ABSTRACT

There are many techniques that are not directly applied to generate finite elements but are extremely useful in serving various aspects to facilitate finite element (FE) mesh generation (MG). The surface verification and preparation presented in Section 8.1 aims at analysing whether a given surface is closed and constitutes a well-defined boundary for MG within a volume. The multi-grid insertion introduced in Section 8.2 is a recursive application of a simple regular grid for Delaunay triangulation (DT) of highly non-uniform point distributions. Multi-grid insertion is a generic concept that can be readily applied also in 3D, and such a procedure is presented in detail in Section 8.3. Mesh refinement, especially in 3D, is a rapid and reliable method in producing valid FE mesh in compliance with an element size specification. Guided by a shape quality measure along with optimisation by geometrical and topological means, high-quality FE meshes can be generated for adaptive refinement analysis. Mesh refinement algorithms over surface and within volume according to an element size function are presented in Section 8.4. Following mesh refinement in Section 8.4, volume bounded by analytical surfaces can be easily meshed into tetrahedral elements in two steps: in the first step, an adaptive refinement is applied with respect to the curvature of the boundary surface, and in the second step, nodal points close to the boundary are snapped on to the boundary surface to obtain the final mesh as detailed in Section 8.5.