Vol 40, No 11 (2019)

The main goal of this paper is to demonstrate that the newest generation of NEC SX-Aurora TSUBASA architecture can perform large-scale graph processing extremely efficiently. This paper proposes approaches, which can be used for the development of high-performance vector-oriented implementations of page rank and shortest paths algorithms, including vectorised graph storage format, efficient vector-friendly graph traversals, optimised cache-aware memory accesses and efficient load-balancing. The developed implementations are optimised according to the most important features and properties of SX-Aurora architecture, which allows them achieve up to 15 times better performance compared to the optimised Intel Skylake parallel implementations and up to 5 times better performance compared to NVGRAPH library implementations for Pascal GPU architecture.

In this article authors present a new method to construct low-rank approximations of dense huge-size matrices. The method develops mosaic-skeleton method and belongs to kernel-independent methods. In distinction from a mosaic-skeleton method, the new one utilizes the hierarchical structure of matrix not only to define matrix block structure but also to calculate factors of low-rank matrix representation. The new method was applied to numerical calculation of boundary integral equations that appear from 3D problem of scattering monochromatic electromagnetic wave by ideal-conducting bodies. The solution of model problem is presented as an example of method evaluation.

The ATLAS experiment at the LHC processes, analyses and stores vast amounts of data, which is either recorded by the detector or simulated worldwide using Monte Carlo methods. ATLAS Computing metadata is generated at very high rates and volumes. The necessity to analyze this metadata is constantly increasing, since the heterogeneous, distributed and dynamically changing computing infrastructure requires sophisticated optimization decisions, made by human or/and by machines. Visual analytics is one of the methods facilitating the analysis of massive amounts of data (structured, semi-structured, and unstructured) which leverages human judgement by means of interactive visual representations. Given the huge number of ATLAS computing jobs that need to be visualized simultaneously for error investigations or other optimization processes, resources of the client application responsible for such visualization may reach its limits. Data objects that share similar feature values can be represented and visualized as a single group, thus initial large data sample would be represented at different levels of detail. This approach will also avoid client overload. In this paper we evaluate implementations of k-means-based Level-of-Detail generator method applied to the metadata of ATLAS jobs. This method is used in the visual analytics application InVEx (Interactive Visual Explorer) that is under development, and which is based on 3-dimensional interactive visualization of multidimensional data.

This article is devoted to the task of developing a software system designed to effectively solve the problem of continuous background identification of users based on an analysis of their behavior when working with traditional input devices like keyboard and mouse. As part of the implemented functionality, data is collected that is generated by a potentially large number of users with active use of input devices for long periods of work. Algorithms traditionally used to solve problems of behavioral biometrics are used and algorithms developed by the authors are proposed to increase the accuracy and efficiency of work when working with large amounts of input data. The architecture of the implemented system, its functionality and the results of experimental use are described.

In this paper decision support algorithm for choosing the processing means of natural language big data arrays is proposed. In the process the algorithm uses the program for evaluating the effectiveness of text analyzers. This program is based on the operation of a fuzzy choice system, which serves to calculate the integral indicator of the text analyzer effectiveness. The quality and efficiency of getting answers to test questions are taken into account when evaluating the effectiveness of text analyzers.

Numerical simulation of the surface ice accretion includes the work of various solvers that are performed iteratively and exchange data with each other. The calculation execution chain consists of the work of the gas-dynamic solver, the calculation of the liquid phase, the calculation of the thickness of the accreted ice on the surface grid and the rebuilding of the surface. After rebuilding is done, the modelling process goes to the next iteration in the gas-dynamic solver. Thus, the performance of a qualitative rebuilding of the surface computational grid taking into account the accumulated ice affects all further calculations. The article discusses approximate methods of rebuilding the surface mesh according to the ice accretion in each cell for the two-dimensional case and estimates their accuracy.

Tensor train is one of the modern decompositions used as low-rank tensor approximations of multidimensional arrays. If the original data is nonnegative we sometimes want the approximant to keep this property. In this work new methods for nonnegative tensor train factorization are proposed. Low-rank approximation approach helps to speed up the computations whereas DMRG technique allows to adapt nonnegative TT ranks for better accuracy. The performance analysis of the proposed algorithms as well as comparison with other nonnegative TT factorization method are presented.

The algebraic operations with the dense matrices and blocks are bounding the scalability of block Lanczos–Montgomery method, that is used for the linear part in the RSA decomposition problem. This paper explores the possibility of implementation of the following algebraic operations over field \(\mathbb{F}_2\) on GPU: (1) multiplication of two 64k × 64k matrices; (2) multiplication of two N × 64k blocks. For matrix multiplication, we consider two algorithms: (a) the “naive” algorithm; (b) the “fast” algorithm by 4 Russians. For block multiplication, we consider just the “naive” algorithm. It seems that by now this is the only work where BLAS acceleration over \(\mathbb{F}_2\) are relatively successful accelerated on GPU.

Expansion, collapse and impact of a gas bubble onto a rigid wall are numerically studied. The bubble is adjacent to the wall, it is initially spherical, at the equilibrium state. Its dynamics results from harmonic variation of the surrounding liquid pressure. The impulse action of the bubble on the wall is realized by means of impact of a cumulative jet arising on the surface of the bubble during its collapse. The expansion of the bubble and its collapse prior to the jet collision with the wall is calculated using the boundary element method under the assumption that the liquid is ideal incompressible and its movement is potential. The jet impact on the wall, during which the liquid compressibility is significant, is calculated using the equations of gas dynamics and the CIP-CUP method. It is found that in the considered frequency range of the liquid pressure oscillations, the shape of the jet at the beginning of its impact remains nearly the same. For the frequency corresponding to the wall pressure maximum, estimates of the pulse loading on the wall are obtained. It is shown that the pressure distribution on the wall during impact is violently nonuniform with a pronounced peak at the periphery of the loaded area. The maximum pressure on the wall averaged over the loaded area is equal to the water hammer pressure, whereas the maximum peripheral pressure is about 2.5 times as much.

The paper presents an efficient numerical technique for 3D-modeling of seismic stability of large buried structures. This technique allows considering the subsoil-structure contact interaction, gravity field effects, the inhomogeneous structure of soil and the varieties location of the earthquake hypocenter. As part of this technique is substantiated sizing of the soil-structure computational domain and continuum model for hard and soft soil foundations describing. The numerical technique for determining the kinematic conditions at the lower boundary of the computational domain from the experimental accelerations at the soil surface is given, offered special non-reflecting waves boundary conditions. The methods described above and algorithms for seismic resistance solving have been implemented in certified software package “Dynamica-3”, parallelization of the algorithm has been held according to the spatial domain decomposition principle. The developed numerical technique allows correctly posing the problem of seismic vibrations of buried structure, reducing computing costs and increasing the efficiency of numerical studies of Earthquake Engineering. Through this, the multiple recalculation of the task with different action scenarios generated from experimental seismograms by probabilistic methods became technically possible. The results of these calculations allow reflecting the experience of many earthquakes, which increases reliability of the estimates. The paper presents the model calculations results of seismic stability of large-sized buried structure—the mutual vertical and horizontal displacement of soil and building walls—which can then be used to assess strength of adjacent underground pipelines. A number of numerical experiments on seismic vibrations of nearby large-sized structures have been carried out to assess the mutual influence of structures on their behavior in an earthquake. It is established that the influence of nearby large-sized objects on seismic vibrations of structures differs for different buildings.

The analysis of energy balance equation for viscous laminar flow of fluid or gas in the cylindrical channel in the area (zone) of warm up bounded along the longitudinal coordinate is made. It was found that at laminar flow of fluid or gas in a round pipe, in each warm up area bounded along the longitudinal coordinate there are the areas of direct and reverse flows separated by a plane that is a locus of points where temperature is maximal for each fixed value of radial coordinate r. The received results also explain occurrence of returnable currents in plasma of the high-frequency induction discharge of atmospheric pressure.

Complex hydrodynamic behavior of circulating fluidized beds makes their scale-up very complicated. In particular, large-scale lateral solids segregation causes a complex two-phase flow pattern which influences significantly their performance. This article discusses the advanced hydrodynamic model developed for circulating fluidized beds based on the two-fluid concept. In this model, the kinetic theory of granular flows (KTGF) was used to solve gas–solids flow behavior. To model the influence of direct particle-particle collisions the kinetic theory for granular flow was applied based on the Chapman–Enskog theory of dense gases. For model validation purposes, a cold flow circulating fluidized bed was employed in which solid particles was transported with air as fluidizing agent. The validity of the presented model has been tested with experimental data and information available in the literature, for both gas–particle and liquid–particle systems.

The problem of finding the minimal eigenvalue and the corresponding positive eigenfunction of the nonlinear Sturm—Liouville problem for the ordinary differential equation with coefficients nonlinear depending on a spectral parameter is investigated. This problem arises in modeling the plasma of radio-frequency discharge at reduced pressures. A sufficient condition for the existence of a minimal eigenvalue and the corresponding positive eigenfunction of the nonlinear Sturm— Liouville problem is established. The original differential eigenvalue problem is approximated by the finite element method with Lagrangian finite elements of arbitrary order on a uniform grid. The error estimates of the approximate eigenvalue and the approximate positive eigenfunction to exact ones are proved. Investigations of this paper generalize well known results for the Sturm—Liouville problem with linear entrance on the spectral parameter.

The work is devoted to supercomputer molecular modeling of gas dynamic spraying of nanoparticles on the substrate. The urgency of this problem is related to the development of production technologies for promising nanocoatings and nanomaterials. The observed increase in the power of modern computer and supercomputer systems makes it possible to use mathematical models based on the first principles in numerical experiments. One of such models is the molecular dynamics method. In this paper, a new results of using of direct molecular simulation for calculating of the acceleration of a nickel nanocluster by a nitrogen flow are presented. The data obtained in the calculations allow to optimize the parameters of the accelerating gas system and predict the speed characteristics of the nanocluster near the substrate surface.

The positive definite ordinary differential nonlinear eigenvalue problem of the second order with homogeneous Dirichlet boundary condition is considered. The problem is formulated as a symmetric variational eigenvalue problem with nonlinear dependence of the spectral parameter in a real infinite-dimensional Hilbert space. The variational eigenvalue problem consists in finding eigenvalues and corresponding eigenfunctions of the eigenvalue problem for a symmetric positive definite bounded bilinear form with respect to a symmetric positive definite completely continuous bilinear form in a real infinite-dimensional Hilbert space. The variational eigenvalue problem is approximated by the mesh scheme of the finite element method on the uniform grid. For constructing the mesh scheme, Lagrangian finite elements of arbitrary order are applied. Error estimates of approximate eigenvalues and error estimates of approximate eigenfunctions in the norm of initial real infinite-dimensional Hilbert space are established. These error estimates coincide in the order with error estimates of mesh scheme of the finite element method for linear eigenvalue problems. Moreover, superconvergence estimates for approximate eigenfunctions in the mesh norm with Gauss quadrature nodes are derived. Investigations of this paper generalize well known results for the eigenvalue problem with linear entrance on the spectral parameter.

The features of the reflection and refraction of an acoustic wave passing through the boundary of two polydisperse multifraction gas suspensions at a right angle are studied in the work. A mathematical model is presented. Dispersion relation is obtained. Formulas for calculating the impedance of a polydisperse multifraction gas suspension, reflection and refraction coefficients are derived. The dependence of the module of the reflection coefficient on the dimensionless frequency is plotted.