5,895 research outputs found
Orthogonal Polynomial Representation of Imaginary-Time Green's Functions
We study the expansion of single-particle and two-particle imaginary-time
Matsubara Green's functions of quantum impurity models in the basis of Legendre
orthogonal polynomials. We discuss various applications within the dynamical
mean-field theory (DMFT) framework. The method provides a more compact
representation of the Green's functions than standard Matsubara frequencies and
therefore significantly reduces the memory-storage size of these quantities.
Moreover, it can be used as an efficient noise filter for various physical
quantities within the continuous-time quantum Monte Carlo impurity solvers
recently developed for DMFT and its extensions. In particular, we show how to
use it for the computation of energies in the context of realistic DMFT
calculations in combination with the local density approximation to the density
functional theory (LDA+DMFT) and for the calculation of lattice
susceptibilities from the local irreducible vertex function.Comment: 14 pages, 11 figure
Galactos: Computing the Anisotropic 3-Point Correlation Function for 2 Billion Galaxies
The nature of dark energy and the complete theory of gravity are two central
questions currently facing cosmology. A vital tool for addressing them is the
3-point correlation function (3PCF), which probes deviations from a spatially
random distribution of galaxies. However, the 3PCF's formidable computational
expense has prevented its application to astronomical surveys comprising
millions to billions of galaxies. We present Galactos, a high-performance
implementation of a novel, O(N^2) algorithm that uses a load-balanced k-d tree
and spherical harmonic expansions to compute the anisotropic 3PCF. Our
implementation is optimized for the Intel Xeon Phi architecture, exploiting
SIMD parallelism, instruction and thread concurrency, and significant L1 and L2
cache reuse, reaching 39% of peak performance on a single node. Galactos scales
to the full Cori system, achieving 9.8PF (peak) and 5.06PF (sustained) across
9636 nodes, making the 3PCF easily computable for all galaxies in the
observable universe.Comment: 11 pages, 7 figures, accepted to SuperComputing 201
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