Hierarchical tree-based finite element mesh generation

Hierarchical grid generation and its use as a basis for Þnite element mesh generation are considered in this paper. The hierarchical grids are generated by recursive subdivision using quadtrees in two dimensions and octrees in three dimensions. A numbering system for e¦cient storage of the quadtree grid information is examined, tree traversal techniques are devised for neighbour Þnding, and accurate boundary representation is considered. It is found that hierarchical grids are straightforward to generate from sets of seeding points which lie along domain boundaries. Quadtree grids are triangularized to provide Þnite element meshes in two dimensions. Three-dimensional tetrahedral meshes are generated from octree grids. The meshes can be generated automatically to model complicated geometries with highly irregular boundaries and can be adapted readily at moving boundaries. Examples are given of two- and three-dimensional hierarchical tree-based Þnite element meshes and their application to modelling free surface waves