Scalability and locality of extrapolation methods for distributed-memory architectures

Abstract

The numerical simulation of systems of ordinary differential equations (ODEs), which arise from the mathematical modeling of time-dependent processes, can be highly computationally intensive. Thus, efficient parallel solution methods are desirable. This paper considers the parallel solution of systems of ODEs by explicit extrapolation methods. We analyze and compare the scalability of several implementation variants for distributed-memory architectures which make use of different load balancing strategies and different loop structures. By exploiting the special structure of a large class of ODE systems, the communication costs can be reduced considerably. Further, by processing the micro-steps using a pipeline-like loop structure, the locality of memory references can be increased and a better utilization of the cache hierarchy can be achieved. Runtime experiments on modern parallel computer systems show that the optimized implementations can deliver a high scalability. © 2010 Springer-Verlag.