Exploring the Feasibility of Novel 3D Polyhedrally-Tiled Computing Arrays

Polyhedral tiled computing arrays (PTCAs) are a largely unexplored paradigm in which the assembly of high performance computing (HPC) structures may be achieved by the multidimensional tiling of particular polyhedral modules, each housing computing devices. Typically, PTCAs form <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">physical</i> three dimensional (3D) topologies which readily support <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">logical</i> three dimensional topologies. PTCAs eliminate the need for traditional backplanes, racks and custom host circuit-board modules, while inherently composing coherent and scalable input/output (IO), power and cooling grids simply by abutting to neighboring modules in one or more dimensions. This highly novel concept offers unique possibilities in all three of those domains, and therefore quantifying PTCA capabilities and limitations is critical in establishing the desirability of such systems for future modular and heterogeneous HPC systems. The questions must then arise: <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">is this a realistic paradigm?</i>, and, <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">can such a system be practically engineered?</i> In this paper we contribute a number of insights, an analytical methodology for the evaluation of a specific class of PTCAs, based upon simple-cube and truncated octahedral modules arranged into cubic arrays, and we demonstrate the use of numerical methods and formulae to analyze the potential capabilities and limits of such novel systems with both existing reference points and future technology expectations. Whilst mapping out all aspects of this novel design-space is somewhat speculative, and beyond the scope of a single paper, we do conclude by identifying key challenges and ’road-map’ goals aimed toward finally reaching that objective.