Parallel discrete event simulation with application to continuous systems

Abstract

Recent advances in discrete event modeling of continuous systems have emphasized the need for high performance simulation engines. This need is particularly acute when discrete event methods are applied to the numerical solution of partial differential equations. Accurate approximations can require thousands, or even millions, of cells. The corresponding requirements for memory and computing power can readily exceed what is available on a single processor computer. Discrete event simulations are characterized by asynchronous and irregular, random, or data dependent behavior. This makes parallel algorithm design particularly challenging. Known parallel discrete event simulation algorithms have been developed in terms of event and process oriented world views. In contrast to this, the Discrete Event System Specification (DEVS) forms the foundation of research into discrete event approximations of continuous systems. While event and process oriented models can be expressed in terms of the DEVS modeling formalism, there are DEVS models that do not seem to have an equivalent representation in the event or process oriented world views. This leaves open the question of how existing parallel discrete event simulation algorithms must be adapted in order to simulate DEVS models. In this dissertation, discrete simulation algorithms are built up from the basic definition of a discrete event system. The parallel algorithms that are developed through this approach are shown to operate correctly. To conclude this study, these algorithms are applied to producing numerical solutions of a hyperbolic conservation law (Sod's shock tube problem) and the wave equation.