Element numbering optimization is an NP-complete problem. This means that it is impossible to prove that an element numbering scheme is optimal without evaluating all possible permutations. Since the evaluation of all possible permutations is impractical, a heuristic method is used instead. Ansys Polydata tests several possibilities, and then selects the best numbering solution and writes it to the specified mesh file.

Two optimization methods are available: the reverse Cuthill-McKee algorithm and the Fiedler vector technique implemented in the Chaco algorithm (developed and licensed by Sandia National Laboratories).

The reverse Cuthill-McKee algorithm is provided with the standard release of Ansys Polyflow, and Chaco is available as an additional licensing option. The reverse Cuthill-McKee algorithm generally yields adequate results for all but the most complex meshes. For very complex meshes with a large number of elements, the Fiedler vector method in Chaco is recommended. The Fiedler vector method is also recommended if you are using the Chaco decomposition method.