Unformatted text preview: tree data structure 2]. The underlying tree structure is also suitable
for load balancing on a parallel computer 8, 7].
The advancing front technique constructs a mesh by \notching" elements from @
and propagating this process into the interior of the domain. An example is shown in
Figure 5.2.7. This procedure provides better shape control than quadtree or octree but
problems arise as the advancing fronts intersect. Lohner 10] has a description of this and
other mesh generation techniques. Carey 6] presents a more recent treatment of mesh
generation. Figure 5.2.7: Mesh generation by the advancing front technique. 5.3 Data Structures
Unstructured mesh computation requires a data structure to store the geometric information. There is some ambiguity concerning the information that should be computed
at the preprocessing stage, but, at the very least, the processing module would have to
the vertices belonging to each element,
the spatial coordinates of each vertex, and
the element edges, faces, or vertices that are on @ .
The processing module would need more information when adaptivity is performed. It,
for example, would need a link to the geometric information in order to re ne elements 10 Mesh Generation and Assembly along a curved boundary. Even without adaptivity, the processing software may want
access to geometric information when using elements with curved edges or faces (cf.
Section 5.4). If the nite element basis were known at the preprocessing stage, space could
be reserved for edge and interior nodes or for a symbolic factorization of the resulting
algebraic system (cf. Chapter 11).
Beall and Shephard 4] introduced a database and data structure that have great
exibility. It is suitable for use with high-order and hierarchical bases, adaptive mesh
re nement and/or order variation, and arbitrarily complex domains. It has a hierarchical
structure with three-dimensional elements (regions) having pointers to their bounding
faces, faces having pointers to their bounding edges, and edges having pointers to their
bounding vertices. Those mesh entities (elements, faces, edges, and vertices) on domain...
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