An example illustrating node-tearing nodal analysis is presented in
figures 64 through 67. The example graph,
presented in figure 64, has two distinct portions
connected at node . Node
meets the selection
criteria for the first node, and the contour tableau is presented in
figure 65. 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 66 illustrates the ordered graph, note that only
the labels on the modes have changed from figure 64. To
illustrate the effect of ordering the matrix, the matrix sparsity
structure for the original and ordered graphs are presented in
figure 67. 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 64: Graph for a Node-Tearing Example
Figure 65: Example Contour Tableau
Figure 66: Relabeled Example Graph
Figure 67: Matrix Representation of the Example Graphs