Layer based solutions for constrained space-time

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

Applied Numerical Mathematics, Volume 46, Issues 3-4, September 2003, Pages 425-443
Special issue from 16th IMACS World Congress on Scientific Computation,Applied Mathematics and Simulation, Lausanne, Switzerland August 21-25, 2000

Abstract:

Space-time discontinuous Galerkin (DG) methods provide a solution for elastodynamic analysis, a problem that serves as a model for DG approximation of second-order hyperbolic problems. To enable a direct element-by-element solution using this technique. the space-time mesh has to satisfy a special constraint. The {\em cone constraint} requires that the mesh faces can not be steeper than a specified angle $\alpha$ with respect to the 2D space. This paper presents two solutions to this constrained space-time meshing problem one using simplicial the other using hexahedral elements. Both methods construct the mesh one layer at a time creating elements with the same height.