Hierarchical Model of a Systolic Array for Solving Differential Equations Implemented as an Upgraded Petri Net

The objective of this paper is to develop a hierarchical model of a systolic array which solves differential equations by using Upgraded Petri Net (UPN). The Upgraded Petri Net presents a formal modeling tool, based on mathematical apparatus, used for simulation and analysis of processes, particularly at the register transfer level. Original software for modeling and simulations of Upgraded Petri Nets, PeM (Petri Net Manager), is developed and used for all models described in this paper. This software supports: UPN formal theory, graphical modeling, simulation and analysis of an UPN model. This paper includes a preface on the UPN theory, the UPN models formulation, the UPN models of a processing element of a systolic array which solves differential equation, their simulation and analysis. The first hierarchical level refers to the high level systolic array modeling. This model shows processing elements that calculate or pass their input to the output. Thus, the next processing element uses the results from the previous one. The second level model is more detailed and refers to a single processing element. This model is capable to generate solution of a differential equation through UPN execution based on Taylor’s method. This execution is based on parralel firing of a group of transitions. The results are stored into a *.mem file inside the PeM. The suitability of UPN for modelling of the systems at different levels of abstraction is examined and established. Key-Words: Upgraded Petri Net, Systolic Architecture, Modeling