminas Technical University, Saulėtekis avenue 11, LT10223, Vilnius, Lithuania

    Raimondas Čiegis, Vadimas Starikovičius & Rima Kriauzienė

  2. Institute of Information and Communication Technologies, Bulgarian Academy of Sciences, Acad. G. Bonchev street, bl. 25A, 1113, Sofia, Bulgaria

    Svetozar Margenov

  3. Vilnius University Institute of Mathematics and Informatics, Akademijos street 4, 08663, Vilnius, Lithuania

    Rima Kriauzienė

Authors
  1. Raimondas Čiegis
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  2. Vadimas Starikovičius
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  3. Svetozar Margenov
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  4. Rima Kriauzienė
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Corresponding author

Correspondence to Raimondas Čiegis .

Editor information

Editors and Affiliations

  1. Czestochowa University of Technology, Czestochowa, Poland

    Roman Wyrzykowski

  2. University of Tennessee, Knoxville, Tennessee, USA

    Jack Dongarra

  3. University of Southern California, Marina Del Rey, California, USA

    Ewa Deelman

  4. Czestochowa University of Technology, Czestochowa, Poland

    Konrad Karczewski

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Čiegis, R., Starikovičius, V., Margenov, S., Kriauzienė, R. (2018). A Comparison of Accuracy and Efficiency of Parallel Solvers for Fractional Power Diffusion Problems. In: Wyrzykowski, R., Dongarra, J., Deelman, E., Karczewski, K. (eds) Parallel Processing and Applied Mathematics. PPAM 2017. Lecture Notes in Computer Science(), vol 10777. Springer, Cham. https://doi.org/10.1007/978-3-319-78024-5_8

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  • DOI: https://doi.org/10.1007/978-3-319-78024-5_8

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-78023-8

  • Online ISBN: 978-3-319-78024-5

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