A stochastic model of nanocrystals (NC) aggregation governing mobilities both of individual nanocrystals and its clusters is developed. The influence of the model parameters on the NC morphology is considered and an analysis is made of the applicability of the model to describe various real physical systems. The model is applied to simulate an aggregation of cadmium sulfide nanocrystals upon evaporation of the Langmuir–Blodgett matrix and as a result a comparison of simulations and experimental results is carried out. We give a comprehensive analysis of the patterns simulated by the model, and study an influence of the surrounding medium (solvent) on the aggregation processes. This system is a typical example from real life and is noteworthy in that the morphology of NC after evaporation of the matrix cannot be described exactly by a model based only on the motion of individual nanocrystals or by a cluster-cluster aggregation model.

In the paper, we implement and compare two randomized algorithms for constructing truncated singular value decompositions (SVD) for large matrices. The first one, a sampling algorithm, is based on a random sampling of a subset of matrix rows and columns to which the standard SVD algorithm is applied. This subset’s singular values and vectors are then used to recover the SVD of the original large matrix. The projection method uses a random Gaussian matrix to find random subspaces of lower dimensions with their orthonormal basis. A low-rank approximation of the original matrix is computed using this orthonormal basis, which subsequently results in the approximation of the truncated SVD. Since the dimension of the subspace is much smaller than the rank of the original matrix, randomized methods speed up the computation of near-optimal decompositions of the large matrix. In this paper, both projection and sampling algorithms are used to apply randomized truncated SVD to the solution of large systems of linear algebraic equations. The accuracy of the algorithms is compared depending on the size of the subspace that captures the dominant actions of the original matrix on two test matrices: a general matrix and a low-rank matrix. We implement parallel versions of the algorithms using the OpenMP interface and compare their performance.

Parallel versions of a genetic algorithm based on the hybrid MPI—OpenMP model are implemented to optimize circulant networks, which are of practical interest in the design of supercomputer systems and systems on a chip. An analysis of the efficiency of parallel programs with different numbers of MPI processes and OpenMP threads on a cluster of Kunpeng processors has been carried out. The speed-up of several hybrid parallel computing schemes was experimentally evaluated and analyzed. Two bottlenecks in terms of efficiency in parallel execution of the algorithm are identified and methods for their solution are proposed. By means of the parallel genetic algorithm the descriptions of circulant networks with better average distance and bisection width for the known large circulant networks were obtained.

The paper discusses the implementation of cellular automata on supercomputers. It outlines the requirements for the software: ease of program construction and usability, ability to handle a wide range of transition functions, compatibility with various platforms, and ability to scale the size of cellular arrays with efficient use of computational resources. A review of software tools suitable for implementing cellular automata was conducted. One of these tools, a library of cellular automata topologies (CATlib), has been extended to implement synchronous cellular automata in parallel on multicomputers. The paper presents performance evaluation results emphasizing the high efficiency of the parallel implementation.

The results of a parallel implementation of a randomized vector algorithm for solving systems of linear equations are presented in the paper. The solution is represented in the form of a Neumann series. The stochastic method computes this series by sampling only random columns, avoiding multiplication of matrix by matrix and matrix by vector. We consider the case when the matrix is too large to fit in random-access memory (RAM). We use two approaches to solve this problem. In the first approach, the matrix is divided into parts that are distributed among MPI processes and stored in the available RAM of the cluster nodes. In the second approach, the entire matrix is stored on each node’s hard drive, loaded into RAM, and processed in parts. Independent Monte Carlo experiments for random column indices are distributed among MPI processes or OpenMP threads for both approaches to matrix storage. The efficiency of parallel implementations is analyzed. Results are given for a system governed by dense matrices of size $$10^4$$ and $$10^5$$ .

Parallel versions of the reduced exhaustive search algorithm based on the Python tools are implemented to optimize chordal ring networks, which are of practical interest in the design of systems on a chip and supercomputer systems. An analysis of the effectiveness of parallel programs with different numbers of MPI processes on Kunpeng processors was carried out. The speed-up of several parallel computing schemes was experimentally evaluated and analyzed. The large dataset of all optimal chordal networks with numbers of up 6 · 10^4 nodes was generated for the first time. A preliminary analysis of experimentally obtained dataset has been carried out and the existence of new families of optimal chordal ring networks with analytical descriptions of parameters has been discovered.

Abstract A stochastic model of nanocrystals clusters formation is developed and applied to simulate an aggregation of cadmium sulfide nanocrystals upon evaporation of the Langmuir–Blodgett matrix. Simulations are compared with our experimental results. The stochastic model suggested governs mobilities both of individual nanocrystals and its clusters (arrays). We give a comprehensive analysis of the patterns simulated by the model, and study an influence of the surrounding medium (solvent) on the aggregation processes. In our model, monomers have a finite probability of separation from the cluster which depends on the temperature and binding energy between nanocrystals, and can also be redistributed in the composition of the cluster, leading to its compaction. The simulation results obtained in this work are compared with the experimental data on the aggregation of CdS nanocrystals upon evaporation of the Langmuir–Blodgett matrix. This system is a typical example from real life and is noteworthy in that the morphology of nanocrystals after evaporation of the matrix cannot be described exactly by a model based only on the motion of individual nanocrystals or by a cluster-cluster aggregation model.

• A synchronous multiparticle cellular automaton simulates electron-hole transport in a semiconductor. • Synchronous cellular automata effectively solve a nonlinear drift-diffusion-Poisson system in a three-dimensional domain. • The speedup of the parallel implementation of the cellular automaton algorithm is close to linear. A parallel implementation of a three-dimensional cellular automaton (CA) model of electron — hole transport in a semiconductor is presented. Carriers transport is described by a nonlinear system of drift-diffusion-Poisson equations. This system includes the drift-diffusion equations in divergence form for electrons and holes and the Poisson equation for the potential, the gradient of which enters the drift-diffusion equations as the drift velocity. We solve the drift-diffusion-Poisson system for the three-dimensional case using the CA approach. A regular mesh is introduced in the three-dimensional domain, and the solution is calculated in all lattice cells. The drift-diffusion-Poisson system is solved by an iterative algorithm consisting of two alternating steps. In the first step, the electron and hole concentrations are calculated. In the second step, the drift velocity is calculated as the gradient of the solution to the Poisson equation with the right-hand side depending on the electron and hole concentrations. The correctness of both CA models is tested against the exact solutions of the drift-diffusion and Poisson equations for some special cases. A parallel implementation of the iterative CA algorithm using the domain decomposition method is presented. The efficiency of the parallel code is analyzed. The simulation results are obtained for the model parameters specific to GaN semiconductors.

The work focuses on the application of Fragmented Programming approach to automated generation of a parallel programs for solving applied numerical problems. A new parallel programming system LuNA-ICLU applying this approach was introduced. The LuNA-ICLU compiler translates a fragmented program of a particular type written in the LuNA language to an MPI program with dynamic load balancing support. The application algorithm representation and the system algorithms used in the LuNA-ICLU system are described. Performance comparison results show a speedup compared to the previous implementation of the LuNA programming system.

In this paper a synchronous multi-particle cellular automaton model of diffusion with self-annihilation is developed based on the multi-particle cellular automata suggested previously by other authors. The models of pure diffusion and diffusion with self-annihilation are described and investigated. The correctness of the models is tested separately against the exact solutions of the diffusion equation for different 3D domains. The accuracy of the cellular automata simulation results is investigated depending on the number of cells per a single physical unit. The calculation time of cellular automaton simulation of diffusion with self-annihilation is compared with the calculation time of the Monte Carlo random walk on parallelepipeds method for different domain sizes. The parallel implementation of the cellular automaton model is developed and efficiency of the parallel code is analyzed.

The fragmented programming system LuNA is based on the Fragmented Programming Technology. LuNA is a platform for building automatically tunable portable libraries of parallel numerical subroutines. This paper focuses on the parallel implementation of the IADE method for solving 1D partial differential equation (PDE) of parabolic type using LuNA programming system. A fragmented numerical algorithm of IADE method is designed in terms of the data-flow graph. A performance comparison of different algorithm's implementations including LuNA and Message Passing Interface are given.

The LuNA library of parallel numerical fragmented subroutines is now under development. It is aimed at automated treatment of a range of important and stubborn properties of numerical subroutines. The method of algorithm and program fragmentation is used. The library is being developed with the LuNA fragmented programming system. It provides all the necessary properties of subroutines and their high portability.

The NumGRID is a middleware for joining geographically distributed computational clusters in order to run large-scale scientific applications that use MPI standards for communication between processes. Intercluster communication system of the NumGRID provides a single communication environment for the processes located on internal nodes of joined clusters. The paper discusses shortcoming of the NumGRID v.1 implementations, suggests new principles for the NumGRID v.2 implementation and presents an experimental evaluation of this principles.

A parallel 3D code for simulation of galaxies and protoplanetary discs is developed. The model includes dust, gas, gravitation and friction between dust and gas. The kinetic equation for dust particles is solved by PIC method. Gas dynamics equations are solved by FLIC method. In parallel implementation a domain decomposition technique is used where each subdomain is processed by a group of processors. Results of parallelization efficiency are presented.

Protoplanetary disc simulation must be done first, with high precision, and second, with high speed. Some strategies to reach these goals are presented in the paper. They include: the reduction of the 3D protoplanetary disc model to quasi-3D, the use of fundamental Poisson equation solution, the simulation in the natural (cylindrical) coordinate system and computation domain decomposition. The domain decomposition strategy is shown to reach the simulation goals the best.

The basic means and methods to increase efficiency of sequential numerical simulation programs are considered. The main components of modern hardware and software that affect programs efficiency are discussed. The most important guidelines and advices for application programmers are given.

The basic means and methods to increase the efficiency of the sequential numerical simulation programs are considered. The main components of the modern hardware and software which affect the programs efficiency are discussed. The most important guidelines and advices for application programmers are outlined.