Tent-Pitcher: A Meshing Algorithm for Space-Time Discontinuous Galerkin Methods

Proceedings, 9th International Meshing Roundtable, Sandia National Laboratories, pp.111-122, October 2000

MESHING
RESEARCH
CORNER

Alper Ungör
Dept of Computer Science, University of Illinois at Urbana-Champaign
Email: ungor@cs.uiuc.edu
Alla Sheffer
Computational Science and Engineering, University of Illinois at Urbana-Champaign
Email: sheffa@uiuc.edu

Abstract
Space-time discontinuous Galerkin (DG) methods provide a solution for a wide variety of numerical problems such as inviscid Berger’s equation and elastodynamic analysis. Recent research shows that in order to solve a DG system using an element-by-element procedure, the space-time mesh has to satisfy a cone constraint, i.e. that the faces of the mesh can not be steeper in the time direction than a specified angle function alpha(). Whenever there is a face that violates the cone constraint, the elements at the fare must be coupled in the solution. In this paper we consider the problem of generating a simplicial space-time mesh where the size of each group of elements that need to be coupled is bounded by a constant number k. We present an algorithm for generating such meshes which is valid for any nDxTIME domain (n is a natural number). The k in the algorithm is based on a node degree in a n-dimensional space domain mesh.

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