hierarchical computations

Data-sparse Methods for Large-scale Applications on Emerging Architectures

David Keyes, Professor, Applied Mathematics and Computational Sciences

Mar 2, 12:00 - 13:00

B9 L2 H1 R2322

hierarchical computations

A traditional goal of algorithmic optimality, squeezing out operations, has been superseded because of evolution in architecture. Arithmetic operations no longer serve as a reasonable proxy for all aspects of complexity. Instead, algorithms must now squeeze memory, data transfers, and synchronizations, while extra operations on locally cached data represent only small costs in time and energy. Hierarchically low-rank matrices realize a rarely achieved combination of optimal storage complexity and high-computational intensity in approximating a wide class of formally dense operators that arise in applications for which exascale computers are being constructed. We describe modules of a KAUST-built software toolkit, Hierarchical Computations on Manycore Architectures (HiCMA), that illustrate these features and are building blocks of KAUST mission applications, such as matrix-free higher-order methods in optimization and large-scale spatial statistics. Early modules of this open-source project have undergone industrial-rigor testing are distributed in the software libraries of major vendors.