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

Alper Üngör, Alla Sheffer

Proc. of the 9th International Meshing Roundtable, New Orleans, LO, October 2000.

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 face 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 $n$D$\times$TIME domain ($n$ is a natural number). The $k$ in the algorithm is based on a node degree in a $n$-dimensional space domain mesh.