130,184 research outputs found
Reproducibility, accuracy and performance of the Feltor code and library on parallel computer architectures
Feltor is a modular and free scientific software package. It allows
developing platform independent code that runs on a variety of parallel
computer architectures ranging from laptop CPUs to multi-GPU distributed memory
systems. Feltor consists of both a numerical library and a collection of
application codes built on top of the library. Its main target are two- and
three-dimensional drift- and gyro-fluid simulations with discontinuous Galerkin
methods as the main numerical discretization technique. We observe that
numerical simulations of a recently developed gyro-fluid model produce
non-deterministic results in parallel computations. First, we show how we
restore accuracy and bitwise reproducibility algorithmically and
programmatically. In particular, we adopt an implementation of the exactly
rounded dot product based on long accumulators, which avoids accuracy losses
especially in parallel applications. However, reproducibility and accuracy
alone fail to indicate correct simulation behaviour. In fact, in the physical
model slightly different initial conditions lead to vastly different end
states. This behaviour translates to its numerical representation. Pointwise
convergence, even in principle, becomes impossible for long simulation times.
In a second part, we explore important performance tuning considerations. We
identify latency and memory bandwidth as the main performance indicators of our
routines. Based on these, we propose a parallel performance model that predicts
the execution time of algorithms implemented in Feltor and test our model on a
selection of parallel hardware architectures. We are able to predict the
execution time with a relative error of less than 25% for problem sizes between
0.1 and 1000 MB. Finally, we find that the product of latency and bandwidth
gives a minimum array size per compute node to achieve a scaling efficiency
above 50% (both strong and weak)
Quenching of Weak Interactions in Nucleon Matter
We have calculated the one-body Fermi and Gamow-Teller charge-current, and
vector and axial-vector neutral-current nuclear matrix elements in nucleon
matter at densities of 0.08, 0.16 and 0.24 fm and proton fractions
ranging from 0.2 to 0.5. The correlated states for nucleon matter are obtained
by operating on Fermi-gas states by a symmetrized product of pair correlation
operators determined from variational calculations with the Argonne v18 and
Urbana IX two- and three-nucleon interactions. The squares of the charge
current matrix elements are found to be quenched by 20 to 25 % by the
short-range correlations in nucleon matter. Most of the quenching is due to
spin-isospin correlations induced by the pion exchange interactions which
change the isospins and spins of the nucleons. A large part of it can be
related to the probability for a spin up proton quasi-particle to be a bare
spin up/down proton/neutron. We also calculate the matrix elements of the
nuclear Hamiltonian in the same correlated basis. These provide relatively mild
effective interactions which give the variational energies in the Hartree-Fock
approximation. The calculated two-nucleon effective interaction describes the
spin-isospin susceptibilities of nuclear and neutron matter fairly accurately.
However 3-body terms are necessary to reproduce the compressibility. All
presented results use the simple 2-body cluster approximation to calculate the
correlated basis matrix elements.Comment: submitted to PR
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