Vol 39, No 4 (2018)

In this article authors analyse the specifics of parallel implementation of numericalmethods based on integral equations. The necessity to create original parallel subroutines implementing fast matrix algorithms for efficient work with big dense matrices is stressed out. Specifics of parallel algorithms and calculating capabilities of integral equations method for some aerodynamics and electrodynamics problems are shown.

We present the detailed description of parallel computational structure of quantum circuits modeling. The deep theoretical and experimental analysis of corresponding algorithms and relations of their features to the nature of quantum computations are considered. Special attention is paid to the extension of modeling to the case of noisy circuits, which appear in realistic quantum computers.

There are several methods of numerical solution of eigenvalue problems by the Monte Carlo method, which are used in the calculation of nuclear reactors. This paper is devoted to the investigation of the possibility of using such methods for solving the stationary Schrodinger equation. The latter equation can easily be transformed into the form of an integral equation of the first kind, very similar to those integral equations that arise in problems of nuclear power. The Monte Carlo method for this form of the stationary Schrodinger equation looks very attractive, since it naturally parallels and is very convenient for calculations on multiprocessor systems. In addition, in this case it is necessary to operate with functions defined on a large-dimensional space. This is also natural for the Monte Carlo method. It is described how the methods long used for the calculation of nuclear reactors are transformed for this case. The main problem is that the wave function of fermions changes its sign under a permutation of identical particles, and can not be nonnegative. The proposed approach is significantly different from the known methods of applying the Monte Carlo method to quantum mechanical problems. In this paper, several examples of the successful application of the proposed new method are given.

The high-fidelity modelling of turbulent flows is one of the actual problems, actively performed on high performance computing systems. The main issue for these simulations is related to the need of long time averaging to obtain reliable statistics of interest for scientists and engineers. The two recent publications deal with the problem of long time integration, suggesting an ensemble averaging approach, which allows to replace the single long time integration with multiple simulations of much shorter time intervals. These papers provide two different simulation scenarios to perform the simulations. The current paper proposes the generalized approach combining them all together. The paper provides the criterion to choose the optimal scenario, minimizing the overall simulation time for a given number of computational resources. The proposed generalization substantially extends the range of applicability for the suggested ensemble averaging methodology. The validation results considered in the paper demonstrate additional 20% simulation speedup for the generalized approach compared to the basic ones proposed earlier.

LRnLA algorithms provide many advantages for stencil computations. In contrast to the traditional stepwise approaches, the performance efficiency does not decrease with the problem data size and the parallel scaling is close to linear. This is achieved by tracing the data dependencies of the problem, taking into account the finite information propagation speed in the numerical scheme. The optimal traversal rule is found from the requirement to use all memory hierarchy levels and all levels of parallelism with higher efficiency. Stencil computing is applied, among others, in wave modeling (FDTD scheme for optics; Levander scheme for seismic waves; finite difference scheme for acoustics), gas and fluid dynamics (RKDG scheme, Lattice–Boltzmann method), plasma physics (particle-in-cell). The experience of the application of LRnLA algorithm approach in all mentioned fields aided the development of its theory. Firstly, for a given computer, given simulation problem, and a given method the achievable performance may be estimated. Secondly, based on these estimates the optimal algorithmmay be found. The conclusions provide a guidance on how to apply the LRnLA method to any local stencil scheme on any relevant computer, to achieve new breakthroughs in the performance efficiency.

This article presents a new high-level parallel computational model named BSF "— Bulk Synchronous Farm. The BSF model extends the BSP model to deal with the computeintensive iterative numericalmethods executed on distributed-memory multiprocessor systems. The BSF model is based on the master-worker paradigm and the SPMD programming model. The BSF model makes it possible to predict the upper scalability bound of a BSF-program with great accuracy. The BSF model also provides equations for estimating the speedup and parallel efficiency of a BSF-program.

We present recent modifications of the SL-AV global atmosphere model parallel structure and algorithms. The modification of the hybridMPI+OpenMP parallelization structure as well as new parallel I/O system is described. The new multigrid algorithm for solving the linear algebraic equations systems arising from discretization at the reduced latitude-longitude grid is introduced and the convergence results for this method are presented.

In this paper, we discuss the true robust pseudomultigrid technique (RMT) for blackbox solving a large class of the boundary value problems on high performance computing systems. RMT has the same number of the problem-dependent components as Gauss-Seidel method and close-to-optimal algorithmic complexity. First, an algebraic approach to parallelization is introduced for a parallel smoothing on the fine levels. The algebraic approach is based on a decomposition of the given problem into a number of subproblems with an overlap. Second, a geometric approach to parallelization is introduced for a parallel smoothing on the coarse levels to avoid communication overhead and idling processes on the very coarse grids. The geometric approach is based on a decomposition of the given problem into a number of subproblems without an overlap. After that we discuss a combination of the algebraic and the geometric approaches for parallel RMT.