SCIDAC - TOPS Terascale Optimal PDE Simulations

Large-scale simulations often involve the solution of partial differential equations (PDEs). In such simulations, continuous (infinite-dimensional) mathematical models are approximated with finitedimensional models. To obtain the required accuracy, the finite-dimensional models must often be extremely large, thus requiring terascale computers. Fortunately, continuous problems provide a natural way to generate a hierarchy of approximate models, through which the required solution may be obtained efficiently by various forms of "bootstrapping." The most dramatic examples are multigrid methods, but we also exploit other hierarchical representations.
We propose an Enabling Technology Center (ETC) that focuses on developing and implementing optimal or near optimal schemes for PDE simulations and closely related tasks, including optimization of PDE-constrained systems, eigenanalysis, and adaptive time integration. The Terascale Optimal PDE Simulations (TOPS) Center will research, develop, and deploy an integrated toolkit of open source, (nearly) optimal complexity solvers for the nonlinear partial differential equations that arise in many Office of Science application areas, including fusion, accelerator design, global climate change, and reactive chemistry. These algorithms - primarily multilevel methods - aim to reduce computational bottlenecks by one of three orders of magnitude on terascale computers, enabling scientific simulation on a scale heretofore impossible.
Along with usability, robustness, and algorithmic efficiency, an important goal of this ETC will be to attain the highest possible computational performance in its implementations by accommodating to the memory bandwidth limitations of hierarchical memory architectures.
The work at U.C. Berkeley in particular will involve automatic performance tuning of sparse matrix kernels that typically form the bottleneck of these large scale computations.