Layer based solutions for constrained space-time meshing

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 underlying space-time mesh has to satisfy a special constraint. The cone constraint requires that the mesh faces cannot be steeper than a specified slope α with respect to the space domain. This paper presents two solutions to this constrained space-time meshing problem for 2D×TIME domains, one using simplicial and the other using hexahedral elements. Both methods construct the mesh one layer at a time creating elements with the same height.