scholarly journals PARALLEL COMPUTING MODEL WITH CONTINUOUS TIME

2021 ◽  
pp. 305-309
Author(s):  
Dmytro Moroz
Keyword(s):  
Parallel Computing ◽  
A Priori ◽  
Parabolic Type ◽  
High Order Accuracy ◽  
Sequential Algorithm ◽  
Mathematical Concepts ◽  
Computing Systems ◽  
Parallel Form ◽  
Numerical Analytical Method ◽  
Priori Information

The aim of this work is to construct a numerical-analytical method of designing efficient algorithms for solution of tasks having the parabolic type. Using a priori information about the smoothness of solutions, great attention is paid to the construction of solutions of high -order accuracy. Creation of parallel computing systems required the development of mathematical concepts for constructing parallel algorithms, i.e. algorithms adapted for implementation in these systems. As the basis for constructing the parallel algorithm we can take both: a sequential algorithm and the task itself as well. The most sensible at parallelization of sequential algorithm is pragmatic approach; actually sequential algorithms detect common elements which further are transformed to a parallel form. It is shown, that the algorithm of numerical - analytical vectorization has the maximal parallel form and, hence, minimally possible time for realization on parallel computing devices.

scholarly journals NUMERICAL AND ANALYTICAL DIAGRAM OF A DISTRIBUTED SIMULATION OF DYNAMIC SYSTEMS

World Science ◽  
2019 ◽  
Vol 1 (3(43)) ◽  
pp. 4-9 ◽  
Author(s):  
Shvachych G. G. ◽  
Pobochii I. A. ◽  
Barteniev H. M. ◽  
Tkachenko O. G. ◽  
Tseluiko N. V.
Keyword(s):  
Distributed Simulation ◽  
A Priori ◽  
Rounding Errors ◽  
Computing Systems ◽  
Multiple Processors ◽  
The Matrix ◽  
Numerical Analytical Method ◽  
Priori Information ◽  
Structure Calculations ◽  
Single Processor

The work is dedicated to the construction of numerical-analytical method of designing efficient algorithms for the solution of problems in economics and engineering. Using a priori information about the smoothness of the solution, great attention is paid to the construction of high-accuracy solutions. The proposed approach eliminates recurrent structure calculations unknown vectors decisions, which leads to the accumulation of rounding errors. Parallel form of the algorithm is the maximum, and therefore has the shortest possible time the implementation on parallel computing systems. Most conventional algorithms for solving these problems (sweep techniques, decomposition of the matrix into a product of two diagonal matrices, doubling, etc.) when multiple processors work typically no faster than if a single processor. The reason for this is substantial sequence computations of these algorithms.

scholarly journals MODELING OF MAXIMALLY PARALLEL STRUCTURES OF ALGORITHMS FOR SOLVING THERMAL PROBLEMS

2021 ◽  
pp. 98-109
Author(s):  
Dmytro Moroz
Keyword(s):  
Parallel Computing ◽  
Heat Conduction Problem ◽  
Low Cost ◽  
Computing Systems ◽  
Parallel Form ◽  
Computational Mesh ◽  
Parallel Structures ◽  
Implementation Time ◽  
Transfer Problems ◽  
Arithmetic Expressions

The paper demonstrates the possibility of creating a maximum parallel form of computational algorithms to solve thermal problems and their mapping to the architecture of multiprocessor systems based on solving thermal problems of mathematical physics. It is shown that an effective tool for studying heat and mass transfer problems in metallurgical production could be parallel computing technologies on distributed cluster systems with a relatively low cost and reasonably easily scalable both in the number of processors and in the amount of RAM. Tridiagonal structure systems' parallelization was implemented by a numerical-analytical approach, which predetermined their maximally parallel algorithmic form. That approach is facilitated by the minimum possible implementation time of the developed algorithm on parallel computing systems. Furthermore, during the arithmetic expressions parallel computations, the developed algorithm separates the error in the output data from rounding operations. Thus, the parallelization of tridiagonal systems based on numerical-analytical discretization methods does not impose any restrictions on the topology of the mesh nodes of the computational domain.Furthermore, as applied to the parallel computation of arithmetic expressions, it separates the initial data error from a real PC's rounding operations. That approach eliminates the recurrent structure of computing the sought-for decision vectors, which, as a rule, leads to the round-off errors accumulation. Such a parallel form of the constructed algorithm is maximal and has the shortest possible implementation time of the algorithm on parallel computing systems. The developed approach to parallelizing the mathematical model is stable for various types of input data. It has the most parallel form and is distinguished by the minimum time for solving the problem as applied to multiprocessor computing systems. That is explained as follows. If it is hypothesized that one processor can be assigned to one processor and one processor can be assigned to one node of the computational mesh domain, the computations can be processed in parallel and simultaneously for all nodes of the computational mesh domain. The simulation process was implemented on a PC cluster. It follows from the simulation results analysis that the developed method for solving the heat conduction problem effectively minimizes residuals.

scholarly journals Best candidate routing algorithms integrated with minimum processing time and low blocking probability for modern parallel computing systems

2020 ◽  
Vol 19 (2) ◽  
pp. 847 ◽  
Author(s):  
Aadel M. Alatwi ◽  
Ahmed Nabih Zaki Rashed ◽  
Ahmed M. El-Eraki ◽  
Iraj Sadegh Amiri
Keyword(s):  
Parallel Computing ◽  
Processing Time ◽  
Blocking Probability ◽  
Routing Algorithms ◽  
Sequential Algorithm ◽  
Computing Systems ◽  
Processing Times ◽  
Blocking Probabilities ◽  
Window Method ◽  
Delay Times

<p>This study has clarified the best candidate routing algorithms integrated with minimum processing times and low blocking probabilities for modern parallel computing systems. Different methods were employed, such as the fast window method (FWM), fast bitwise window method (FBWM), and fast improved window method (FIWM), to upgrade the processing time and reduce the network delay time. In addition, different algorithms were studied such as the fast window ascending, the fast window descending, the fast window sequential algorithm, and the fast window sequential down algorithms; these were studied to show the numerical results of the networks’ blocking probabilities, processing times, and delay times.</p>

Innovative Approach to Information Search by Example of a Patent Analysis of an Important Substitution Plan

2020 ◽  
pp. 143-157
Author(s):  
Maria A. Milkova
Keyword(s):  
Information Search ◽  
Topic Modeling ◽  
Cognitive Biases ◽  
A Priori ◽  
Import Substitution ◽  
Innovative Approach ◽  
Iterative Search ◽  
Comprehensive Picture ◽  
Priori Information ◽  
Selection Of

Nowadays the process of information accumulation is so rapid that the concept of the usual iterative search requires revision. Being in the world of oversaturated information in order to comprehensively cover and analyze the problem under study, it is necessary to make high demands on the search methods. An innovative approach to search should flexibly take into account the large amount of already accumulated knowledge and a priori requirements for results. The results, in turn, should immediately provide a roadmap of the direction being studied with the possibility of as much detail as possible. The approach to search based on topic modeling, the so-called topic search, allows you to take into account all these requirements and thereby streamline the nature of working with information, increase the efficiency of knowledge production, avoid cognitive biases in the perception of information, which is important both on micro and macro level. In order to demonstrate an example of applying topic search, the article considers the task of analyzing an import substitution program based on patent data. The program includes plans for 22 industries and contains more than 1,500 products and technologies for the proposed import substitution. The use of patent search based on topic modeling allows to search immediately by the blocks of a priori information – terms of industrial plans for import substitution and at the output get a selection of relevant documents for each of the industries. This approach allows not only to provide a comprehensive picture of the effectiveness of the program as a whole, but also to visually obtain more detailed information about which groups of products and technologies have been patented.

scholarly journals Computational Method for Wavefront Sensing Based on Transport-Of-Intensity Equation

Photonics ◽  
2021 ◽  
Vol 8 (6) ◽  
pp. 177
Author(s):  
Iliya Gritsenko ◽  
Michael Kovalev ◽  
George Krasin ◽  
Matvey Konoplyov ◽  
Nikita Stsepuro
Keyword(s):  
A Priori ◽  
Spherical Wave ◽  
Computational Method ◽  
Optical Systems ◽  
Radius Of Curvature ◽  
Imaging Method ◽  
Wavefront Sensing ◽  
Phase Imaging ◽  
Transport Of Intensity Equation ◽  
Priori Information

Recently the transport-of-intensity equation as a phase imaging method turned out as an effective microscopy method that does not require the use of high-resolution optical systems and a priori information about the object. In this paper we propose a mathematical model that adapts the transport-of-intensity equation for the purpose of wavefront sensing of the given light wave. The analysis of the influence of the longitudinal displacement z and the step between intensity distributions measurements on the error in determining the wavefront radius of curvature of a spherical wave is carried out. The proposed method is compared with the traditional Shack–Hartmann method and the method based on computer-generated Fourier holograms. Numerical simulation showed that the proposed method allows measurement of the wavefront radius of curvature with radius of 40 mm and with accuracy of ~200 μm.

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