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Building spacetime meshes over arbitrary spatial domains

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Abstract

We present an algorithm to construct meshes suitable for spacetime discontinuous Galerkin finite-element methods. Our method generalizes and improves the ‘Tent Pitcher’ algorithm of Üngör and Sheffer. Given an arbitrary simplicially meshed domain X of any dimension and a time interval [0, T], our algorithm builds a simplicial mesh of the spacetime domain X × [0, T], in constant time per element. Our algorithm avoids the limitations of previous methods by carefully adapting the durations of spacetime elements to the local quality and feature size of the underlying space mesh.

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Acknowledgements

The authors thank David Bunde, Michael Garland, Shripad Thite, and especially Bob Haber for several helpful comments and discussions. We also thank Shripad Thite for correcting a bug in our proof of Lemma 1. Jeff Erickson supported in part by a Sloan Fellowship and NSF CAREER award CCR-0093348. Damrong Gouy supported in part by DOE grant LLNL B341494. John M Sullivan supported in part by NSF grant DMS-00-71520. Alper Üngör This research was performed while this author was a student at the University of Illinois, with the additional support of a UIUC Computational Science and Engineering Fellowship.

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Authors and Affiliations

  1. Department of Computer Science, University of Illinois at Urbana-Champaign, Urbana-Champaign, IL, USA

    Jeff Erickson

  2. Center for Simulation of Advanced Rockets, Computational Science and Engineering Program, University of Illinois at Urbana-Champaign, Urbana-Champaign, IL, USA

    Damrong Guoy

  3. Department of Mathematics, University of Illinois at Urbana-Champaign, Urbana-Champaign, IL, USA

    John M. Sullivan

  4. Center for Geometric and Biological Computing, Department of Computer Science, Duke University, Durham, NC, USA

    Alper Üngör

Authors
  1. Jeff Erickson
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  2. Damrong Guoy
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  3. John M. Sullivan
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  4. Alper Üngör
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Corresponding author

Correspondence to Jeff Erickson.

Additional information

This work was supported in part by The Center for Process Simulation and Design at the University of Illinois, Urbana-Champaign, under NSF ITR grant DMR-0121695. A preliminary version of this paper was presented at the 11th International Meshing Roundtable [9].

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Erickson, J., Guoy, D., Sullivan, J.M. et al. Building spacetime meshes over arbitrary spatial domains. Engineering with Computers 20, 342–353 (2005). https://doi.org/10.1007/s00366-005-0303-0

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