Graph-theoretic Methods in Simulation Using SPARK

TitleGraph-theoretic Methods in Simulation Using SPARK
Publication TypeConference Proceedings
Year of Publication2004
AuthorsSowell, Edward F., Michael A. Moshier, and Philip Haves
Conference NameHigh Performance Computing Symposium of the Advanced Simulation Technologies Conference
Series TitleSociety for Modeling Simulation International
Date Published04/2004
Conference LocationArlington, VA
Abstract

This 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 opposed