Four Horizons for Enhancing the Performance of Parallel Simulations Based on Partial Differential Equations

Simulations of PDE-based systems, such as flight vehicles, the global climate, petroleum reservoirs, semiconductor devices, and nu- clear 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 al- gorithmic sources for performance improvement. Some of these improve- ments 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 formu- lations of the discrete systems to be solved, and new horizons in adaptiv- ity. Each category is motivated by recent experiences in computational aerodynamics at the 1 Teraflop/s scale.