SCAIM Seminar: Efficient High-Order Hybrid Elements for the Wave Equations

Gauss-Lobatto spectral elements, based on hexahedral meshes, provide a very efficient way to solve transient wave equations in terms of storage and of computational time. Unfortunately, it is very difficult and almost impossible in some cases to produce pure hexahedral meshes for complex geometries. Until now, we have remedied this shortcoming by using tetrahedral meshes in which tetrahedral were split into four hexahedra, but this technique provides very distorted meshes which imply tu use about three times more unknown than pure hexahedral meshes to get the same accuracy. For this reason, we developed a strategy of solvers based on hybrid meshes containing mainly hexahedra and some tetrahedral, pyramids and wedges. First results show a dramatical gain in performance versus split tetrahedra.