scholarly journals Development of parallel structures of differential tasks of mathematical physics

2020 ◽  
Vol 3 (128) ◽  
pp. 36-45
Author(s):  
Gennady Shvachych ◽  
Volodymyr Konovalenkov ◽  
Olena Ivaschenko ◽  
Larysa Sushko
Keyword(s):  
Parallel Computing ◽  
Finite Difference ◽  
Mathematical Models ◽  
Numerical Models ◽  
Splitting Method ◽  
Metallurgical Industry ◽  
Mathematical Physics ◽  
Separate Determination ◽  
Sequential Method ◽  
Sustainable Implementation

The paper is devoted to the construction of parallel forms of mathematical models of a tridiagonal structure. Two methods of discretization of differential problems are considered by the example of solving the mathematical physics equation. Moreover, the application of the numerical-analytical straight line method and sweep methods to parallelization of mathematical models with a tridiagonal structure allows constructing its exact node-by-node solutions with the maximum parallel form and the least implementation time on parallel computing devices. This paper proposes to apply finite-difference and numerical-analytical methods in combination with the splitting method as a methodological basis for constructing numerical methods for solving such problems. The splitting method provides an economical and sustainable implementation of numerical models by the scalar sweep method. For such systems, acceptable acceleration in most cases is achieved by parallelizing operations in the corresponding sequential method, forming linear sections.It is convenient to implement the parallelization algorithm and its mapping to parallel computing systems on the two schemes proposed in this paper: finite-difference and numerical-analytical. This approach allows arranging separate determination of the thermophysical characteristics of the structures’ material, i.e. allows obtaining solutions of coefficient and other inverse problems of thermal conductivity.The proposed approach to the development of methods, algorithms and software can be applied in various branches of metallurgical thermal physics, economics, as well as for environmental problems of the metallurgical industry.

scholarly journals THE ENVIRONMENT DYNAMICS IDENTIFICATION BASED ON THE MODULAR COMPUTING COMPLEX

World Science ◽  
2021 ◽  
Author(s):  
Borys Moroz ◽  
Gennady Shvachych ◽  
Valentyna Chorna ◽  
Nataliiya Voroshylova
Keyword(s):  
Mathematical Models ◽  
Numerical Models ◽  
Linear Equations ◽  
Industrial Area ◽  
Matrix Computations ◽  
Sustainable Implementation ◽  
Multidimensional Equation ◽  
The Difference ◽  
Dynamics Identification

The research aims at covering the mathematical modeling issues of multidimensional applied problems of ecology based on the application of a modular computing complex. The problem of modeling air pollution processes is solved by mathematical models that adequately describe fundamental processes. That reveals issues such as a detailed analysis of the atmosphere of the city or industrial area, short-term forecast of air quality in the region, assessment of long term air purification programs, optimal emission management, transboundary transfer, etc. At the same time, the formulation and methods of solving problems of environmental dynamics identification are considered, which essence is to estimate the input parameters based on the factual information about the modeled system known from the experiment. In these studies, the multidimensional equation of harmful impurities transfer was reduced to a sequence of schemes involving unknown values in a single direction, alternately in the longitudinal, transverse and vertical.The implicit schemes lead to systems of algebraic linear equations with a three-diagonal structure. Thus, the methodological basis of the difference splitting schemes provides the economic and sustainable implementation of numerical models by the scalar runs method. That approach focuses on the fact that the greatest effect of a parallel processor is achieved when it is used to perform matrix computations of linear algebra.In order to analyze the feasibility of mathematical models, a package of applications was developed to compute the transfer of harmful impurities. A solution to several applied problems for the identification of the environmental dynamics is given.

scholarly journals EFFICIENT ALGORITHMS FOR PARALLELIZING TRIDIAGONAL SYSTEMS OF EQUATIONS

2021 ◽  
Vol 5 (136) ◽  
pp. 110-119
Author(s):  
Gennady Shvachych ◽  
Nataliіa Vozna ◽  
Olena Ivashchenko ◽  
Oleksandr Bilyi ◽  
Dmytro Moroz
Keyword(s):  
Parallel Computing ◽  
Mathematical Models ◽  
Metallurgical Industry ◽  
Peak Performance ◽  
Computing Systems ◽  
Modern Computer ◽  
Mass Transfer Processes ◽  
Parallel Forms ◽  
Method Of Straight Lines ◽  
Straight Lines

The article is devoted to the development of the maximal parallel forms of mathematical models with a tridiagonal structure. The example of solving the Dirichlet and Neumann problems by the method of straight lines and the sweep method for the heat equation illustrates the direct fundamental features of constructing parallel algorithms. It is noted that the study of the heat and mass transfer processes is run through their numerical modeling based on modern computer technology.It is shown that with the multiprocessor computing systems’ development, there disappear the problems of increasing their peak performance. On the other hand, building such systems, as a rule, requires standard network technologies, mass-produced processors, and free software. The noted circumstances aim at solving the so-called big problems.It should be borne in mind that the classical approach to solving the tridiagonal structure models based on multiprocessor computing systems is far more time-consuming compared to single-processor computing facilities. That is explained by the recurrence relations that make the basis of classical methods. Therefore, the proposed studies are relevant and aim at the distributed algorithms development for solving applied problems.The proposed research aims to construct the maximal parallel forms of mathematical models with a tridiagonal structure.The paper proposes the schemes to implement parallelization algorithms for applied problems and their mapping to parallel computing systems.Parallelization of tridiagonal mathematical models by the method of straight lines and the sweeping method allows designing absolutely stable algorithms with the maximum parallel form and, therefore, the minimum possible time for their implementation on parallel computing devices. It is noteworthy that in the proposed algorithms, the computational errors of the input data are separated from the round-off errors inherent in a PC.The proposed approach can be used in various branches of metallurgical, thermal physics, economics, and ecology problems in the metallurgical industry.

scholarly journals Investigate Impact Force of Dam-Break Flow against Structures by Both 2D and 3D Numerical Simulations

Water ◽  
2021 ◽  
Vol 13 (3) ◽  
pp. 344
Author(s):  
Le Thi Thu Hien ◽  
Nguyen Van Chien
Keyword(s):  
Impact Force ◽  
Numerical Models ◽  
Splitting Method ◽  
Dam Break ◽  
Navier Stokes ◽  
Dynamic Force ◽  
Exact Mass ◽  
Initial Water ◽  
Dam Break Flow ◽  
2D And 3D

The aim of this paper was to investigate the ability of some 2D and 3D numerical models to simulate flood waves in the presence of an isolated building or building array in an inundated area. Firstly, the proposed 2D numerical model was based on the finite-volume method (FVM) to solve 2D shallow-water equations (2D-SWEs) on structured mesh. The flux-difference splitting method (FDS) was utilized to obtain an exact mass balance while the Roe scheme was invoked to approximate Riemann problems. Secondly, the 3D commercially available CFD software package was selected, which contained a Flow 3D model with two turbulent models: Reynolds-averaged Navier-Stokes (RANs) with a renormalized group (RNG) and a large-eddy simulation (LES). The numerical results of an impact force on an obstruction due to a dam-break flow showed that a 3D solution was much better than a 2D one. By comparing the 3D numerical force results of an impact force acting on building arrays with the existence experimental data, the influence of velocity-induced force on a dynamic force was quantified by a function of the Froude number and the water depth of the incident wave. Furthermore, we investigated the effect of the initial water stage and dam-break width on the 3D-computed results of the peak value of force intensity.

scholarly journals History, observation and mathematical models in the seismic analysis of the Valadier abutment area in the Colosseum

1995 ◽  
Vol 38 (5-6) ◽  
Author(s):  
G. Croci ◽  
D. D'Ayala ◽  
R. Liburdi
Keyword(s):  
Mathematical Models ◽  
Seismic Analysis ◽  
Numerical Models ◽  
Time History ◽  
Historical Records ◽  
Direct Integration ◽  
Structural Behaviour ◽  
Seismic Behaviour ◽  
Before And After ◽  
Xix Century

The present work aimed to outline the need to investigate different fields of research to interpret the structural behaviour of a monument as complex as the Colosseum. It is shown how defining the numerical models first. then refining them, followed by interpretation of results. is strictly linked with the inforination gathered from historical records and observation of the ~nonumenta s it is today. The study is confined to the area of the Valadier abutment. analysing its state and its seismic behaviour before and after the XIX century restoration using different ilumerical tools, from the elastic modal analysis to the non linear step by step time history direct integration. The procedure comparati\ely evaluates the reliability in the interpretation of the results and identifies future lines or research.

The Free Kelvin Wave in Finite-Difference Numerical Models

1983 ◽  
Vol 13 (8) ◽  
pp. 1383-1397 ◽  
Author(s):  
William W. Hsieh ◽  
Michael K. Davey ◽  
Roxana C. Wajsowicz
Keyword(s):  
Finite Difference ◽  
Numerical Models ◽  
Kelvin Wave

Non-Newtonian Fluid Flow Analysis with Finite Difference and Finite Volume Numerical Models

2001 ◽  
Vol 11 (6) ◽  
pp. 325-335
Author(s):  
Jure Marn ◽  
Marjan Delic ◽  
Zoran Zunic
Keyword(s):  
Finite Difference ◽  
Finite Volume ◽  
Numerical Models ◽  
Flow Analysis ◽  
Mesh Size ◽  
Newtonian Flow ◽  
Driven Cavity ◽  
Commercial Code ◽  
Fluid Flow Analysis ◽  
Volume Method

Abstract Suitability of finite difference method and finite volume method for computation of incompressible non newtonian flow is analyzed. In addition, accuracy of numerical results depending of mesh size is assessed. Both methods are tested for driven cavity and compared to each other, to results from available literature and to results obtained using commercial code CFX 4.3.

Sensitivity Analysis of Hybrid Split-Step Fourier/Finite Difference Parabolic Equation Models

2018 ◽  
Vol 26 (02) ◽  
pp. 1850006 ◽  
Author(s):  
Mustafa Aslan ◽  
Kevin B. Smith ◽  
Geoffrey Moss
Keyword(s):  
Finite Difference ◽  
Numerical Models ◽  
Surface Boundary ◽  
Flat Surfaces ◽  
Pressure Release ◽  
Air Interface ◽  
Alternative Approach ◽  
Bottom Interface ◽  
Release Condition ◽  
Benchmark Solutions

Traditionally, ocean acoustic propagation models assume the sea surface can be treated as an idealized pressure release boundary. For flat surfaces, this can easily be accomplished through a variety of modeling techniques. Rough surfaces, however, introduce additional complexities in numerical models which assume a pressure release condition. An alternative approach is to model the physical water/air interface in a manner analogous to the water/sediment interface of the bottom. However, the ocean surface boundary introduces a much larger interface discontinuity than the bottom interface. In this work, a previously developed hybrid split-step Fourier/finite-difference approach is implemented at the water/air interface. Results are compared with standard SSF smoothing approaches. Normal mode and finite element models are utilized to provide benchmark solutions. Tradeoffs between accuracy and stability are discussed, as well as the model’s ability to accurately compute transmission across the water/air interface.

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