Abstract
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.
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Keyes, D.E. (2000). Four Horizons for Enhancing the Performance of Parallel Simulations Based on Partial Differential Equations. In: Bode, A., Ludwig, T., Karl, W., Wismüller, R. (eds) Euro-Par 2000 Parallel Processing. Euro-Par 2000. Lecture Notes in Computer Science, vol 1900. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44520-X_1
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DOI: https://doi.org/10.1007/3-540-44520-X_1
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