A Proposal for Research on VLSI Engines for Lattice Calculations

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This research deals with the problems of designing and building practical, custom VLSI-based computers for lattice calculations. These computational problems are characterized by being iterative, defined on a regular lattice of points, uniform in space and time, local, and relatively simple. Examples include numerical solution of differential equations, iterative image processing, and cellular automata. The recently invented lattice gas automata, which are microscopic models for fluid dynamics, are a testbed for the work. The machines envisaged--lattice engines--would typically consist of many instances of a custom chip and a general-purpose host machine for support. In many practical situations, the performance of such machines is limited, not by the speed and size of the actual processing elements, but by the communication bandwidth on- and off-chip, and by the memory capacity of the chip. The specific research consists of three phases to be conducted concurrently: (1) performance analysis of existing architectures, (2) extension of current theory to give bounds on achievable throughput rate as a function of chip I/O bandwidth and memory capacity for the particular lattices of interest, and (3) construction and testing of prototype machines. Examples of computational problems amenable to lattice calculations include the numerical solution of differential equations, iterative image processing, and cellular automata. These are all very important problems. The focus of this project on the problems of designing and building practical custom VLSI-based computers aimed specifically at this class of calculations offers the potential of much faster problem solutions than on general-purpose computers.