Advertisement

Graph Transformations for Modeling Parallel hp-Adaptive Finite Element Method

  • Maciej Paszyński
  • Anna Paszyńska
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4967)

Abstract

The paper presents composition graph (CP-graph) grammar, which consists of a set of CP-graph transformations, suitable for modeling all aspects of parallel hp adaptive Finite Element Method (FEM) computations. The parallel hp adaptive FEM allows to utilize distributed computational meshes, with finite elements of various size (thus h stands for element diameter) and polynomial orders of approximation varying locally, on finite elements edges and interiors (thus p stands for polynomial order of approximation). The computational mesh is represented by attributed CP-graph. The proposed graph transformations model the initial mesh generation, procedure of h refinement (breaking selected finite elements into son elements), and p refinement (adjusting polynomial orders of approximation on selected element edges and interiors), as well as partitioning of computational mesh into sub-domains and enforcement of mesh regularity rules over the distributed data structure.

Keywords

Parallel computations Finite Element Method hp adaptivity CP-graph grammar graph transformations 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Grabska, E.: Theoretical Concepts of Graphical Modeling. Part One: Realization of CP-Graphs. Machine Graphics and Vision 2(1), 3–38 (1993)Google Scholar
  2. 2.
    Grabska, E.: Theoretical Concepts of Graphical Modeling. Part Two: CP-Graph Grammars and Languages. Machine Graphics and Vision 2(2), 149–178 (1993)Google Scholar
  3. 3.
    Grabska, E., Hliniak, G.: Structural Aspects of CP-Graph Languages. Schedae Informaticae 5, 81–100 (1993)Google Scholar
  4. 4.
    Demkowicz, L.: Computing with hp-Adaptive Finite Elements, vol. I. Chapman & Hall/Crc Applied Mathematics & Nonlinear Science (2006)Google Scholar
  5. 5.
    Demkowicz, L., Kurtz, J., Pardo, D., Paszynski, M., Rachowicz, W., Zdunek, A.: Computing with hp-Adaptive Finite Elements, vol. II. Chapman & Hall/Crc Applied Mathematics & Nonlinear Science (in press, 2007)Google Scholar
  6. 6.
    Paszyński, M., Kurtz, J., Demkowicz, L.: Parallel Fully Automatic hp-Adaptive 2D Finite Element Package. Computer Methods in Applied Mechanics and Engineering 195(7-8,25), 711–741 (2006)CrossRefMathSciNetGoogle Scholar
  7. 7.
    Paszyński, M., Demkowicz, L.: Parallel Fully Automatic hp-Adaptive 3D Finite Element Package. Engineering with Computers 22(3-4), 255–276 (2006)CrossRefGoogle Scholar
  8. 8.
    Paszyński, Agent based hierarchical parallelization of complex algorithms on the example of hp adaptive Finite Element Method. LNCS (in press, 2007)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Maciej Paszyński
    • 1
  • Anna Paszyńska
    • 2
  1. 1.Department of Computer ScienceAGH University of Science and TechnologyCracowPoland
  2. 2.International School of Business and TechnologyBielsko-BialaPoland

Personalised recommendations