Scalability and locality of extrapolation methods on large parallel systems
Time-dependent processes can often be modeled by systems of ordinary differential equations (ODEs). Solving such a system for a detailed model can be highly computationally intensive. We investigate explicit extrapolation methods for solving such systems efficiently on current highly parallel supercomputer systems with shared-or distributed-memory architecture. We analyze and compare the scalability of several parallelization variants, some of them using multiple levels of parallelization. For a large class of ODE systems, data access costs are reduced considerably by exploiting the special structure of the ODE system. Furthermore, by employing a pipeline-like loop structure, the locality of memory references is increased for such systems resulting in a better utilization of the cache hierarchy. Runtime experiments show that the optimized implementations can deliver a high scalability. Copyright (C) 2011 John Wiley & Sons, Ltd.
scalability locality ordinary differential equations parallel extrapolation methods shared memory distributed memory numa