Efficient modeling of 3D geometries using octree‐meshes combined with SBFEM and transfinite elements

Abstract

Hierarchical octree‐meshes constitute an extremely efficient approach to representing complicated three‐dimensional structures. This is due to their capability to refine meshes locally and adjust the cell size over several orders of magnitude very effectively. As octree‐meshes consist solely of cuboid cells, the mapping of the geometry is trivial. On the other hand, exploiting these advantages in the context of finite‐element‐based modeling strategies is not straightforward due to the presence of hanging nodes. Recently, it has been demonstrated that the scaled boundary finite element method (SBFEM) provides a promising tool for creating discretizations based on such octree‐meshes. In this approach, each cell of the mesh is treated as a three‐dimensional SBFEM subdomain whose boundary is discretized using two‐dimensional finite elements. However, in previous work, an additional triangulation was still required to create conforming meshes on some of the subdomains' faces. In the current contribution, we improve this technique by combining the SBFEM with particular transition elements based on transfinite mappings. The combined approach requires only quadrilateral elements and circumvents any hanging nodes from the beginning. Furthermore, the utilization of transfinite mappings allows for local p‐ and h‐refinement and even combining different classes of shape functions without introducing additional constraints.