Four Horizons for Enhancing the Performance of Parallel
Simulations based on Partial Differential Equations
by David E. Keyes
Mathematics & Statistics Department
Old Dominion University, Norfolk, VA USA
and
Institute for Scientific Computing Research
Lawrence Livermore National Laboratory, Livermore, CA USA
and
Institute for Computer Applications in Science & Engineering
NASA Langley Research Center, Hampton, VA USA
Abstract:
Simulations of PDE-based systems, such as flight vehicles, the global
climate, petroleum resevoirs, semiconductor devices, and nuclear weapons,
typically perform an order of magnitude or more below other scientific
simulations (e.g., from chemistry and physics) with dense linear algebra
or N-body kernels at their core. In this presentation, we briefly review
the algorithmic structure of typical PDE solvers that is responsible for
this situation and consider possible architectural and algorithmic sources
for performance improvement. Some of these improvements are also
applicable to other types of simulations, but we examine their
consequences for PDEs: potential to exploit orders of magnitude more
processor-memory units, better organization of the simulation for today's
and likely near-future hierarchical memories, alternative formulations of
the discrete systems to be solved, and new horizons in adaptivity. Each
category is motivated by recent experiences in computational aerodynamics
at the 1 Teraflop/s scale.
Last modified: Mon Jun 5 14:21:26 MET DST 2000