An initialisation algorithm to solve systems of nonlinear equations arising from process simulation problems

An algorithm is presented that, given an initial guess for the solution to a set of algebraic nonlinear equations, produces a new estimate (expected to be better). The algorithm finds a partition of the domain into two sets of variables-an initialised (i.e., fixed) set and a "solved for" set. The dimension of the former is much smaller than the latter, and the variables of the "solved for" set can be found by solving reduced problems with initial values given for those variables in the initialised set. Four examples are presented on which a Newton solver fails to find the solution while it converges when the new initial point produced by the algorithm is used. The Aspen Custom Modeler(TM) commercial simulator is used to pose the examples.