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The dune-subgrid module and some applications

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Abstract

We present an extension module for the Dune system. This module, called dune-subgrid, allows to mark elements of another Dune hierarchical grid. The set of marked elements can then be accessed as a Dune grid in its own right. dune-subgrid is free software and is available for download (External Dune Modules: www.dune-project.org/downloadext.html). We describe the functionality and use of dune-subgrid, comment on its implementation, and give two example applications. First, we show how dune-subgrid can be used for micro-FE simulations of trabecular bone. Then we present an algorithm that allows to use exact residuals for the adaptive solution of the spatial problems of time-discretized evolution equations.

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References

  1. Babuška I, Chleboun J (2003) Effects of uncertainties in the domain on the solution of Dirichlet boundary value problems. Numer Math 93(4): 583–610

    Article  MATH  MathSciNet  Google Scholar 

  2. Bank RE, Smith RK (1993) A posteriori error estimates based on hierarchical bases. SIAM J Num Anal 30(4): 921–935

    Article  MATH  MathSciNet  Google Scholar 

  3. Bastian P, Birken K, Johannsen K, Lang S, Neuß N, Rentz-Reichert H, Wieners C (1997) UG: a flexible software toolbox for solving partial differential equations. Comp Vis Sci 1: 27–40

    Article  MATH  Google Scholar 

  4. Bastian P, Blatt M, Dedner A, Engwer C, Klöfkorn R, Kornhuber R, Ohlberger M, Sander O (2008) A generic interface for parallel and adaptive scientific computing. Part II: Implementation and tests in DUNE. Computing 82(2–3): 121–138

    Article  MATH  MathSciNet  Google Scholar 

  5. Bastian P, Blatt M, Dedner A, Engwer C, Klöfkorn R, Ohlberger M, Sander O (2008) A generic interface for parallel and adaptive scientific computing. Part I: Abstract framework. Computing 82(2–3): 103–119

    Article  MATH  MathSciNet  Google Scholar 

  6. Bekas C, Curioni A, Arbenz P, Flaig C, van Lenthe GH, Müller R, Wirth AJ (2008) Extreme scalability challenges in micro-finite element simulations of human bone. In: Proc international supercomputing conference ISC’08. Dresden, Germany

  7. Blatt M, Bastian P (2007) The iterative solver template library. In: Applied parallel computing. State of the art in scientific computing. Lecture Notes in Scientific Computing, vol 4699, pp 666–675. Springer, Heidelberg

  8. Bornemann F (1991) An adaptive multilevel approach for parabolic equations in two space dimensions. PhD thesis, Freie Universität Berlin

  9. Burri A, Dedner A, Klöfkorn R, Ohlberger M (2005) An efficient implementation of an adaptive and parallel grid in DUNE. In: Proc. of the 2nd Russian–German advanced research workshop on computational science and high performance computing

  10. Ciarlet PG (1988) Mathematical elasticity. North-Holland, Amsterdam

    MATH  Google Scholar 

  11. Deckelnick K, Dziuk G, Elliott CM, Heine C-J (2009, to appear) An h-narrow band finite element method for elliptic equations on implicit surfaces. IMA J Numer Anal

  12. DUNE. Distributed and Unified Numerics Environment. http://dune-project.org/

  13. DUNE-FEM. http://dune.mathematik.uni-freiburg.de/

  14. Engwer C. Private communication

  15. Engwer C, Bastian P (2008) An unfitted finite element method using discontinuous Galerkin. Int J Numer Meth Eng (Accepted)

  16. External DUNE Modules. www.dune-project.org/downloadext.html

  17. Gräser C, Kornhuber R (2009) Adaptive multigrid methods for Cahn–Hilliard equations with logarithmic potential (in preparation)

  18. Gräser C, Kornhuber R, Sack U (2009) Adaptive multigrid methods for anisotropic Allen–Cahn equations with logarithmic potential (in preparation)

  19. Kornhuber R (1997) Adaptive monotone multigrid methods for nonlinear variational problems, 1st edn. Teubner, Stuttgart

  20. Kornhuber R, Yserentant H (1994) Multilevel methods for elliptic problems on domains not resolved by the coarse grid. Contemp Math 180: 49–60

    MathSciNet  Google Scholar 

  21. Schmidt A, Siebert KG (2005) Design of adaptive finite element software: the finite element toolbox ALBERTA. Lecture notes in computational science and engineering. Springer, Heidelberg

  22. van Rietbergen B, Weinans H, Huiskes R, Odgaard A (1995) A new method to determine trabecular bone elastic properties and loading using micromechanical finite-element models. J Biomech 28: 69–81

    Article  Google Scholar 

  23. Veldhuizen T (2000) Techniques for scientific C++. Technical Report, vol 542. Indiana University Computer Science

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Authors and Affiliations

  1. Fachbereich Mathematik und Informatik, Freie Universität Berlin, Arnimallee 6, 14195, Berlin, Germany

    Carsten Gräser & Oliver Sander

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  1. Carsten Gräser
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  2. Oliver Sander
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Correspondence to Carsten Gräser.

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Communicated by W. Hackbusch.

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Gräser, C., Sander, O. The dune-subgrid module and some applications. Computing 86, 269–290 (2009). https://doi.org/10.1007/s00607-009-0067-2

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  • DOI: https://doi.org/10.1007/s00607-009-0067-2

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