Forest-Core Partitioning Algorithm for Speeding Up Analysis of Water Distribution Systems

AbstractCommonly, water distribution networks have many treed or branched subgraphs. The equations for these systems are often solved for the steady-state flows and heads with a fast implementation of Newton’s method such as the global gradient algorithm (GGA). Applying the GGA to the whole of a network that has a treed portion means using a nonlinear solver on a problem that has separable linear and nonlinear parts. This is not optimal, and the flows and heads of treed networks can be found more quickly if the flows and heads of the treed portions are first solved explicitly by a linear process and then only the flows and heads of the smaller looped part of the network are found using the nonlinear GGA solver. The main contributions in this paper are the following: (1) development of a forest-core partitioning algorithm (FCPA), which separates the linear treed part of the network (the forest) from the nonlinear looped part (the core) by inspecting the incidence matrix; this allows the linear and nonlinea...

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