01717nas a2200133   4500008004100000245005400041210005300095260002700148520125500175100002301430700002501453700001801478856008701496       2004                        eng d00aGraph-theoretic Methods in Simulation Using SPARK0 aGraphtheoretic Methods in Simulation Using SPARK  aArlington, VAc04/20043 aThis paper deals with simulation modeling of nonlinear, deterministic, continuous systems. It describes how the Simulation Problem Analysis and Research Kernel (SPARK) uses the mathematical graph both to describe models of such systems, and to solve the embodied differential-algebraic equation systems (DAEs). Problems are described declaratively rather than algorithmically, with atomic objects representing individual equations and macro objects representing larger programming entities (submodels) in a smooth hierarchy. Internally, in a preprocessing step, graphs are used to represent the problem at the level of equations and variables rather than procedural, multi-equation blocks. Benefits obtained include models that are without predefined input and output sets, enhancing modeling flexibility and code reusability, and relieving the modeler from manual algorithm development. Moreover, graph algorithms are used for problem decomposition and reduction, greatly reducing solution time for wide classes of problems. After describing the methodology the paper presents results of benchmark tests that quantify performance advantages relative to conventional methods. In a somewhat contrived nonlinear example we show O performance as opposed1 aSowell, Edward, F.1 aMoshier, Michael, A.1 aHaves, Philip  uhttps://simulationresearch.lbl.gov/publications/graph-theoretic-methods-simulation