2,918 research outputs found
SPH-EXA: Enhancing the Scalability of SPH codes Via an Exascale-Ready SPH Mini-App
Numerical simulations of fluids in astrophysics and computational fluid
dynamics (CFD) are among the most computationally-demanding calculations, in
terms of sustained floating-point operations per second, or FLOP/s. It is
expected that these numerical simulations will significantly benefit from the
future Exascale computing infrastructures, that will perform 10^18 FLOP/s. The
performance of the SPH codes is, in general, adversely impacted by several
factors, such as multiple time-stepping, long-range interactions, and/or
boundary conditions. In this work an extensive study of three SPH
implementations SPHYNX, ChaNGa, and XXX is performed, to gain insights and to
expose any limitations and characteristics of the codes. These codes are the
starting point of an interdisciplinary co-design project, SPH-EXA, for the
development of an Exascale-ready SPH mini-app. We implemented a rotating square
patch as a joint test simulation for the three SPH codes and analyzed their
performance on a modern HPC system, Piz Daint. The performance profiling and
scalability analysis conducted on the three parent codes allowed to expose
their performance issues, such as load imbalance, both in MPI and OpenMP.
Two-level load balancing has been successfully applied to SPHYNX to overcome
its load imbalance. The performance analysis shapes and drives the design of
the SPH-EXA mini-app towards the use of efficient parallelization methods,
fault-tolerance mechanisms, and load balancing approaches.Comment: arXiv admin note: substantial text overlap with arXiv:1809.0801
The Perfect Binary One-Error-Correcting Codes of Length 15: Part II--Properties
A complete classification of the perfect binary one-error-correcting codes of
length 15 as well as their extensions of length 16 was recently carried out in
[P. R. J. \"Osterg{\aa}rd and O. Pottonen, "The perfect binary
one-error-correcting codes of length 15: Part I--Classification," IEEE Trans.
Inform. Theory vol. 55, pp. 4657--4660, 2009]. In the current accompanying
work, the classified codes are studied in great detail, and their main
properties are tabulated. The results include the fact that 33 of the 80
Steiner triple systems of order 15 occur in such codes. Further understanding
is gained on full-rank codes via switching, as it turns out that all but two
full-rank codes can be obtained through a series of such transformations from
the Hamming code. Other topics studied include (non)systematic codes, embedded
one-error-correcting codes, and defining sets of codes. A classification of
certain mixed perfect codes is also obtained.Comment: v2: fixed two errors (extension of nonsystematic codes, table of
coordinates fixed by symmetries of codes), added and extended many other
result
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