"FPGA-based Modeling of Spatio-temporal Interactive Systems"

Jonathan D. Phillips, Vignesh Hariharan, and Aravind Dasu
Utah State University


Systems in the real world such as those in fluid dynamics or calcium signaling in cells or stomata networks in plants are examples of complicated real-world problems that involve a spatial organization of nodes or processing elements that interact with each other over time and influence each other over a spatial neighborhood. Attempts to model these problems using traditional software approaches generally involve extremely lengthy execution times. Field-Programmable Gate Arrays (FPGAs) naturally promote parallel processing and hold the potential to lend well to this type of spatial computing.

In this paper we present an implementation of a general, application-independent FPGA-based circuit for modeling differential equation-based, spatially distributed problems. The paper focuses on the specifics of the design of such a system. The internals of a single processing node are discussed, including an implementation of a Runge-Kutta fourth-order differential equation approximation algorithm. The polymorphic hardware design language Viva is introduced, and examples are given of how it is used to implement the system. The design platform of choice is a Hyper Computer from Starbridge Systems, which consists of several Xilinx Virtex II FPGAs.  Details of the architecture are discussed. Techniques used to optimize the design are also discussed, including the reduction of floating-point multiplications and divisions and the tradeoff between physical circuit size and execution time. Difficulties and problems encountered are also mentioned, including issues with Viva floating-point implementations and the lack of support for double-precision floating-point numbers.  Results are presented for an array of nodes that coordinate in space and time to solve simultaneous differential equations, with reference to a well observed stomata network.  Comparisons between our implementation and a traditional software implementation in terms of speed and accuracy are provided, and a vision of future work is provided.   


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