MPI Technology Research Articles

The Queue Distribution in Multiprocessor Systems with the Waiting Time Restriction

A queueing system model is considered, consisting of m (m ≥ 1) servicing devices and a maximum number of tasks with n (n ≥ 1) in the waiting queue. Each task is characterized by three random parameters (ν, β, ω), where ν is the number of servicing devices required to perform the task, β is the maximum time required to complete the task and ω is the possible time that the task can wait before assigning to run, after which it leaves the system without service. Tasks are accepted for service in the order of their entry into the system, i.e., FIFO (First-In-First-Out) discipline is used. In paper the equations are obtained for the state probabilities of the system in the stationary mode, which can serve as an assessment for real multiprocessor systems using MPI and OpenMP technologies.

Scalability of a parallel Schur complement method given the limitations for memory

In decomposition methods, the memory costs for solving the interface problem are increasing significantly with the number of subdomains increasing. Using of the Schur complement method allows you to reduce the number of iterations when the system is being solved. At the same time, the Schur complement matrix takes up more memory in comparison with global stiffness matrix. This imposes restrictions on the maximum size of the problem for which you can apply this method. Different approaches to reduce the costs and limitations of memory on stage of the construction and solving of the interface system exist. Parallel algorithm of the construction S with distributed storage of the matrix are considered when implementing using OpenMP and MPI technologies. This approach allows not only to reduce the limits on the maximum size of the solved problem, but also to resolve conflicts of shared memory access by increasing the number of independent parallel tasks.

The impact of an additional inlet point on the hot outlet side on the vortex tube productivity

Based on numerical simulation, the production of cold and hot air on a modified countercurrent vortex tube is studied. A feature of the modification under study is an additional air inlet area along the axis of the pipe from the hot outlet side. An additional point of blowing air is designed to redistribute the gas flows at the cold and hot outlets. Computational experiments were performed in the OpenFOAM software package using the sonicFoam solver based on the k−ε turbulence model under the assumption of an ideal gas. The dependence of the flow rate and temperature at the cold and hot outlets for different lengths of the main channel of the vortex tube was studied. For all considered pipe lengths, finite-volume grids were prepared in which the rectangular shape of the cells was preferably observed and their excessive stretching was avoided. To speed up the simulations, MPI technology was used; spatial decomposition of the original mesh was performed by decomposePar utility into equal parts along the pipe. This approach allowed us to reduce the computation time by approximately 3.5 times when running on six processes. The results of parallel modeling were combined with the reconstructPar utility and further processed by a Python program written using the vtk library. Thus, average values of the main physical characteristics by time and space at the cold and hot outlets were obtained. Results are discussed that demonstrate the effect of the vortex tube length on temperature and air flow at the respective outputs. The behavior of its main characteristics, non-standard for a vortex tube, is shown, an assumption is made about the reason for this behavior: the collision of very fast flows makes instability. Preliminary conclusions are made about choosing the effective length of the vortex tube with an additional air inlet channel at which the ratio of air temperature at the hot and cold outlets is the largest.

QTM: Computational package using MPI protocol for Quantum Trajectories Method.

The Quantum Trajectories Method (QTM) is one of the frequently used methods for studying open quantum systems. The main idea of this method is the evolution of wave functions which describe the system (as functions of time). Then, so-called quantum jumps are applied at a randomly selected point in time. The obtained system state is called as a trajectory. After averaging many single trajectories, we obtain the approximation of the behavior of a quantum system. This fact also allows us to use parallel computation methods. In the article, we discuss the QTM package which is supported by the MPI technology. Using MPI allowed utilizing the parallel computing for calculating the trajectories and averaging them—as the effect of these actions, the time taken by calculations is shorter. In spite of using the C++ programming language, the presented solution is easy to utilize and does not need any advanced programming techniques. At the same time, it offers a higher performance than other packages realizing the QTM. It is especially important in the case of harder computational tasks, and the use of MPI allows improving the performance of particular problems which can be solved in the field of open quantum systems.

Development and validation of the hybrid code for numerical simulation of detonations

The present paper describes a numerical code for simulation of detonation flows on hybrid computational clusters (CPU/GPU). The code can solve 1D, 2D and 3D unsteady Euler equations for multispecies chemically reacting flows using high-order shock-capturing TVD schemes and a finite-rate chemistry solver. The implementation is based on the OpenMP, MPI and CUDA technologies allowing for both flexibility and computational efficiency of the code. The program is verified on the analytical Zeldovich-von Neumann-Doering solution for the 1D detonation wave in H2/O2 mixture. Some examples of 2D computations are also given.

High Performance Computing in Multiscale Problems of Gas Dynamics

The work is devoted to the organization of high performance computing in the solution of multiscale problems of gas dynamics relevant for the implementation of modern nanotechnologies. The base of the presented computing technology is a multiscale two-level approach that combines calculations at macro- and microlevels. The approach makes it possible to study micro- and nanoflows of a gaseous medium under conditions of complex geometry of technical systems used in the production cycle in order to obtain new nanomaterials and nanocoatings. Within the framework of the approach a system of the quasigasdynamic (QGD) equations and a system of the molecular dynamics (MD) equations are considered as two basic mathematical models. These models are aggregated using the method of splitting by physical processes and scales. The QGD system is solved by the finite volume method on grids of arbitrary type. The MD equations are solved according to the Verlet integration. In view of the complexity of the problem a high performance computing is used for realization of the approach. Parallel implementation of the approach is based on the methods of domain decomposition and functional parallelism and is oriented towards the use of computer systems with hybrid architecture. The implementation uses MPI, OpenMP and CUDA technologies. Testing of the developed approach and parallel tool was performed using the example of the problem of spraying the nanoparticles on a substrate. Numerical experiments confirm the effectiveness of the developed computing technology.

Modeling of wave processes in blocky media with porous and fluid-saturated interlayers

The wave processes in blocky media are analyzed by applying different mathematical models, wherein the elastic blocks interact with each other via pliant interlayers with the complex mechanical properties. Four versions of constitutive equations are considered. In the first version, an elastic interaction between the blocks is simulated within the framework of linear elasticity theory, and the model of elastic–plastic interlayers is constructed to take into account the appearance of irreversible deformation of interlayers at short time intervals. In the second one, the effects of viscoelastic shear in the interblock interlayers are taken into the consideration using the Poynting–Thomson rheological scheme. In the third option, the model of an elastic porous material is used in the interlayers, where the pores collapse if an abrupt compressive stress is applied. In the fourth case, the model of a fluid-saturated material with open pores is examined based on Biot's equations. The collapse of pores is modeled by the generalized rheological approach, wherein the mechanical properties of a material are simulated using four rheological elements. Three of them are the traditional elastic, viscous and plastic elements, the fourth element is the so-called rigid contact, which is used to describe the behavior of materials with the different resistance to tension and compression. It was shown that the thermodynamically consistent model is provided, which means that the energy balance equation is fulfilled for an entire blocky structure, where the kinetic and potential energy of the system is the sum of the kinetic and potential energies of the blocks and interlayers. Under numerical implementation of the interlayers models, the dissipationless finite difference Ivanov's method was used. The splitting method by spatial variables in the combination with the Godunov gap decay scheme was applied in the blocks. As a result, robust and stable computational algorithms are built and tested. Using MPI technology, the parallel software was designed for the modeling of wave processes in 2D setting. The numerical results are presented, discussed and future studies are outlined.

Approaches to numerical solution of 2D Ising model

Parallel algorithm of partition function calculation of two-dimensional Ising model for systems with a finite number of spins was developed. Within a method of complete enumeration by using MPI technology with subsequent optimization of a parallel code time of calculations was reduced considerably. Partition function was calculated for systems of 16, 25, 36 Ising spins. Based on the obtained results, main thermodynamic and magnetic values dependences (such as heat capacity, magnetic susceptibility, mean square magnetization) for ferromagnetic and antiferromagnetic interactions was investigated. The analysis of a different configurations contribution showed, that states with the minimum energy have essential influence on dependences of thermodynamic values. Comparison with the results obtained by the Wang Landau algorithm was performed.

Using Parallel Computing in Queueing Network Simulation

The paper is devoted to the simulation of queueing networks on high performance computer clusters. The objective is to develop a mathematical model of queueing network and simulation approach to the modelling of the general network functionality, as well as to provide a software implementation on a high-performance computer cluster. The simulation is based on a discrete-event approach, object oriented programming, and MPI technology. The model of the queueing networks simulation system was developed as an application that allows a user to simulate networks of rather free configuration. The experiments on a high performance computer cluster emphasize the high efficiency of parallel computing.

Teaching Formal Models of Concurrency Specification and Analysis

There is a widespread and rapidly growing interest to the parallel programming nowadays. This interest is based on availability of supercomputers, computer clusters and powerful graphic processors for computational mathematics and simulation. MPI, OpenMP, CUDA and other technologies provide opportunity to write C and FORTRAN code for parallel speed-up of execution without races for resources. Nevertheless concurrency issues (like races) are still very important for parallel systems in general and distributed systems in particular. Due to this reason, there is a need of research, study and teaching of formal models of concurrency and methods of distributed system verification. The paper presents an individual experience with teaching Formal Models of Concurrency as a graduate elective course for students specializing in high-performance computing. First it sketches course background, objectives, lecture plan and topics. Then the paper presents how to formalize (i.e. specify) a reachability puzzle in semantic, syntactic and logic formal models, namely: in Petri nets, in a dialect of Calculus of Communicating Systems (CCS) and in Computation Tree Logic (CTL). This puzzle is a good educational example to present specifics of different formal notations. The article is published in the author’s wording.

CFD Problems Solving Parallel Approaches on Supercomputers

The work is devoted to developing and testing parallel algorithms, suit of computer programs for numerical solution of CFD-problems on modern supercomputers. The paper summarizes our experience in solving various practical problems of gas dynamics. These problems include research of gas flow around bodies of complex shape by viscous gas flows with radiation processes near the surface of the bodies, calculations of jet streams in the open space and flows in micro channels of technical systems. We have developed approaches combining unstructured grids, domain decomposition technique, parallel implementation via MPI technology, OpenMP, CUDA. Calculations are performed on the heterogeneous computer systems with Graphical Processing Units, classical microprocessors (Central Processing Units) and use advanced parallel approaches.

Molecular dynamic simulation of thermodynamic equilibrium establishment in nickel

This work is devoted to the molecular dynamic simulation of heat action on a metal sample consisting of nickel atoms. For the decision of this problem a continuous mathematical model based on equations of the Newton classical mechanics and a numerical method with the Verlet scheme; are used a parallel algorithm is proposed that is implemented within the MPI and OpenMP technologies. The developed program was used for the investigation the process of establishing thermodynamic equilibrium for nickel atoms at heating the sample up to the specified temperature. In the numerical experiment, both the optimal parameters of the calculation procedure and the physical parameters of the simulated process have been determined. The obtained numerical results are in good agreement with the known theoretical and experimental data.

Естественные модели параллельных вычислений

Course “Natural models of parallel computing”, given for senior students of the Faculty of Computational Mathematics and Cybernetics, Moscow State University, is devoted to the issues of supercomputer implementation of natural computational models and is, in fact, an introduction to the theory of natural computing, a relatively new branch of science, formed at the intersection of mathematics, computer science and natural sciences (especially biology). Topics of the natural computing include both already classic subjects such as cellular automata, and relatively new, introduced in the last 10–20 years, such as swarm intelligence. Despite its biological origin, all these models are widely applied in the fields related to computer data processing. Research in the field of natural computing is closely related to issues and technology of parallel computing. Presentation of theoretical material of the course is accompanied by a consideration of the possible schemes for parallel computing, in the practical part of the course it is supposed to perform by the students a software implementation using MPI technology and numerical experiments to investigate the effectiveness of the chosen schemes of parallel computing.

Трехмерное молекулярно-динамическое моделирование термодинамического равновесия нагретого никеля

This work is devoted to molecular dynamic modeling of the thermal impact processes on the metal sample consisting of nickel atoms. For the solution of this problem, a continuous mathematical model on the basis of the classical Newton mechanics equations has been used; a numerical method based on the Verlet scheme has been chosen; a parallel algorithm has been offered, and its realization within the MPI and OpenMP technologies has been executed. By means of the developed parallel program, the investigation of thermodynamic equilibrium of nickel atoms’ system under the conditions of heating a sample to desired temperature has been executed. In numerical experiments both optimum parameters of calculation procedure and physical parameters of analyzed process have been defined. The obtained numerical results are well corresponding to known theoretical and experimental data.

A Parallel Implementation of 3D Computed Tomography Algorithm

A computed tomography problem as a 3D reconstruction of density distribution is considered. The input data are obtained as a result of irradiations. The solution of the computed tomography problem is presented as a set of cross-section images. The reconstruction in a single cross-section is performed by algorithm of convolution and back projection. The parallelization is fulfilled over a set of cross-sections by use of the MPI technology.

Реализация поиска слайдовых пар для алгоритма шифрования Магма с использованием технологии MPI

Реализация поиска слайдовых пар для алгоритма шифрования Магма с использованием технологии MPI

MapReduce: Simplified Data Analysis of Big Data

Abstract With the development of computer technology, there is a tremendous increase in the growth of data. Scientists are overwhelmed with this increasing amount of data processing needs which is getting arisen from every science field. A big problem has been encountered in various fields for making the full use of these large scale data which support decision making. Data mining is the technique that can discovers new patterns from large data sets. For many years it has been studied in all kinds of application area and thus many data mining methods have been developed and applied to practice. But there was a tremendous increase in the amount of data, their computation and analyses in recent years. In such situation most classical data mining methods became out of reach in practice to handle such big data. Efficient parallel/concurrent algorithms and implementation techniques are the key to meeting the scalability and performance requirements entailed in such large scale data mining analyses. Number of parallel algorithms has been implemented by making the use of different parallelization techniques which can be listed as: threads, MPI, MapReduce, and mash-up or workflow technologies that yields different performance and usability characteristics. MPI model is found to be efficient in computing the rigorous problems, especially in simulation. But it is not easy to be used in real. MapReduce is developed from the data analysis model of the information retrieval field and is a cloud technology. Till now, several MapReduce architectures has been developed for handling the big data. The most famous is the Google. The other one having such features is Hadoop which is the most popular open source MapReduce software adopted by many huge IT companies, such as Yahoo, Facebook, eBay and so on. In this paper, we focus specifically on Hadoop and its implementation of MapReduce for analytical processing.

EFFICIENCY ANALYSIS OF PARALLEL ROUTINE USING PROCESSOR TIME VISUALIZATION

The coarse-grain parallel algorithm of modular neural networks training with dynamic mapping onto processors of parallel computer is described in this paper. Parallelization of the algorithm is done on parallel computer 300 using MPI technology. The efficiency of this algorithm is estimated using modification of MPE visualization library, which measures processor executing time of parallel routines.

Modeling 3D seismic problems using high-performance computing systems

This paper examines some issues in numerical modeling of seismology in three-dimensional space on high-performance computing systems. As a method of modeling, the grid-characteristic method is used. This method allows accurate staging of different contact conditions and is suitable for the most physically correct solutions of problems of seismology and seismic prospecting in complex heterogeneous media. We use the grid-characteristic schemes up to the 4th order accuracy inclusive. The software package is parallelized for work in a distributed clustered medium using the MPI technology. We present the results of the simulation of the Love and Rayleigh surface seismic waves, as well as the passage of seismic waves initiated by an earthquake’s hypocenter to the earth’s surface through a multilayer geological formation.

Оптимизация моделирования белковых взаимодействий на многопроцессорных системах с предоставлением доступа к алгоритму через веб-интерфейс

In this work were introduced parallel versions based on OpenMP and MPI technologies of sequential program for modeling immobilized protein interactions. Both versions have shown good scalability and better time indices to compare with the sequential version when running on single processor. Need to mention that modeling of immobilized protein interactions for some compounds have taken more than twenty hours of computations on several hundreds of processors, that is why for such modeling tasks with the great quantity of positions availability of nondeterministic algorithms, providing biologically correct result in reasonable time, seems to be rather important. Selection of stochastic algorithms has proved its value: both Monte-Carlo and simulated bee colony algorithms had found conformation corresponding minimal energy state. Supplying of access to the algorithm via web-interface measures up modern specifications of remote computations and allows the wide circle of specialists use computational power of Moscow State University and, taking into account extending the sphere of application tasks of molecular simulation, the presence of open web-interface providing remote access to the computational clusters is quite an important task.