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Graph Grammar Based Petri Nets Model of Concurrency for Self-adaptive hp-Finite Element Method with Rectangular Elements

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Parallel Processing and Applied Mathematics (PPAM 2009)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6067))

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Abstract

The paper presents the Petri nets model describing the process of rectangular finite element mesh generation and h adaptation. This is the first step towards the formal analysis of all the parts of the existing graph grammar based parallel adaptive hp-Finite Element Method algorithms expressed by graph grammar productions. The mesh transformations are expressed as composite programmable graph grammar productions. The transitions on Petri nets correspond to the execution of graph grammar productions. The graph grammar based algorithms modeled as a Petri net can be analyzed for deadlocks, starvation or infinite execution. The parallel adaptive algorithms have many applications in the area of numerical simulations of different engineering problems, including material science, heat transfer, wave propagation and other.

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Author information

Authors and Affiliations

  1. Department of Computer Science, AGH University of Science and Technology, Al. Mickiewicza 30, 30-059, Cracow, Poland

    Arkadiusz Szymczak & Maciej Paszyński

Authors
  1. Arkadiusz Szymczak
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  2. Maciej Paszyński
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Editor information

Editors and Affiliations

  1. Institute of Computational and Information Sciences, Czestochowa University of Technology,  

    Roman Wyrzykowski

  2. Department of Electrical Engineering and Computer Science, University of Tennessee, TN 37996-3450, Knoxville, USA

    Jack Dongarra

  3. Institute of Computer and Information Science, Czestochowa University of Technology, Dabrowskiego 73, PL-42-200, Czestochowa, Poland

    Konrad Karczewski

  4. Department of Informatics and Mathematical Modeling, Technical University of Denmark, Richard Petersens Plads, Building 321, 2800, Kongens Lyngby, Denmark

    Jerzy Wasniewski

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Szymczak, A., Paszyński, M. (2010). Graph Grammar Based Petri Nets Model of Concurrency for Self-adaptive hp-Finite Element Method with Rectangular Elements. In: Wyrzykowski, R., Dongarra, J., Karczewski, K., Wasniewski, J. (eds) Parallel Processing and Applied Mathematics. PPAM 2009. Lecture Notes in Computer Science, vol 6067. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14390-8_11

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  • DOI: https://doi.org/10.1007/978-3-642-14390-8_11

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-14389-2

  • Online ISBN: 978-3-642-14390-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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