A Multiprocessor Architecture for Solving Nonlinear Partial Differential Equations

This paper presents the architecture of a special-purpose multiprocessor system, which we call the Broadcast Cube System (BCS), for solving non-linear Partial Differential Equations (PDEs). The BCS has the following important features: (a) Being based on the conceptually simple bus interconnection scheme it is easily understood. The use of homogeneous Processing Elements (PEs) which can be realized as standard VLSI chips makes the hardware less costly. (b) The interconnection network is simple and regular. The network can easily be extended to vast number of PEs by adding buses with new PEs on them and by slightly increasing the number of PEs on existing buses. The interconnection pattern is highly redundant to support fault tolerance in the event of PE failures. (c) In terms of the switching delays, the delay a message undergoes between a pair of PEs connected to a common bus is zero. The maximum delay between any pair of PEs is one unit and thus a strong localization of communicating tasks is not needed to avoid long message delays even in networks of thousands of PEs. The effectiveness of the BCS has been demonstrated by both analytical and simulation methods using heat transfer and fluid flow simulation, which requires solution of non-linear PDEs, as a benchmark program