Communications of the ACM
Journal of Computational Physics
Parallel Newton--Krylov--Schwarz Algorithms for the Transonic Full Potential Equation
SIAM Journal on Scientific Computing
Achieving high sustained performance in an unstructured mesh CFD application
SC '99 Proceedings of the 1999 ACM/IEEE conference on Supercomputing
The working set model for program behavior
Communications of the ACM
Exploiting compression opportunities to improve SpMxV performance on shared memory systems
ACM Transactions on Architecture and Code Optimization (TACO)
Exploiting dense substructures for fast sparse matrix vector multiplication
International Journal of High Performance Computing Applications
Peano—A Traversal and Storage Scheme for Octree-Like Adaptive Cartesian Multiscale Grids
SIAM Journal on Scientific Computing
PRACE DECI (distributed european computing initiative) minisymposium
PARA'12 Proceedings of the 11th international conference on Applied Parallel and Scientific Computing
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Simulations of PDE-based systems, such as flight vehicles, the global climate, petroleum reservoirs, 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.