Subdivision of PDE's on FPS scientific computers

Abstract

AbstractThe usefulness of multiprocessors in solving PDE's has become well established. Many iterative and direct methods exhibit performance which is nearly linear with the number of processors; the ‘parallelable’ fraction of the code can be made to approach unity by increasing the problem size. The resulting push for parallel architectures has been inhibited by ‘Amdahl's argument’, which states that because the speed of any task is dominated by its slowest step, parallel computers are inevitably limited by the serial fraction of most problems. Because this fraction varies, computer designers have faced a choice between a generally cost‐effective machine with a balanced parallel/serial ratio, and a potentially faster machine with high parallelism which performs well on a more restricted class of problems. Software and hardware tools now exist to allow configurable ratios of parallel to serial speed. The recent development of low‐cost Class VI scientific computers permits high‐performance multicomputing without sacrificing performance/cost. The economic consequences of Amdahl's argument can be cicumvented in view of a statistical stream of jobs into a configurable system.