An example illustrating node-tearing nodal analysis is presented in
figures 33 through 36. The example graph,
presented in figure 33, has two distinct portions
connected at node . Node
meets the selection
criteria for the first node, and the contour tableau is presented in
figure 34. There is a distinct local minimum in the
contour number at
which identifies node
as the node
that couples the two mutually independent graph partitions.
Figure 35 illustrates the ordered graph, note that only
the labels on the modes have changed from figure 33. To
illustrate the effect of ordering the matrix, the matrix sparsity
structure for the original and ordered graphs are presented in
figure 36. In these figures, original data values are
represented with + symbols while fillin are denoted with F
characters. Within the sub-blocks, the values would be ordered with a
minimum-degree ordering algorithm. For this sample matrix, minimum
degree ordering for the entire matrix would yield the same results.
Figure 33: Graph for a Node-Tearing Example
Figure 34: Example Contour Tableau
Figure 35: Relabeled Example Graph
Figure 36: Matrix Representation of the Example Graphs