Abstract
Partial differential equation-based applications of multi-scale, multiphysics phenomena have driven the quest for extreme architectural scales since the foundation of modern digital computing and will continue to be principal among a broader set of science drivers for the foreseeable future. However, scientific and engineering drivers ceased long ago to dominate the computing industry and any commercially viable path to the petascale would seem to be through architectures that are assembled from components designed without the balance of resources required by scientific and engineering simulations foremost in mind. Concurrency will be massive and will involve many cores sharing common memory at the finest scales and severely dividing available memory bandwidth. As a result, algorithm designers will have to look beyond the message-passing-based SPMD paradigm that dominates today’s most successful large-scale applications and solver frameworks, with stronger than ever emphasis on locality or operands and synchronization avoidance.