TENSOR METHOD DUAL NETWORKS TO CALCULATE COMPLEX SYSTEMS BY PARTS

A tensor method dual network enables you to create network models of processes and structures of the system. Network models provide calculation processes in restructuring, including calculation of parts. For example, changes in the destruction of the elements of the technical system, or calculation of design options when designing systems. In the network model flows are represented in space structure with bases open or closed paths. When you change the structure of flows is obtained as coordinate transformation caused by the change of paths. This ensures by constancy sum of the metric tensors in restructuring dual networks. In physics, the invariant is the law of conservation of energy flow.

If you change the structure, including the system partition into parts or the connection from the parts the whole system, change metrics and flows in this network reflect the corresponding changes in the dual network that contains only changed ways. This allows calculation of parts without iterations, which reduces the volume of calculations. This allows the use of parallel computing, including supercomputers and distributed computing systems. There is an example of network calculating by parts dividing.

Keywords

Tensor method, dual networks, processes, structure, network models, calculations by parts, parallel computing.

Issue number: 3
Year: 2017
ISBN:
UDK: 338.26.015: 658.5
DOI:
Authors: Petrov A.E.

About authors: Petrov A.E., Doctor of Technical Sciences, Professor, e-mail: Helen_pet@mail.ru, Institute of Information Technologies and Automated Control Systems, National University of Science and Technology «MISiS», 119049, Moscow, Russia.

REFERENCES:

1. Petrov A. E. Tenzornaya metodologiya v teorii sistem (Tensor methodology in systemtheory), Moscow, Radio i svyaz’, 1985, 152 p.

2. Petrov A. E. Tenzornyy metod dvoystvennykh setey (Tensor method of dual networks),Moscow, OOO TsITiP, 2007, 496 p, available at: http://www.uni-dubna.ru///images/data/gallery/70_971_tenzorny_method25_02.pdf , 2009.

3. Petrov A. E. Gornyy informatsionno-analiticheskiy byulleten’. 2014, no 8, pp. 285–291.

4. Petrov A. E. Gornyy informatsionno-analiticheskiy byulleten’. 2014, no 9, pp. 139–148.

5. Petrov A. E. Gornyy informatsionno-analiticheskiy byulleten’. 2016, no 3, pp. 61–76.

6. Kron G. Issledovanie slozhnykh sistem po chastyam (diakoptika) (Diakoptics – thepiecewise solution of large-scale systems), Moscow, Nauka, 1972, 544 p.

7. Khepp Kh. Kh. Diakoptika i elektricheskie tsepi (Diakoptics and networks), Moscow,Mir, 1974.

8. Sokhor Yu. N. Vychislitel’nye modeli i algoritmy tenzornogo analiza setey. Uchebno-metodicheskoe posobie (Computational models and algorithms for tensor analysis of networks. Textbook), Pskov, Izd-vo PPI, 2008, 162 p.

9. Petrov A. E. Tenzornyy analiz setey i parallel’nye vychisleniya (Tensor analysis of networks and parallel computations), Moscow, MIFI, 1991, 24 p.

TENSOR METHOD DUAL NETWORKS TO CALCULATE COMPLEX SYSTEMS BY PARTS

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