Building spacetime meshes over arbitrary spatial domains

  • Authors:

  • Jeff Erickson;Damrong Guoy;M. Sullivan;Alper Üngör

  • Affiliations:

  • Department of Computer Science, University of Illinois at Urbana-Champaign, Urbana-Champaign, IL, USA;Center for Simulation of Advanced Rockets, Computational Science and Engineering Program, University of Illinois at Urbana-Champaign, Urbana-Champaign, IL, USA;Department of Mathematics, University of Illinois at Urbana-Champaign, Urbana-Champaign, IL, USA;Center for Geometric and Biological Computing, Department of Computer Science, Duke University, Durham, NC, USA

  • Venue:
  • Engineering with Computers
  • Year:
  • 2005

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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.