Evaluation of Directive-Based GPU Programming Models on a Block Eigensolver with Consideration of Large Sparse Matrices

Achieving high performance and performance portability for large-scale scientific applications is a major challenge on heterogeneous computing systems such as many-core CPUs and accelerators like GPUs. In this work, we implement a widely used block eigensolver, Locally Optimal Block Preconditioned Conjugate Gradient (LOBPCG), using two popular directive based programming models (OpenMP and OpenACC) for GPU-accelerated systems. Our work differs from existing work in that it adopts a holistic approach that optimizes the full solver performance rather than narrowing the problem into small kernels (e.g., SpMM, SpMV). Our LOPBCG GPU implementation achieves a 2.8$${\times }$$–4.3$${\times }$$ speedup over an optimized CPU implementation when tested with four different input matrices. The evaluated configuration compared one Skylake CPU to one Skylake CPU and one NVIDIA V100 GPU. Our OpenMP and OpenACC LOBPCG GPU implementations gave nearly identical performance. We also consider how to create an efficient LOBPCG solver that can solve problems larger than GPU memory capacity. To this end, we create microbenchmarks representing the two dominant kernels (inner product and SpMM kernel) in LOBPCG and then evaluate performance when using two different programming approaches: tiling the kernels, and using Unified Memory with the original kernels. Our tiled SpMM implementation achieves a 2.9$${\times }$$ and 48.2$${\times }$$ speedup over the Unified Memory implementation on supercomputers with PCIe Gen3 and NVLink 2.0 CPU to GPU interconnects, respectively

Theoretical investigation of TbNi_{5-x}Cu_x optical properties

In this paper we present theoretical investigation of optical conductivity for intermetallic TbNi_{5-x}Cu_x series. In the frame of LSDA+U calculations electronic structure for x=0,1,2 and on top of that optical conductivities were calculated. Disorder effects of Ni for Cu substitution on a level of LSDA+U densities of states (DOS) were taken into account via averaging over all possible Cu ion positions for given doping level x. Gradual suppression and loosing of structure of optical conductivity at 2 eV together with simultaneous intensity growth at 4 eV correspond to increase of Cu and decrease of Ni content. As reported before [Knyazev et al., Optics and Spectroscopy 104, 360 (2008)] plasma frequency has non monotonic doping behaviour with maximum at x=1. This behaviour is explained as competition between lowering of total density of states on the Fermi level N(E_F) and growing of number of carriers. Our theoretical results agree well with variety of recent experiments.Comment: 4 pages, 3 figure

Optical spectroscopy and electronic structure of the GdCux compounds (x = 1, 2, 5)

Optical properties of the GdCu, GdCu2, and GdCu5 compounds with various crystal lattices have been investigated using ellipsometry in a spectral range of 0. 22-16 μm. Theoretical calculations of the electronic structure of these intermetallic compounds have been performed in the approximation of local electron density with the correction for strong electron correlations in a 4f shell of gadolinium ions. Based on the results of calculations, the interpretation of experimental spectra of interband optical conductivity has been proposed. The plasma and relaxation frequencies of conduction electrons have been determined. © 2013 Pleiades Publishing, Ltd

Specific features of the electronic structure and spectral properties of NdNi5 - xCux compounds

The spectral properties of the intermetallic compounds NdNi5 - xCux (x = 0, 1, 2) have been studied using optical ellipsometry in the wavelength range 0.22-16 μm. It has been established that substitution of copper atoms for nickel leads to noticeable changes in the optical absorption spectra, plasma frequencies, and relaxation frequencies of conduction electrons. Spin-polarized calculations of the electronic structure of these compounds have been performed in the local spin density approximation allowing for strong electron correlations (LSDA + U method) in the 4f shell of the rare-earth ion. The calculated electron densities of states have been used to interpret the experimental dispersion curves of optical conductivity in the interband light absorption region. © 2013 Pleiades Publishing, Ltd

Influence of aluminum impurity on the electronic structure and optical properties of the TbNi5 intermetallic compound

The electronic structure of the TbNi5 - xAlx intermetallic compounds (x = 0, 1, 2) is calculated in the local electron density approximation with the correction to strong electron correlations in 4f shell of terbium ions. Spectral properties of these compounds are measured by ellipsometry in a wavelength range of 0. 22-16 μm. Frequency dependences of optical conductivity in the region of interband optical absorption are interpreted based on the results of calculations of electron densities of states. The relaxation and plasma frequencies of conduction electrons are determined. © 2013 Pleiades Publishing, Ltd

Method of variational calculation of influence of the propulsion plants of forestry machines upon the frozen and thawing soil grounds

The forests, which grow in the conditions of complete expansion of the perpetually frozen ground, are unique forests in accordance with their taxational characteristics, quality indicators of the felled timber, and the ecological functions, which these forests perform in the nature. They are characterised by the low biological productivity, as well as by the high vulnerability due to climatological changes and human economic activities. It is fair to say that conservation of the permafrost is one of the main functions of the forests, which grow within the cryolithozone. Because of this, it is necessary to ensure special regimes for the forestry management and forest exploitation within the forests of the cryolithozone. We formulated the variational problem in order to determine influence of the changeability of the physical and mechanical properties of the thawing soil ground at the boundary with the permafrost ground. © 2019 SERSC

Detection of mechanical resonance of a single-electron transistor by direct current

We have suspended an Al based single-electron transistor whose island can resonate freely between the source and drain leads forming the clamps. In addition to the regular side gate, a bottom gate with a larger capacitance to the SET island is placed underneath to increase the SET coupling to mechanical motion. The device can be considered as a doubly clamped Al beam that can transduce mechanical vibrations into variations of the SET current. Our simulations based on the orthodox model, with the SET parameters estimated from the experiment, reproduce the observed transport characteristics in detail.Comment: 4 pages, 3 figure

JUSTIFICATION OF THE NEED FOR A UNIFIED APPROACH TO THE MANAGEMENT OF THE PUBLIC EXTERNAL DEBT OF THE PARTICIPATING COUNTRIES OF THE EURASIAN ECONOMIC UNION

In article it is told about the Eurasian Economic Union, stages of his formation and features of his budget, the question of the main macroeconomic indicators of the countries-participants of the Union, and also a question of dynamics and structure of their public debt

JUSTIFICATION OF THE NEED FOR A UNIFIED APPROACH TO THE MANAGEMENT OF THE PUBLIC EXTERNAL DEBT OF THE PARTICIPATING COUNTRIES OF THE EURASIAN ECONOMIC UNION

In article it is told about the Eurasian Economic Union, stages of his formation and features of his budget, the question of the main macroeconomic indicators of the countries-participants of the Union, and also a question of dynamics and structure of their public debt

JUSTIFICATION OF THE NEED FOR A UNIFIED APPROACH TO THE MANAGEMENT OF THE PUBLIC EXTERNAL DEBT OF THE PARTICIPATING COUNTRIES OF THE EURASIAN ECONOMIC UNION

In article it is told about the Eurasian Economic Union, stages of his formation and features of his budget, the question of the main macroeconomic indicators of the countries-participants of the Union, and also a question of dynamics and structure of their public debt