Novel scalable scientific algorithms are needed in order to enable key science applications to exploit the computational power of large-scale systems. This is especially true for the current tier of leading petascale machines and the road to exascale computing as HPC systems continue to scale up in compute node and processor core count. These extreme-scale systems require novel scientific algorithms to hide network and memory latency, have very high computation/communication overlap, have minimal communication, and have no synchronization points.

Scientific algorithms for multi-petaflop and exa-flop systems also need to be fault tolerant and fault resilient, since the probability of faults increases with scale. Resilience at the system software and at the algorithmic level is needed as a crosscutting effort. Finally, with the advent of heterogeneous compute nodes that employ standard processors as well as GPGPUs, scientific algorithms need to match these architectures to extract the most performance. This includes different system-specific levels of parallelism as well as co-scheduling of computation. Key science applications require novel mathematical models and system software that address the scalability and resilience challenges of current- and future-generation extreme-scale HPC systems.