A diverse body of science is poised for breakthroughs by means of simulation - given the ability to resolve more scales, sample larger ensembles, and/or couple together more phenomena simultaneously. For every model that is ready today for predictive simulation at the petascale (e.g., Lattice Gauge Theory, Maxwell, Navier-Stokes, Schrödinger), there is another (e.g., in biology, meteorology, nanotechnology, subsurface hydrology) that will most rapidly achieve predictive power through petascale experimentation. However, there is a daunting dichotomy between the steady improvements in the capabilities and price performance of computer hardware and the difficulty of fully exploiting it by the majority of practicing computational scientists, whose expertise lies, instead and appropriately, in their science. The TOPS ("Towards Optimal Petascale Simulations") project responds directly to this dichotomy, by developing, demonstrating, and disseminating scalable solver software. The TOPS agenda addresses one of the chief challenges of petascale simulation: solvers whose scaling lags the rest of the simulation, and several other challenges relating to the usability of sophisticated solvers. TOPS responds specifically to these objectives of the 2006 SciDAC RFP:
- Develop applied mathematics and computer science methodology focused on computational science at the petascale and work with application teams to apply innovations.
- Create scientific simulation codes that achieve high single node performance, scale to hundreds of thousands of nodes and millions of processors, and can be readily ported to other computer architectures.
- Integrate computational science with discipline-driven applications through teaming and partnerships with computer scientists and applied mathematicians.
The TOPS agenda is ripe because of the confluence of similar demands from diverse multiscale applications - allowing great leverage, the maturation of scientific software engineering - leading to consensus practices, and the soon availability of petascale architecture - creating an urgency for addressing the bottlenecks. Scientific applications from the DOE Office of Science and beyond use TOPS software and require its continued support as part of their own lifecycle plans. However, our ambition is to move these applications "higher up" the solver ladder, e.g., from operator-split scalar Poisson-like solves to nonlinearly implicitly coupled systems, and from "one-off" heroic solutions to quotidian sensitivity and stability analysis of solutions and to optimization of the systems being modeled.