Edge fields

Figure 181: Node per edge relationship

During the mesh refinement no middle nodes are considered. Consequently, edges only contain two nodes. They are numbered according to their storage in field iedg(1..3,*) (Figure 181). In this field entry iedg(1,i) contains the first node of edge i and iedg(2,i) contains the second node, such that iedg(1,i) $<$ iedg(2,i). For a node j ipoed(j) points to an edge in field iedg for which j is the smallest node number. If there is more than one such edge iedg(3,i) points to the next entry in iedg containing an edge for which j is again the smallest node number. If no more such edge exists the value of iedg(3,..)=0. This is a construct similar to field ieln. An actual free entry in field iedg is pointed to by ifreeed, and for any free line k iedg(3,k) points to a next free line.

Fields containing a similar number of lines as iedg are d(*) containing the length of the edges, n(*) containing the number of new nodes to be inserted on the edge for the mesh refinement (can only take the value 0 or 1 in each iteration depending on whether a node is to be inserted), r(*) containing the bias for the node insertion (if any) and iedgmid(*) containing the number of the midnode on the edge. The latter field is only introduced at the end of the mesh refinement (in projectnodes.f) and only if quadratic tetrahedral elements are requested. Finally, there is the field iexternedg(*) which takes the value:

• -1 if the edge is external but is not part of an edge of the unrefined mesh
• 0 if the edge is not external
• i $>$ 0 if the edge is external and part of an external edge i of the unrefined mesh. This edge i is described by its nodes $n_1$, $n_2$ (middle node, if any, else 0) and $n_3$ which are stored in field iedgext(1..3,i). Field iedgext is a static field (i.e. it does not change during refinement) since it describes the unrefined mesh. Entries iedgeextfa(1..2,i) are the two external faces to which external edge i belongs. Data on these external faces, e.g. j=iedgeextfa(1,i) is stored in ifacext(1..6,j) and ifacexted(1..3,j). These fields are discussed in the face field section. Finally, isharp(i) indicates whether an external edge is sharp. Whether an external edge is sharp is decided on at the end of the refinement at the time of the node projection. An external edge is sharp if
  • it is used as parent edge for at least one newly generated edge during mesh refinement AND
  • the normals on the adjacent external faces have an angle of less than about 0.05$^\circ$.
  Fields iedgeextfa, ifacext, ifacexted and isharp are static, the contents of field isharp, however, is modified at the end of the refinement in routine projectnodes.f. All of these fields are needed for the projection of the newly generated nodes after mesh refinement.

Figure 182: Element per edge relationship

The last fields ipoeled(i) and ieled(2,*) point to the elements to which edge i belongs in the same way the element per node relationship is stored in ipoeln(*) and ieln(2,*), Figure 182.