A latent macromodular approach to large-scale sparse networks

Abstract

Two major topics are discussed: macromodularity and latency. The macromodular approach uses the tearing procedure, modified nodal analysis, symbolic <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">LU</tex> factorization techniques, and separate updating and convergence tests, to take full advantage of large sparse networks with highly repetitive subnetworks. An efficient algorithm requiring only the updating of a small portion of the Jacobian matrix when individual solution vectors do not converge is presented, and the storage requirements and computation efforts to obtain a complete solution are estimated. The latent approach takes advantage of the temporary cessation of network activity between stimulation and response through knowledge of actual stimulation and the history of the internal node voltages. This approach is fully utilized by defining latent directed paths. A "latent graph" theory is proposed, and some results are presented.