Extreme-Speed Eigensolver Suite

One of the most important numerical problems in science and engineering is that of finding the eigenvalues and eigenvectors of large-scale matrices. Methods for the solution of these problems, usually called eigensolvers, are fundamental to many industrial and scientific applications ranging from computational chemistry problems to structural design, to other modeling- and simulation- intense disciplines that are at the core of DOEs scientific priorities, such as weather prediction, nuclear energy, nuclear weapon certification, and wind turbine design, among many others. Scientists working in these areas are always striving for increased computational performance. Modern heterogeneous supercomputing architectures (made of arbitrary combinations of CPUs, GPUs, FPGAs, and possibly other types of cores) could provide the computational performance needed by large-scale eigensolvers. However, increasing performance in eigensolvers through heterogeneous computing is hard to achieve. The reason is that most eigensolvers and numerical software scale inefficiently when targeted to a large number of processors due to (1) communication becoming a primary burden, and (2) this burden being aggravated when transitioning into heterogeneous high-speed architectures. No industrial-quality scalable eigensolver library exists today that can efficiently exploit modern heterogeneous cores to deliver breakthrough speedups for eigenvalue-centric computations. Accelogic proposes to deploy the worlds fastest eigensolver numerical library, equipped to exploit heterogeneous HPC systems made of arbitrary combinations of CPUs, GPUs, FPGAs, and possibly other types of cores integrated in the same supercomputing network. We propose two major innovations to attack the above-mentioned hurdles by: (1) implementing communication-avoiding eigensolver algorithms; and (2) introducing innovative approaches to guarantee scaling based on talent-aware heterogeneous load-balancing. Talent-aware heterogeneous load- balancing exploits the abilities that different computing cores have to execute particular numerical tasks. Accelogic has raised private sector matching funds tied to this SBIR project for an additional $1,000,000 such an investment is a testament to the strong commercialization potential of the proposed technology. The Phase I work demonstrated more than 10x acceleration factors for both direct and iterative solvers, in both single-processor and distributed environments. This result establishes the perfect foundation for a successful Phase II effort, which targets the first release of an industrial library of eigensolvers designed for heterogeneous HPC systems. The resulting library is expected to provide from two to three orders of magnitude speedups compared against existing eigensolver solutions. It will incorporate both direct (dense) and iterative (sparse) eigensolvers. A strong emphasis of the project is on achieving successful integration with high-impact HPC software, producing, shortly after the end of Phase II, breakthrough acceleration for a wide number of users. Commercial Applications and Other Benefits: This technology will have potentially large impact in industries such as structural design, chemistry, bioengineering, and computational physics, as well as in DOEs research programs in fusion energy, climate/weather modeling, nanoscale science, genomics, and study of nuclear matter, among many others.