Numerical Methods for Unconstrained Optimization and Nonlinear Equations (Classics in Applied Mathematics, 16)
Convergence of Newton method in nonlinear network analysis
Mathematical and Computer Modelling: An International Journal
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The considerable computation time of a practical application of sequential algorithms for simulating thermal and flow distribution in pipe networks is the motivating factor to study their parallel implementation. The mathematical model formulated and studied in the paper requires the solution of a set of nonlinear equations, which are solved by the Newton-Raphson method. An object-oriented solver automatically formulates the equations for networks of an arbitrary topology. The hydraulic model that is chosen as a benchmark consists of nodal flows and loop equations. A general decomposition algorithm for analysis of flow and temperature distribution in a pipe network is presented, and results of speedup of its parallel implementation are demonstrated.