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  5. VOL 40, NO 2 (2018)
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  7. 2014 год
  8. 36-6

Electronic Modeling

VOL 36, NO 6 (2014)

CONTENTS

Mathematical Modeling and Computation Methods

  ARISTOV V.V. Integro-Algorithmic Method for Computation the Matrix Logarithm with Arbitrary Accuracy (end of the article) 3-22

Informational Technologies

  IEVDIN E.A. Technology of Integrating Mathematical Models into the Decision Support Systems in the Sphere of Environment Safety Based on the Distributied Wrapper Object 23-42 

Parallel Computations

  SERGIYENKO A.M., SIMONENKO V.P. Optimization methods for synchronous dataflow graphs 43-60 

Application of Modelling Methods and Facilities

  YEVDOKIMOV V.F., PETRUSHENKO E.I., KUCHAEV V.A. Integral Model of Three-Dimensional Distribution of Eddy Flows in Continuous Casting of Round Cross-Section under Electromagnetic Stirring in Vertical MCC. II 61-82 
  MUSTAFAEV R.A. Mathematical Modeling an Unsteady Process of Motion Two Non-mixing Liquids in Porous Medium with Allowance for Anisotropy of Stratum Permeability 83-98 
  GRUTS Yu.N. Stereooperators for 3D-system with Mirror 98-108 
  CHYRVA A.A. Modeling of Nonstationary Thermal Processes in The Plate Heat Exchangers, Taking into Account the External Flow 109-118 

 

  New Rules of Paper Presentation to the Journal «Electronic Modeling» 119-122 
  Author Index to Volume 36 (2014) 123 

INTEGRO-ALGORITHMIC METHOD FOR COMPUTATION THE MATRIX LOGARITHM WITH ARBITRARY ACCURACY

V.V. Aristov

ABSTRACT

The integro-algorithmic method of approximation and iteration correction for high-accuracy computation of matrix logarithms is proposed. Themethod is based on the use of linearmultistep formulas of numerical integration of the difference type as well as the Obreshkov difference-differential formulas with allowance for higher derivatives. Due to iterations in this case there is not a necessity to choose a high-fidelity primary approximating formula and a basic criterion is a receipt of high-rate of convergence. A method also summarizes the well-known algorithms of taking the logarithm based on the Pade formulas and increases their order and accuracy due to the additional use of iterative correction. The proposed relations and program solutions permit determining necessary parameters for organizing the processes of matrix logarithms computation with arbitrary preset high accuracy.

KEYWORDS

matrix logarithms, numerical integration, integro-algorithmic method, multistep formulas of integration, transfer function, equivalent transformations.

REFERENCES

1. Gantmacher F.R. The Theory of Matrices.—Moscow: Nauka, 1988.—552 p. (in Russian).
2. Culver W.J. On the existence and uniqueness of the real logarithm of a matrix // Proc. of the American Mathematical Society.— 1966. — Vol. 17, No 5. — P. 1146—1151.
3. Al-Mohy A., Higham N. Improved inverse scaling and squaring algorithms for the matrix logarithm // SIAM J. Sci. Comput. — 2012. — Vol. 34, No 4. — P. C.153—C.169.
4. Cheng S.H., Higham N.J., Kenney C.S., Laub A.J. Approximating the logarithm of a matrix to specified accuracy // SIAM J. Matrix Anal. Appl.—2001.—Vol. 22.—P. 1112—1125.
5. Kenney C., Laub A. Condition estimates for matrix functions // Ibid.—1989.—Vol. 10.—P. 707—730.
6. Kenney C., Laub A. A Schur-Frechet algorithm for computing the logarithm and exponential of a matrix // Ibid. — 1998.— Vol. 19, No 3. — P. 640—663.
7. Higham N.J. Functions of matrices. Theory and computation // Society for Industrial and Applied Mathematics. SIAM-2008. Philadelphia, 2008.—425 p.
8. Aristov V.V. Functional macrooperation: basics of iterative algorithms. — Kiev: Nauk. Dumka, 1992.— 280 p. (in Russian).
9. Aristov V.V. Model multistep difference-differential methods integration with regard to the influence of the starting section // Electronic Modeling.—2013.—Vol. 35, No 6.—P. 3—26 (in Russian).
10. Aristov V.V. Integro-algorithmic computations.—Kiev: Nauk. Dumka, 1980.—192 p. (in Russian).
11. Aristov V.V. Mathematical models of iterative relations generalized CORDIC-algorithms // Electronic Modeling.— 2011.— Vol. 33, No 1. — P. 3—29 (in Russian).
12. Higham N.J. Evaluating Pade approximants of the matrix logarithm // SIAM J. Matrix Anal. Appl. — Vol. 22, No 4. — P. 1126—1135.

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TECHNOLOGY OF INTEGRATING MATHEMATICAL MODELS INTO THE DECISION SUPPORT SYSTEMS IN THE SPHERE OF ENVIRONMENT SAFETY BASED ON THE DISTRIBUTIEDWRAPPER OBJECT

E.A. Ievdin

ABSTRACT

New information technology based on the distributed wrapper object (DWO) of integration of computational models is developed. DWO is communicational object between DSS and model, which is distributed at runtime between the different components of the system and provides a logical, visual and technical integration of mathematical models into the DSS. Data types developed for model integration are shown. Models are classified based on input/output requirements, which affects logical structure of the DWO. For each model type separate software template can be developed to facilitate model integration. Two types of model chain approaches are shown: pull and push-driven, which affects logical structure of DWOmanager. Step by step process of integrating newmodels using DWO is described, which minimizes the emergence of errors and permits finding and correcting them in time.

KEYWORDS

model integration, decision support system, communication.

REFERENCES

1. Jagers B. Linking Data, Models and Tools: an Overview//Intern. Congress on Environmental Modelling and Software. Fifth Biennial Meeting. — Intern. Environmental Modelling and Software Society. Ottawa, Canada, July 2010. — P. 1150—1157.
2. Lavrischeva Ê. Assembly programming. Theory and practice // Cybernetics and Systems Analysis. — 2009.— No 6. — P. 3—12 (in Russian).
3. Litvinov V., Kazimir V., Gavsievich I. Distributed simulation system based on the CORBA architecture // Mathematical Machines and Systems.—2000.—No 2, 3.— P. 76—87 (in Russian).
4. Doroshenko A., Kotiuk M., Nikolaev S. Software platform for scientific research // Problems in Programming. — No 4. — P. 49—59 (in Russian).
5. Knapen R. et al. Evaluating OpenMI as a model integration platform across disciplines // Environmental Modelling & Software. — 2013. — Vol. 39. — P. 274—282 .
6. Rizzoli A. E. et al. Semantic links in integrated modelling frameworks // Mathematics and Computers in Simulation.— 2008.— Vol. 78. — P. 412—423.
7. Hofman D. Application of the software system LIANA for integrating applications, GIS and databases in a model based decision support system // Mathematical Machines and Systems.—1998. –— No 1. — P. 75—88.
8. Hofman D., Krause P., Kralisch S., Fl ugel W. LIANA Model Integration System — architecture, user interface design and application in MOIRA DSS // Advances in Geosciences.—2005.— No 4. — P. 9—16.
9. Moore R.V., Tindall C.I. An overview of the open modelling interface and environment (the OpenMI) // Environmental Science and Policy.—2005.—Vol. 8, Issue 3.—P. 279—286.
10. Donchyts G., Hummel S., Vanecek S. et al. OpenMI 2.0 - What's new? // Intern. Congress on Environmental Modelling and Software. Fifth Biennial Meeting. — Intern. Environmental Modelling and Software Society. Ottawa, Canada, July 2010. — P. 1177—1184.
11. Rahman J.M., Perraud S.P., Hotham H. et al. Evolution of TIME. Eds. A. Zerger and R. Argen.—Intern.Congress on Modelling and Simulation (MODSIM 2005). —Modelling and Simulation Society of Australia and New Zealand, December, 2005. — P. 697—703.
12. Hillyer C. Bolte J., van Evert F., Lamaker A. et al. TheModCom modular simulation system // European Journal of Agronomy. 2003. — Vol. 18, Issues 3—4. — p. 333—343.
13. Moore A.D., Holzworth D.P., Herrmann N.I. et al. The common modelling protocol: a hierarchical framework for simulation of agricultural and environmental systems // Agricultural Systems. — 2007.— Vol. 95, Issues 1—3. — P. 37—48.
14. Altintas I., Berkley C., Jaeger E. et al. Kepler: an Extensible System for Design and Execution of Scientific Workflows // Proc. of the 16 Intern. Conf. on Scientific and Statistical Database Management (SSDBM 2004). — IEEE Computer Society Washington, DC, USA. — 2004.—P. 423—424.
15. Ievdin Ie. Development of architecture of the cross-platform distributed decision support systems based on mathematical models // Mathematical Machines and Systems.—2011.— No 1. — P. 72—81 (in Russian).
16. Ievdin Ie., Zheleznyak M., Trybushnyi D. Development of the cross-platform version of the decision support system for radiation accidents JRODOS // Ibid.—2012.—No 1.— P. 45—59 (in Russian).
17. Litvinov V. et al. Object-oriented modeling in the design of embedded and real-time systems // System Analysis and Design of Computer Information Systems. — Cherkasy: Bohdan Khmelnytsky National University at Cherkasy, 2011. — 376 p. (in Russian).
18. Ievdin Ie., Trybushnyi D., Zheleznyak M., Raskob W. RODOS reengineering: aims and implementation details // Radioprotection—2010.—Vol. 45, No 5.—P. 181—189. (in Russian).
19. Raskob W., Trybushnyi D., Ievdin Ie., Zheleznyak M. JRODOS: Platform for improved long term countermeasures modeling and management // Radioprotection. — 2011. — Vol. 46, No 6. — P. 731— 736. (in Russian).
20. Kolomiets P. et al. Forecasting and mapping flooding floods areas system based on numerical solution of two-dimensional shallow water equations // Proc. of the Int. Conf. Modelling- 2012— Kiev, Ukraine, 2012.— P. 224—227 (in Russian).

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OPTIMIZATION METHODS FOR SYNCHRONOUS DATAFLOW GRAPHS

A.M. Sergiyenko, V.P. Simonenko

ABSTRACT

Methods for the synchronous dataflow graph (SDF) retiming, and mapping it into pipelined datapaths are considered. A method of retiming the spatial SDF is proposed. The method is based on the SDF representation in the multidimensional space. The dimensions of this space are spatial coordinate of the processing unit, coordinate of the operator firing, and operator type. At the first stage of the datapath synthesis the operator nodes are placed in the space according to a set of rules and theorems providing the minimum hardware volume and minimum clock period for the given number of clock periods in the algorithm cycle. At the second stage of the synthesis this spatial SDF is balanced and optimized providing the minimum register and multiplexor number in the resulting datapath. The resulting spatial SDF is described in VHDL language and is modeled and compiled using proper CAD tools. The method is successfully proven by the synthesis of a set of infinite impulse response filters for FPGA.

KEYWORDS

retiming, synchronous dataflow, scheduling, pipelining, folding, datapath.

REFERENCES

1. Sergiyenko A. M., Simonenko V. P. Algorithmic models of dataflow processing // Electronic Modeling. — 2008.— Vol. 30, No 6. — P. 49—60 (in Russian).
2. Handbook of Algorithms for Physical Design Automation / Editors C.J. Alpert, D.P. Mehta, S.S. Sapatnekar — Auerbach Publications, 2008. — 1024 p.
3. Bhattacharyya S.S., Murthy P.K., Lee E.A. Software Synthesis from Dataflow Graphs. — Kluwer Academic Publ., 1996.
4. Khan S.A. Digital Design of Signal Processing Systems. — John Wiley & Sons, 2011. — 586 p.
5. Lee E.A.,Messerschmitt D.G. Synchronous data flow // Proc. IEEE—1987.—Vol. 75, No 9.— P. 107—119 (in Russian).
6. Edwards S., Lavagno L., Lee E.A., Sangiovanny-Vincentelli A. Design of Embedded Systems: Formal Models, Validation, and Synthesis // Proc. of the IEEE. —1997. —Vol. 85, No 3. — P. 366—390.
7. Lee E.A., Messerschmitt D.G. Static scheduling of synchronous data flow programs for digital signal processing // IEEE Trans. on Computers.—1987.—Vol. 36, No 1.—P. 24—35.
8. O'neil T.W., Sha E.H.M. Retiming synchronous data-flow graphs to reduce execution time // IEEE Trans. on Signal Processing. — 2001. — Vol. 49, No 10. — P. 2397—2407.
9. Ito K., Parhi K.K. Determining the Iteration Bounds of Single-Rate and Multi-Rate Data-Flow Graphs // Proc. 1994 IEEE Asia-Pacific Conf. on Circuits and Systems. Taipei, Taiwan. — 5—8 Dec. 1994.— P. 163—168.
10. Leiserson C.E., Saxe J.B. Retiming Synchronous Circuitry // Algorithmica.—1991.— No 6. — P. 5—35.
11. Potkonjak M., Rabaey J.M. Maximally and Arbitrarily Fast Implementation of Linear and Feedback Linear Computations // IEEE Trans. on Computer Aided Design of Integrated Circuits and Systems. — 2000.— Vol. 19, No 1. — P. 30—43.
12. Petersen W.P., Arbenz P. Introduction to Parallel Computing.— Oxford University Press, 2004.— 259 p.
13. The Systhesis Approach to Digital System Design / Editors P. Micheli, U. Lauther, P. Duzy.— Kluwer Academic Pub., 1992. — 415 p.
14. Kun S. VLSI Array Processors. — Moscow: Mir, 1991. — 672 p. (in Russian).
15. Sergiyenko A.M., Simonenko V.P. Mapping of periodic algorithms onto programmed logic integral circuits // Electronic Modeling. — 2007. — Vol. 29, No 2. — P. 49—61 (in Russian).
16. Kanyevskiy Ju.S., Ovramenko S.G., Sergiyenko A.M. Mapping of regular algorithms onto structures of specialized processors // Ibid. — 2002. — Vol. 24, No 2. —P. 46—59 (in Russian).
17. Sergiyenko A.M. Perfect frame of the algorithm graph // Visnyk NTUU «KPI». Informatics, operation and computer science. —2007. — Vol. 46. —P. 62—67 (in Ukrainian).
18. Sergiyenko A.M. Methods of design of digital filters with the help of VHDL // Collected Scientific Works. Pukhov Institute for Modeling in Energy Engineering. – Modeling and Information Technologies.— 2002.— Vol. 12. — P. 99—107 (in Russian).
19. Sergiyenko A.M., Lesyk T.M. Dynamic modified digital filters on PLIS // Electronic Modeling.— 2010.— Vol. 32, No 6. — P. 47—56 (in Russian).
20. Sergiyenko A.M., Lepekha V.L., Lesyk T.M. Special processors for two-dimensional discrete cosinus transformation // Visnyk NTUU «KPI». Informatics, operation and computer science. — 2007.— Vol. 47. — P. 49—52 (in Ukrainian).
21. Sergiyenko A.M. Special processory for autoregression analysis of signals // ElectronicModeling.— 2010.— Vol. 32, No 2. — P. 87—96 (in Rusian).
22. Sergiyenko A., Maslennikow O., Lepekha V. et al. Parallel Implementation of Cholesky LLT Algorithm in FPGA—Based Processor // Lecture Notes in Computer Science. — Berlin: Springer, 2008.— Vol. 4967.— Ð. 137—147.

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INTEGRAL MODEL OF THREE-DIMENSIONAL DISTRIBUTION OF EDDY FLOWS IN CONTINUOUS CASTING OF ROUND CROSS-SECTION UNDER ELECTROMAGNETIC STIRRING IN VERTICAL MCC. II

V.F. Yevdokimov, E.I. Petrushenko

ABSTRACT

The scalar set of integral equations has been obtained which describes in cylindrical system of coordinates the three-dimensional distribution of eddy flows in the system continuous casting (CC) of round cross-section—mould under electromagnetic stirring in vertical CC. It is based on the vector set of integral equations. An auxiliary problem is considered in Part I of the paper: scalar integral equations describing three-dimensional distribution of eddy flows in continuous casting of round cross-section. The effect of eddy flows is not taken in the account.

KEYWORDS

integral model, three-dimensional distribution, eddy flows, continuous casting, round cross-section, electromagnetic stirring.

REFERENCES

1. Yevdokimov V.F.,Petrushenko E.I. Integral model of three-dimensional distribution of eddy flows in continuous casting of round cross-section under electromagnetic stirring in vertical MCC. I. // Electronic Modeling.— 2014. — Vol. 36, No 5. —P. 67—79 (in Russian).
2. Yevdokimov V.F., Petrushenko E.I. Integral model of three-dimensional distribution of eddy flows in continuous casting of square cross-section under electromagnetic stirring in vertical MCC. I // Ibid. — 2013.— Vol. 35, No 6. — P. 49—62 (in Russian).
3. Yevdokimov V.F., Petrushenko E.I. Integral model of three-dimensional distribution of eddy flows in continuous casting of square cross-section under electromagnetic stirring in vertical MCC. II // Ibid. — 2014.— Vol. 36, No 1. — P. 81—95 (in Russian).
4. Yevdokimov V.F., Kuchaev A.A., Petrushenko E.I., Kuchaev V.A. Model of three-dimensional magnetic field of the stator of cylindrical electromagnetic stirrer with allowance for magnetization currents distribution on themagnetic circuit surface. I // Ibid.—2012.—Vol. 34, No 1.— P. 81—92 (in Russian).

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