Hexahedral meshing using midpoint subdivision and integer programming Original Research Article

The generation of finite element meshes of 3D hexahedral elements can be performed by subdividing the model into a number of simple bodies like hexahedra, triangular prisms, etc. Within these bodies, regular or simple transition meshes can be generated. In this paper, a method called midpoint subdivision will be discussed which enables the user to build the model using a number of high level subregions, which satisfy certain simple topological conditions. These subregions can be automatically subdivided into meshes of hexahedral elements for analysis. The distribution of elements within the mesh is typically controlled by specifying the division numbers of certain edges. However, for a given set of subregions there are a number of constraints on the edge division numbers that will yield a compatible mesh. The use of integer programming will be discussed: this finds the compatible division numbers which are nearest to, but not less than, the target values specified.