Generation of 2D Space-Time Meshes Obeying the Cone Constraint

Alla Sheffer, Alper Üngör, Robert Haber and Shang-Hua Teng

International Conference on Computational Engineering Science Los Angeles, CA, 20-25 August 2000

Abstract:

Space-time discontinuous Galerkin (DG) methods provide a solution for elastodynamic analysis, a problem that serves as a model for DG approximations of second-order hyperbolic problems. A direct element-by-element solution motivates the generation of three dimensional (2D$\times$time) space-time meshes that satisfy a special cone constraint, which requires that the angle between each interior mesh face and the 2D space does not exceed a specified angle $\alpha$. The cone constraint precludes the use of existing meshing techniques for generating the 3D space-time mesh, so new approaches are needed. This paper provides a new algorithm for generating hexahedral meshes that satisfy the cone constraint.