4,434 research outputs found
Geometry-Oblivious FMM for Compressing Dense SPD Matrices
We present GOFMM (geometry-oblivious FMM), a novel method that creates a
hierarchical low-rank approximation, "compression," of an arbitrary dense
symmetric positive definite (SPD) matrix. For many applications, GOFMM enables
an approximate matrix-vector multiplication in or even time,
where is the matrix size. Compression requires storage and work.
In general, our scheme belongs to the family of hierarchical matrix
approximation methods. In particular, it generalizes the fast multipole method
(FMM) to a purely algebraic setting by only requiring the ability to sample
matrix entries. Neither geometric information (i.e., point coordinates) nor
knowledge of how the matrix entries have been generated is required, thus the
term "geometry-oblivious." Also, we introduce a shared-memory parallel scheme
for hierarchical matrix computations that reduces synchronization barriers. We
present results on the Intel Knights Landing and Haswell architectures, and on
the NVIDIA Pascal architecture for a variety of matrices.Comment: 13 pages, accepted by SC'1
A Parallel Adaptive P3M code with Hierarchical Particle Reordering
We discuss the design and implementation of HYDRA_OMP a parallel
implementation of the Smoothed Particle Hydrodynamics-Adaptive P3M (SPH-AP3M)
code HYDRA. The code is designed primarily for conducting cosmological
hydrodynamic simulations and is written in Fortran77+OpenMP. A number of
optimizations for RISC processors and SMP-NUMA architectures have been
implemented, the most important optimization being hierarchical reordering of
particles within chaining cells, which greatly improves data locality thereby
removing the cache misses typically associated with linked lists. Parallel
scaling is good, with a minimum parallel scaling of 73% achieved on 32 nodes
for a variety of modern SMP architectures. We give performance data in terms of
the number of particle updates per second, which is a more useful performance
metric than raw MFlops. A basic version of the code will be made available to
the community in the near future.Comment: 34 pages, 12 figures, accepted for publication in Computer Physics
Communication
Synthesis of Clock Trees with Useful Skew based on Sparse-Graph Algorithms
Computer-aided design (CAD) for very large scale integration (VLSI) involve
Proceedings of the 5th International Workshop on Reconfigurable Communication-centric Systems on Chip 2010 - ReCoSoC\u2710 - May 17-19, 2010 Karlsruhe, Germany. (KIT Scientific Reports ; 7551)
ReCoSoC is intended to be a periodic annual meeting to expose and discuss gathered expertise as well as state of the art research around SoC related topics through plenary invited papers and posters. The workshop aims to provide a prospective view of tomorrow\u27s challenges in the multibillion transistor era, taking into account the emerging techniques and architectures exploring the synergy between flexible on-chip communication and system reconfigurability
The Universe at Extreme Scale: Multi-Petaflop Sky Simulation on the BG/Q
Remarkable observational advances have established a compelling
cross-validated model of the Universe. Yet, two key pillars of this model --
dark matter and dark energy -- remain mysterious. Sky surveys that map billions
of galaxies to explore the `Dark Universe', demand a corresponding
extreme-scale simulation capability; the HACC (Hybrid/Hardware Accelerated
Cosmology Code) framework has been designed to deliver this level of
performance now, and into the future. With its novel algorithmic structure,
HACC allows flexible tuning across diverse architectures, including accelerated
and multi-core systems.
On the IBM BG/Q, HACC attains unprecedented scalable performance -- currently
13.94 PFlops at 69.2% of peak and 90% parallel efficiency on 1,572,864 cores
with an equal number of MPI ranks, and a concurrency of 6.3 million. This level
of performance was achieved at extreme problem sizes, including a benchmark run
with more than 3.6 trillion particles, significantly larger than any
cosmological simulation yet performed.Comment: 11 pages, 11 figures, final version of paper for talk presented at
SC1
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