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An Algorithm for Tensor Product Approximation of Three-Dimensional Material Data for Implicit Dynamics Simulations

  • Krzysztof Podsiadło
  • Marcin Łoś
  • Leszek Siwik
  • Maciej Woźniak
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10861)

Abstract

In the paper, a heuristic algorithm for tensor product approximation with B-spline basis functions of three-dimensional material data is presented. The algorithm has an application as a preconditioner for implicit dynamics simulations of a non-linear flow in heterogeneous media using alternating directions method. As the simulation use-case, a non-stationary problem of liquid fossil fuels exploration with hydraulic fracturing is considered. Presented algorithm allows to approximate the permeability coefficient function as a tensor product what in turn allows for implicit simulations of the Laplacian term in the partial differential equation. In the consequence the number of time steps of the non-stationary problem can be reduced, while the numerical accuracy is preserved.

Notes

Acknowledgments

This work was supported by National Science Centre, Poland, grant no. 2014/15/N/ST6/04662. The authors would like to acknowledge prof. Maciej Paszyński for his help in this research topic and preparation of this paper.

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Krzysztof Podsiadło
    • 1
  • Marcin Łoś
    • 1
  • Leszek Siwik
    • 1
  • Maciej Woźniak
    • 1
  1. 1.AGH University of Science and TechnologyKrakowPoland

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