Solution of large nonlinear engineering systems through subsystems

Abstract

The ability to break a large system into physically realizable subsystems can greatly simplify both the modelling and computer algorithm aspects for the analyst. Common procedures to solve nonlinear systems, where the Newton-Raphson method is applied directly to a formulated set of system equations, do not easily suggest a way to do this. In this paper we present a simple method to solve nonlinear problems through subsystems founded on well-established graph-theoretical methods. The key to the approach is to address the nonlinear problem at the component level, before the system equations are formulated. The approach is attractive since it permits the formulation methods of linear systems but retains all of the properties of the Newton-Raphson method. Iterations are carried out in a hierarchical manner by alternating between individual subsystems and the assembled subsystems. Furthermore, with the introduction of symbolic programming systems such as MAPLE, many avenues open up to simplify greatly the model building of nonlinear problems, especially when the system contains subsystems of a similar structure. © 1997 Elsevier Science Limited