Meeting Minutes - 7 December 1999
Connectivity
For the majority of simple problems, the existing scheme of connectivity specification used in CMGUI can be used. That means that faces (or elements of dimension one less than the parent element occurring on the parent's boundary) which are connected should be assigned the same global face index in each element declaration. The global face index strategy is powerful and will work for all element types but still relies on an arbitrary (but systematic and intuitive) ordering of faces within each element.
In the example in Figure 1, two adjacent square elements are defined, as well as the connection between them, using the global face index "1". The face ordering used in this element is x1 = 0, x1 = 1, x2 = 0, x2 = 1 so if the local coordinate axes point right and up respectively, then the right edge of the first element is joined to the left edge of the second element. Note that global indices are not specified (indicated by a "0") for the unconnected faces, although in practice every face will normally have a designated global index making it convenient to specify boundary conditions and so on.
Figure 1. The specification for a mesh containing two adjacent square elements, with the x1 = 1 face in element 1 connected to the x1 = 0 in element 2.
Having determined that specifying connectivity is useful, and having determined a means of describing it for simple meshes, then three problems become significant. The first is specifying the connectivity of elements that share only part of a face, as shown in Figure 2. The second is specifying meshes at multiple resolutions. The third is dealing with connections between elements that do not occur over regions of dimension one less than the parent element, as shown in Figure 3.
Figure 2. A sample problem in which only parts of element faces are shared on boundaries, making specifying connectivity a non-trivial problem.
Figure 3. Another problem in which 2D and 3D elements are joined by line boundaries.
Partial Face Sharing
Ideally, one would like to be connect any part of an element's face with any part of the faces of numerous elements. In practice, it is probably impossible to describe this kind of connectivity in any kind of consistent (ie, validatable) manner. Assembling partial faces from lines that connect vertices specified in terms of local coordinates has been considered, but dismissed as it is too hard to check if a line between any two vertices lies on an element boundary, let alone a face.
Anyhow, this stuff has just been ruled too complicated for now, and we've moved on to describing fields again. See the next set of meeting minutes for more details.