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The Node-Tearing Implementation

The software implementation to perform node-tearing nodal analysis utilizes the basic concept of building a contour tableau to identify independent sub-matrices and the coupling equations in an undirected graph representing a sparse matrix. In our implementation, the search for the local minimum of the contour number is limited to within the range , . When an independent sub-matrix is found, this iterating set is moved into a set , where . After the sets and are determined, the equations corresponding to the sets and are further ordered independently using the multiple minimum-degree ordering algorithm.

Figure gif illustrates the major steps in the node-tearing ordering algorithm that produces block-bordered-diagonal form matrices with minimum fillin. The algorithm examines all nodes essentially once, where the size of the independent subgraphs are limited to . The computational complexity of this algorithm is

due to the fact that all nodes in the graph must be examined, and for each element in the contour tableau --- all elements of the adjacency set must be examined for the next node. The value of must be less than N, and because the graphs will be sparse, the maximum number in the adjacency set will be substantially less than N, so the computational complexity of the algorithm is substantially less than .

 
Figure: The Node-Tearing Algorithm 



David P. Koester
Sun Oct 22 17:27:14 EDT 1995