HIERARCHICAL TEARING: AN EFFICIENT HOLOGRAPHIC ALGORITHM FOR SYSTEM DECOMPOSITION

We review foundational aspects of Kron's Method of Tearing including Roth and Amari's derivation of Tearing using Homology Theory or Algebraic Topology and Bowden's proposal that Huygens' Principle is sufficient to justify the method. Some of the questions asked in [Bowden 1990a] are answered, in particular with respect to the limitations of Huygens' Principle and the relationship between Huygens' Principle and Homology Theory. It is proposed that multilevel, hierarchical system decomposition would be a good approach to Engineering analysis. A time and storage efficient algorithm for the direct solution of hierarchically decomposed linear continuous systems with a topology is described. We make some comments on the optimal level of tearing. It is shown that the approach is valid for any simply or multiply connected discrete system and that information is transmitted between the subsystems by a holographic process. It is this that gives rise to its efficiency. The paradigm proposed is similar to Bohm's hol...