KAUST’s HiCMA Library: Hierarchical Computations on
Manycore Architectures
Author/Presenter
Event Type
Workshop
Applications
Government Strategies, Programs, and Funding
HPC Center Planning and Operations
TimeMonday, November 13th10:45am -
11am
Location708
DescriptionFMM and H-matrices share a rare combination of
optimally low O(N) arithmetic complexity and high
arithmetic intensity (flops/Byte), with important phases
being nearly compute-bound. This stands in contrast to
workhorse solvers that have either low arithmetic
complexity with low arithmetic intensity (e.g., Fast
Fourier Transform and multigrid), or high arithmetic
intensity with high arithmetic complexity (e.g., dense
linear algebra and direct N-body summation). In short,
fast multipole and H-matrix methods are mathematically
efficient algorithms that are and likely will remain
computationally efficient, in the sense of being
compute-bound, on future architectures. Furthermore,
when it comes to distributed memory applications, these
methods have a communication complexity of O(log P) for
P processors, and permit high asynchronicity in their
communication. They are therefore amenable to
asynchronous programming models, which have been gaining
popularity as purely bulk synchronous models appear
stressed by energy-austere exascale hardware trends.
Much research exists on the mathematics of
hierarchically low-rank methods and many
high-performance implementations are available for
traditional full rank methods. HiCMA’s target is their
intersection on accelerators, where the hierarchy needs
flattening. Some modules of this open source project
have already been adopted in the software libraries of
major vendors. We describe currently available modules
of this work in progress.
Author/Presenter
