3,359 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
Spectral/hp element methods: recent developments, applications, and perspectives
The spectral/hp element method combines the geometric flexibility of the
classical h-type finite element technique with the desirable numerical
properties of spectral methods, employing high-degree piecewise polynomial
basis functions on coarse finite element-type meshes. The spatial approximation
is based upon orthogonal polynomials, such as Legendre or Chebychev
polynomials, modified to accommodate C0-continuous expansions. Computationally
and theoretically, by increasing the polynomial order p, high-precision
solutions and fast convergence can be obtained and, in particular, under
certain regularity assumptions an exponential reduction in approximation error
between numerical and exact solutions can be achieved. This method has now been
applied in many simulation studies of both fundamental and practical
engineering flows. This paper briefly describes the formulation of the
spectral/hp element method and provides an overview of its application to
computational fluid dynamics. In particular, it focuses on the use the
spectral/hp element method in transitional flows and ocean engineering.
Finally, some of the major challenges to be overcome in order to use the
spectral/hp element method in more complex science and engineering applications
are discussed
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