JPRS ID: 9146 USSR REPORT CYBERNETICS, COMPUTERS AND AUTOMATION TECHNOLOGY

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JPRS L/9146
17 June 1980
~
USSR R~ ort
p
_
- CYBERNETICS, COMPUTERS AND
= AUTOMATION TECHNOLOGY
(FOUO 9/SO)
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JPRS L/91.46 -
- 17 June 1980
- USSR REPORT
CYBERNETICS, COMPUTERS AND AUTOMATION TECHNOLOGY
(FOUO 9/80) -
Kiev ELEKTRONNOYE MODELIROVANIYE in Russian No 1, 1980
[Excerpts from New Journal "Electronic Modeling"]
CONTENTS
NEW JOURNAL: ~;LECTRONIC MODELING -
Annotation 1
Journal Editors ~
New Problems of Simulation of Large Technical Systems......... 3 ~
Problems of the Analysis and S~mthesis of Generalized Quasianalog
Models 5
Quasianalog Simulation of Queueing Systems 7
Analysis of Table and Table-Algorithmic Methods of Reproduction
of Elementary Functions 10
Paralleling Methods for the Solution of Systems of Equations of
Large DimensionaZity on Multiprocessor Structures........... 14
Application of Mj~roprocessor Systems for the Simulation of
Nonlinear Electronic Circuits 16
Organization of the Counting-Register Structures for Simulation
of the Problem of Reserve Distribution 18
- Automatic Commutation Systems for Analog Processors of Hybrid -
Computer Systems 21
Structure of the Digital Model for Solving Systems of
Algebraic Equations 26
- a- [III - USSR - 21C S&T FOUO]
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- Solution of the Inverse Problems of Thermal Conductivity on
~lectrical Models 29
Hybrid Computer With Specialized Multifunctional Memory....... 30
= Construction of Multichannel Analog Commutators Based on Standard
M.icrocircuits 39
Second A11-Union Conference on the Prospects and �robleme of
- Development of CompLter Engineering 40
.
Calculation of the Lower Bounds of the Reliability Indexes of
Certain ~ystems Using Series Consolidation of States........ 42
Procedure f~r Simulation of Complex Digital Devices With
Faults 43
Rasic Procedural Principles of Building a Specialized Hybrid
Computer To Solve the Problems of Operative Control of the
Operating Conditions of Gas Transport Systems 44
Study of a Discrete Semimarkov System With Independent
Increments of Profits and Losses 46
Analog Simulation of the Random Process of 'Wandering About
Spheres' . 47
Fo~,rth All-Union Conference on Technical Diagnoatics.......... 4g
Meeting of the National Committee of the USSR International
Association on Analog Computations (IMACS-AICA) 51 ~
Nonpositional Representations in Multidimensional Number
Syatemsl--Book Review 53
Hybrid Computer Complexes Oriented Toward Studying Thermal and
Stress-Strain States of Structural Elements--Annotation of
Doctor's Dissertation 55
Author.s of This Issue of Electronic Simulation 57
Synthesis of Nonlinear Systems. Nonrecursive Systems, Deter-
ministic Case 60
Diakoptics of the Equations of State of Electric Circuits..... 61
A Method of Analyzing., a Stationary Magnetic Field in a Nonlinear
Medium 62
Photographs....... 64
-b-
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NEW JOURNAL: ELECTRONIC MODELING
ANNOTATION '
Kiev EL~KTROY~iOYE MODELIROVANIYE in Russian No 1, 1980 p 1 i
[ExcerptJ -
USSR Academy of Sciences
Division of Physical-Technical Prohlems of Power Engineering;
Academy of Sciences of the Ukrain.ian SSR
Division of Physical-Technical Problems of Power Engineering;
,
The Scientific-Theoretical Journal was founded in 1979.
It is published 6 times a year.
COPYRIGHT: Izdatel'stvo "Naukova dumka". "Elektronnoye modelirovaniye",
1980
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rux ur~r't~1tu, US~; uNLY
JOURNAL EDITORS
Kiev ELEKTRONNOYE MODELIROVANIYE in Russian No l, 1980, inside front cover
[Text] Board of Editors: ~ ~
- Pukhov, G. Ye. editor-in-chief '
Burtsev, V. S.
Vasil'yev, V. S., deputy editor-in-chief
Verl.an' , A. F.
Crezdov, G. I.
_ Grinevich, F. B. ~
Demirchyan, K. S.
Uodonav, A. G.
Luk'yanov, A. T.
Makukhin, A. N.
Merenkov, A. P.
Smolov, V. B.
Stepanov, ti. Ye.
Ki~orushevskiy, V.
Tsukernik, L. V,
Shlkhin, A. Ya.
Executive secretary of the board of editors L. Ye. Zborovskaya
Address of the board of editors:
252680, Kiev-57~ GSP~ ~
Brest-Litovskiy pr. 102,
Electronics and Simulation Section of the IED Institute of the Ukrainian
SSR Academy of Science~
Tel.ephone 46-05-60 ~
[201-10845]
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UDC 62-50.007
NEW PROBLEMS OF SIMULATION OF LARGE TECHNICAL SYSTF:MS
Kiev ELEKTRONNOYE MODELIROVANIYE in Russian No 1~ 1980 pp 3-11 _
[Article by K. D. Zhuk]
_ [Excerpts) A significant number of papers in Soviet and foreign literature -
_ [6-10] hav~ been devoted tfl the inveatigation of the problems of the
design af complex systems. In the work on complex syatems, large size
systems with differential dynamics have been isolated [6], systems with
many levels and complex nature of interaction but having discrete natv.re
of functioning of the network type [9]. The compiex systems, the
functioning of which is repre9ented by models with probability
characteristics [10], have besome widespread.
The enumerated versions of the models of complex systems were investigated
for the description of the laws of functioning of individual classes of
_ ob~ects, at the same time not permitting mathematical matching of these ~
models for investigation of other processes (for example, the depletion
and recovery of the reserves of large technical aystems) and properties
(the attainability of goals, the reliability of performance of operations, -
and so on).
The models discussed in this article make it possible to solve many -
applied problems of the simulation of ~arge technical systeme in which -
quite strict conditions of matriematical agreement of the differential ~
dynamic models with the automated models, their "hybrids" with alternative
networks, thus obtaining models of dynamic operations, are obtained. This
makes it possible also to construct and investigate packages of dynamic
operations.
BIBLIOGRAPHY
1. Zhuk, K. D. "Problem.s of the Axiomatic Approach to the Construction
of the Theory of Logical-Dynamic Control Systems," AVTOMATIKA
[AutomationJ, Nos S, 6, 1971, pp 11-17, 9-14. _
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2. Zhuk, It. D. "Study of the Problems o~ Optimizing Hierarchical ~
- Systems with Controllable Structure," PREPRLNT INSTITUTA
KIBERidETIKI AN USSR [Preprint of the Cybernetics Institute of the
Ukrainian SSR Academy of Sciencea], Nos 74-4, Parta 1, 2~ Kiev, ~
1974~ 40 pp; 42 pp.
3. Zhuk~ K. D. "Methods of SyeCeme Planning and Design as the Baeis
for Developing SAPR," PREPRINT INSTITUTA KIBERNETIKI AN USSR,
Noa 76-1, Kiev~ 1976~ 26 pp. ~
4. Zhuk, iC. D.; Timchenko, A. A.; Dolenko, T. I. ~SSLEDOVANIYE
STRUKTUR I MODELIROVANIYE LOGIKO-DINAMICHESKIKH SISTEM [Study of
the Structures and Simulation of the Logical-Dynamic Systems],
Kiev, Nauk. dumka, 1975~ 199 pp.
5. Zhuk~ K. D. "Some New Problems of Systems Planning and Design of
Control Complexes," UPRAVLYAYUSHCHIYE SISTEMY I MASHINY [Control
_ Syatems and Machines], No 3, 1973, pp 18-25.
6. Atans, M,; ralb, P. OPTIMAL'NOYE UPRAVLENIYE [Optimal Control],
- Moscow,.MashinoaLroyeniye~ 1968~ 764 pp.
7. Kalman, R.; Falb, P.; Arbib, M. OCHERKI PO MATEMATICHESKOY TEORII
SISTEM [Outlines of the Mathematical Systems Theory], Moscow~ -
Mir, 1971, 400 pp, -
8. Sarkisyan, S. A., et al. BOL'SHIYE TEI~iNICHESKIYE SISTEMY [Large
Technical Systems], Moscow, Nauka, 1977~ 350 pp. �
9. Vilkas, E. "Some Problems of Combining Goals," PROBLEMY PLANIROVANIYA
I UPRAVLENIYA EKONOriICHESKIMI TSELENAPRAVI,ENNYMI SISTEMAMI [Problems
of Planning and Control of Economical Purposeful ~ystems]~
Novoaibirsk~ Izd. SO AN SSSR, 1972, pp 12-18,
10. Yermol'yev, Yu. M. METODY STOKHASTICHESKOGO PROGRAMMIROVANIYA
[Methods of Stochastic ProgrammingJ, Moscow, Nauka, 1976, 240 pp. -
COPYRIGHT: Izdatel'stvo "Naukova dumka". "Elektronnoye modelirovaniye",
1980
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_
~ UDC 681.3:53.072
PROBLEMS OF THE ANALYSIS AND SYNTHESIS OF GENERALIZEA QUASIANALOG MODELS
Kiev ELEKTRONNOYE MODELIROVANIYE in Russian No 1, 1980 pp 11-16
[Article by G. Ye. Pukhov, A. F. Verlan', I. Ye. Yefimov]
[Excerpts] The principle of aimilarity of the simulated and simulating
phenomena which forms the basis for the application of physical models
in research practice permita use of the similarity criteria to transform
information about the behavior of a model into information about the
behavior of the object. At the same time thia principle ia the basic
factor limiting the possibilities of phyaical simulation. Hence it follows
that the expanaion of th~e zange of application of phyaical models can be
achieved as a result of replac~ent of the similarity principle requirfng
_ the presence of aimple analogies_by the more general principle, for
example, equ~.valence �orming the basis for the theory of quasianalog
aimulation [1]~ the application of which in the f ield of electronic sim-
ulation hae led to the creation of new types of models.
The investigaced clasa .~f problema connected with the generalized quasi-
analog ejmulation is not exhaustive, but it gives a sufficient idea of
the possibilities of generalized quasianalo& models, the natu.re and the
vol�ame of the research and also the paths of solution ~f the problems
arising when creating this type of nodel.
BIBLIOGRAPHY
1. Pukhov, G. Ye. METODY ANALIZA I SINTEZA KVASIANALOGOVYKH
ELEKTRONNYKH TSEPEY [Methods of Analysis and Synthesia of Quasi-
analog Electronic Circuit~], Kiev, Nauk,, dumka, 1967, 568~pp.
2. Malinovskiy, B. N.; Rabedzhanov, N. '~Methods ~f Mathematical Simula-
tion for a Hybrid Computer System," KIBERNETIKA [Cybernetics]~ No 1,
- 1969, pp 53-57.
' 3. Berestov, L. M. MODELIROVANIYE DINAMIKI VERTOLETA V POLETE [Simulation ~
of the Dynamica o� a Helicopter in Flight], Moacow, Mashinoatroyeniye,
1g78, 158 pp.
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4. Belman, J. "Equivalent for Investigating Flight Charactexistics
Using the X-~2A Aircra�t with Variable Stability," EKSpRESS-
INFORMATSIYA VINITI. VOZDUSHNXY TRANS~ORT [Expresa Information of
the VINITI Tnetitute. Air Tranaport], No 24~ 1974, pp 1-8.
5. Verlan'~ A. F. "Quality Indexee of Controllable Phyaical Modela,"
TOCHNOST' I NADEZHIdOST' KIBE~tNETICHESKIKH SISTEM [Accuracy and
Reliab~.li~y of Cybernetic Syatems], No 5, 1977, pp 3-5.
6. Yefimov~ I. Ye. "Neceaeary and Sufficient Conditions of the Reallza-
tion of Natural Sisnulatore~" TOCHNOST' I NADEZHNOST' KIBERNETICHESKIIQi
SISTEM], No 6~ 1978~ pp 83-86.
7. Verlan'~ A. F.; Yefimov, I. Ye.; Shatalov~ V. N. METODY OBESPECHENIYA
PODOBIYA PODVIZHNYKH TRENAZHEROV LETATEL'NYKH APPARATOV [Methods of
� I~tsur~:i~ ~imilarity of Mobile Flight Vehicle Trainers], Kiev, 1977~
6` pp (IED Institute of the.Ukrainian SSR Academy of Sciences;
preprint No 128).
8. Yefimov, I. Ye.; Latyahev, A. V. METODY KONTROLYA CHISLENNOGO
RESHENIYA DIFFERENTSIAL'NYI~I UR~,'VNENIy [Methods of Monitoring the,
Numerical Solution of Differentia~ Equationa], Kiev, 1978, 60 pp
(IED Institute of tne Ukrainian SSR Academy of Sciences; preprint
No 171) .
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1980
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UDC 681.3
QUASIANALOG SIMUI.ATION OF QUEUEING SYSTEMS
Kiev ELEKTRONNOYE MODELIROVANIYE in Russian No 1, 1980 pp 17-21
[Article by G. Ya. Beregovenko]
[Excerpta) In simulation theory there are two different approacties to the
simulation of dynamic aystems. The first approach is based on the similar-
ity principle which offers the possibility of establishing a one-to-one
correapondence of similar variables describing the behavior of the model
and the investigated ob~ect se a result of introduction of conetant scales.
In this case the equations of the ob~ ect and the model are di$tinguiahed
~ unly by constant sets with coefficients. Such equations are called similar -
but the model, the equations of which are si.milar to the equatioas of the
aimulated ob,ject, is callPd analog. The cl:~bs of such modele turns out to
be quite narrow and, strictly speaking, does not include the onea which
. are constructed uaing the resolvers of the series analog computers. In
rEality, during mathematical deacription of these modules, along with the
basic variables offering the poasibility of determining the input effect
and the reaction of th2 module, "excess" variablea appear cauaed by the
_ peculiarl.ties of the operatio~ of the modules. By com~arison with the
basic variables these variablea are quite small, but thearetically they
_ cannot be reduced to zero. Frequently they are neglected, by calling them
machine zeros. ~Nevertheless, it is qufte obvious that the equatioas of
the model and the ob~ect in the general case are different, and the compar-
ison of the results of the simulation with the reaults of natural tesCs
or with the solution of the equations of the ob~ecC occurs only on satis-
faction of def ined conditions. -
- Thus, even when using the traditional means of eimulation, the equations
of the model and the simulated ob~ect do not compare, and on interpreta- -
tion of the reaults of the simulation it is necessary to point out the
_ conditiona, on satisfaction of which theae reaults can be compared wfth the
resuits of natural tests or with the solution of the equations of the
aimulated ob~ ect.
- On the basis of what has been stated it is poesible to create epecialized
computers, the equationa of which would differ from the equations of
simulated ob~ ects. However, when satisfying de~ined conditions called the
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conclitiona of equivalence, the results of the simulation coincide with
the solution of the equations of the ob~ect with accuracy to constant
factora. Such devices are called quasianalog simulatoxs. On construction
of them, the second approach ia used based on the principle of equivalence
- in the aenae of the results obtained otherwise called the principZe of
quasianalogiea [1]. Although this principle was firat formulated and
- became widespread when synthesizing nonalgorithmic computers, it has
fuadamental significance when constructing any models. This is caused by
the fact that the intuitive underatanding of the relations between the -
model and the simulated ob~ect ueing the principle of quasianalogies is
reinforced by quantitative relationa in the forar of conditione of equiva-
lence.
Referring, in pIIrticular, to queueing systems, it is necessary to indi-
cate the general trend in the use of the methods of statistical simula-
tion for them [2-4]. Here, as a result of simulatioa the researcher
obtaine the mean values of the weighting time, the sizes of the queue, ~
and so on. It is natural that theae values must compare with the results
- of ti~e natural studies of the ob~ects represented by the corresponding
quEUeing ayetems. A characterist3c feature of the atatistical simulation
is the fact that the individual tests of the model permit us to determine
the average characteristics only on the development of these tests in
significant time intervals. The magnitudes of these intervals are diffi-
cult to estimate in advance, but in actual research they are determined
by the time of occurrence of the tranaient process.
The conditions of equivalence in the senae ~f the rasults obtained during
statistical aimulation reduce to comparison of defined mean characteris-
tica in the steady state mode.
_ The statistical models belong to the clasa of simulation models, and they
d;, not presuppose the description of the investigated object using equa-
ti.ons. Ar. the same time the quasianalog simulation usea the equation of -
- model, on solution of which, considering the conditions of equivalence
it is poasible to ~udge the behavior of the ob~ect.
Equations and conditiona.of equivalence are presented below which define
- the quasianalog model of the queueing system. Theae equationa are usually
realized on a digital computer and can, in contrast to the above-meationed
nonalgorithmic quasianalogs, the investigated model is algorithmic.
The basis for constructing the algorithmic quasianalog of the queueing
system is the system made up of the aeries-connected modulea performing
the functions of accumulation (the accumulator) and delay (the procesa
cycle).
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BIBLIOGRAPHY
1. Pukhov, G. Ye. METODY ANAI,IZA I SINTEZA KVAZIANALOGOVYKH
- ELEK~RONNYKH TSEPEY [Methods of Analyais and Synthesie of Quaei-
analog Electronic Circuita]~ Kiev, Nauk~. dumka, 1967, 354 pp.
2. Buslenko, N. P. METOD STATISTICHESKOGO MODII,IROVANIYA [Method of
Statiatica~ Simulation]~ Moacow, Statistika, 1970, 154 pp.
_ 3. Lifahits, A. L.; Mal'ts, E. A. STATIS2ICHESKOYE MODELIROVANIYE
SISTEM MASSOVOGO OBSLUZHIVANIYA [Statistical Simulation of Queueing
Systems], Moscow, Sov. radio, 1978, 214 pp.
4. Aniakov, V. V.; Vitenberg, T. M. Liberov, A. B.; Ogorodov, I. K.
MODELIROVANIYE ZADAC~i ISSLEDOVANIYA OPE&ATSIY (ANALOGOVYYE SREDSTVA
I METODY) [Simulation of the Problems of Investigation Operationa
(Analog Means and rsethoda)], Moscow, Energiya, 1978, 216 pp.
5. Beregovenko, G. Ya. "A Method c,f Inveatigation of Traasient Processee
in El~ctrical Circuits," MATEMATICHESKOYE MODELIROVANIYE I TEORIYA
ELEKTRICHESKIKH TSEPEY [Mathematical Simulation and the Theory of
Electric Circuite], No 12, 1974, pp 43-52.
6. Beregovenko, G. Ya. "Problem of Mathematical Simulation of Networks
with a Del~y," ELEKTRON. I MODELIROVANIYE [EI.ectronics and Simulation],
No 9, 1975, pp 39-43.
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r
UDC 681.325.5:518.5
ANALYSIS OF TABLE AND TABLE ALGORITHMIC METHODS OF REPRODUCTION OF
ELEMENTARY FUNCTIONS ~
Kiev ELEKTRONNOYE MODELIROVANIYE in Ruasian No l, 1980, pp 22-27
[Article bq V, B. Smolov, V. D. BaykovJ
[Excerptsj At the present time in connection with the appearance of
economical permanent memories in the integral execution, interest has been
aroused in the probleme connected with the investigation and the realiza-
tion of table and table-algorithmic me;hods of calculation [1-6].
The clasa of problems, the aolution of which can be realized ueing tables
ie extraordinarily broad. First of all, in addition to arithmetic opera- ~
tions these include various operationa of code conversion: from decimal
code to ~even-segment deexcitation code, binary to decimel conversiona, '
the conversion of radians to degreea and back, and so on. Secondly, it !
ia posaible on the basia of tablea to solve the problems of the organiza- i
tion of varioua methods of addreasing, the search and sorting algorithms. ~
Finally~ one of the effective spheres of application of the tAblea is j
repxoduction of the elementary functions. ~
The term "reproduction" inetead of "calculation" was not selected randomly, i
for with reapect to their operation the tables reflect not the calculation ~
procesa, but only its results. The more complex the functional relation
~
be~.ween the input and output of the tables, the more effective their appli- ~
cation. ,
~
The reproduction on a table base of the functions of one variable, for !
example, of the type of yQainX�ehX+cosX�chX requires no more time than '
realization of the functiong zsainX. By this property the table realiza-
tion differs theoretically from the regiater which for ca3.culation of the '
function y requires much more time than for z. On the other hand~ the ~
matrix realization of the function y by comparison with z requires sig-
nificantly more equipment. In addition, for table realizat~.on of the
volume of preliminary calculationa increases which in a number of casea ~
can be the brake in the application of the table methode directly.
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For example, when reproducing the elementary functiona of the argumente
containir~ 3^�. to 64 binary bite, it ie neceesary in advance to calculate
232 to 26~ values of the function. The minimum time achievable by modern
high-speed computers when calculating only one value of the functional
will be no less thrin 10 microseconds; consequently, for calculation of
264 ~alues a time of 18.4�1013 sec=6x106 years is required. Consequently,
in order to make the preiiminary table calculation time realistic it is
necessary to increase the epeed of the computer means by at least 10
million timea. .
Accordingly~ in particular when working with large word-lengthe~ not
purely table but table-algorithmic methods of calculg.tion have become wide-
spread. A general characteristtc of the gfven methods is the combination
of the table search in accordance with the high-order part of the argument -
with the introduction of a correction which depends on the low-order part.
When calculating the correction, both the general and specialized .
approach are used.
In conclusion, let us present the generalizing tabl:e of basic characteris-
tice of the deacribed versiona of the table-algorithmic methods of cal-
culating elementary functions. The methods are primarily arranged in
- order of decreasing required volume of permanent memory (Tabte 4).
BIBLIOGR~?PHY
1. MINI-EVM. PRINTSIPY POSTROYENIYA I PROYEKTIROVANIYA [Mini-computer.
Principles of Construction, Planning and Design], Kiev, Nauk. dumka,
1975, 200 pp.
2. Kuz'min, I. V., et al. SINTEZ VYCHISLITEL'NYKH ALGORITMOV -
UPtZAVLENIYA I KONTROLYA [Synthesis of Computer Monitoring and Control
Algorithms], Kiev, Tekhnika, 1975, 246 pp.
3. Oranskiy, A. M. APPARATNYYE METODY V TSIFROVOY VYCHISLITEL'NOY
TEKIiY~1IKE [Equipment Methods and Digital Computer Engineering], ,
Minsk, Izd-vo BGU, 1977, 208 pp.
4. I1'in, V. A.; Popov~ Yu. A.; Druzhinina, I. I. "Utilization of -
Abbreviated Tablea when Calculating Elementary Functiona,"
UPRAVLYAYUSHCHIYE SISTEMY I MASHINY [Control Syatems and Machines],
No 1, 1979, pp 58-60. :
~
5. Mikhaylova, N. V.; 9hauman, A. M. "Table-Iteration Method of Extract-
ing the Square Root," VYCHISLITEL'NAYA TEI~IIKA I VPPROSY
KIBERNETIKI,[Computer Engineering and Prcblems of Cybernetics], ,
Izd-vo LGU, No 15, 1978, p~ 40-50.
12
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_ 1
,
_ FOR OFFICIAL U~': ONLY
1
~
6. Potapov, V. I.; Florensov, A. N. "Tgble-Algorithmic Method of
- Executing the Function of a Logarithm on a Digital Computer~"
- UPRAVLYAYUSHCHIYE SISTEMY I MASHINY, No 4, 1978, pp 90-94.
7. Pukhov, G. Ye. "Method of Fixed Incrementa~" ELEKTRONIKA I
MODELIROVANIYE [Electronica snd Simulation], No 9~ 1975, pp 5-8.
8. Smolov, V. B.; Baylcov, V. D. "Principles and Prospects of the Appli- -
cation of the Method of 'Digit by Digit' Calculation," ELEKTRONIKA
I METODY GIBRIDNYI~I VYCHISLENIY [Electronice and Methods of Hybrid
Calculationa]~ Kiev, Nauk. dumlca, 1978.
9. Balashov, Ye. P.; Smolov, V. B., et al. "Problem of the Application
of Abbreviated Tablea of Functions to Conatruct High-Output
- Uniform Processors," UPRAVLYAYUSHCHIYE SISTEMY I MASHINY, No 3,
1975, pp 99-102.
10. Ariatav, V. V. "Introduction to the Theory of the Method of
'Digit by Digit' Calculations," MASHINNYY ANALIZ I MODELIROVANIYE
ELEKTRZCHESKII~i TSEPEY [Machine Analysis and Simulation of Electric
Circuite], Kiev, Nauk. dumka~ 1978, pp 186-196.
COPYRIGHT: Izdatel'atvo "Naukova dumka". "Elektronnoye modelirovaniye",
1980
[201-10845]
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~CSO: 1863
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, i
~ UDC 621.372.0.61:681.142
PARALLELING METHODS FOR THE SOLUTION OF SYSTEMS OF EQUATIONS OF LARGE
DIMENSIONALITY ON MULTIPROCESSOR STRUCTURES
Kiev ELEKTRONNOYE MODELIROVANIYE in Russian No 1, 1980 pp 28-32
[Article by L. Ya. Nagornyy~ '
[Excerpta] Increasing the output capacity and the efficiency of modern
meana of digital and hybrid computer engineering is one of the urgent
problema. At the present time a trend is being observed toward the crea-
tion of high-output computer means based on multiprocessor structures.
Among the variety of problems which must be solved on such structures, the
solution of large systems of linear and nonlinear algebraic and differen-
tial equations with.denae and .sparse. matrices is of great interest. -
It is posaible to increase the putput capacity and the efficiency of
eapecially multiple solution of systems of such equations as a result of
applying the methoda permitting par~llel solution of these problems on
multiproceseor etructures.
In the given paper, on the baeis of diakoptics [1-8] methods are proposed ,
for modular parallel solution of the systeme of equations of large dimen-
sionality with a apa~se matrix on multiprocessor structures.
_ In conclusion it is necesaary to note that if we realize linearization and
algebraization of the nonlinear equations, the proposed methoda cAn be ,
used for paralleling the aolution of systema of equations of large dimen-
- sionality with sparse matrices on N processors. Thus, in reference [5]
u~~e of the algorit~ims is preaented for conversion from the~~nonlinear sys-
tem of diff erential equations with sparae" matrix to the system of
linear algebraic equatione with modular-diagonal matrix with a frame.
- This representation of the aystem of initial equationa will permit the ~
application of tr: method of paralleling the solution of the systema of
equations with mo.,slar-diagonal matrix with a frame to it. � ~
BIBLIOGRAPHY ;
1. Pukhov, G. Ye. "Theory of the Method of Subnetworks," ELEKTRICHESTVO
[L~lectricityj, No 8~ 1952, pp 58-61. ;
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2. Kron, G. ISSLIDOVANIYE SLOZFIlQYKH SISTEM PO CHASTYAM. DIAKOPTIKA,
[Investigation of the Complex Systems by Parts. Diakoptica],
Moacow, Nauka~ 1972, 542 pp.
3. Nagornyy, L. Ya. "Method of Subnetworks for Computer Calculation
of Electronic Circuita with Respect to a Matrix of Hybrid Parameters,"
IZV. WZOV. SER. RADIOELEKTRONIKA [Newe of the Institutions of
Higher Learning. Radio Electronics Series], Vol 18~ No 6, 1975,
pp 60-67. _
4. Nagornyy, L. Ya. "A Method of Solution of Large Systeme of Equatione -
with Sparae Matrix on a Digital Computer," ELEkTRON. I
MODII.IROVANIYE [Electronics and Simulatiion], No 11, 1976, pp 84-86. -
5. Nagornyy~ L. Ya.; Zhukov, I. A. "Computer Solution of Large Systems
of Nonlinear D.ifferential Equationa with � Sparse Structure,"
AVTOMATIZATSIYA PROYEKTIROVANIYA V ELEKTRON. [Automation of Planning
and De~ign in Electronica], No 17, 1978, pp 61-65.
6. Nagornyy, L. Ya. MODELIROVANIYE ELEKTRONNYKH TSEPEY [Simulation of
Electronic Circuits], Kiev, Tekhnika, 1974, 360 pp.
7. Petrenko, A. I.; Vlasov, A. I.; Timchenko, Aa P. TABLICHNYYE
METODY MODELIROVANIYA E..ERTRONNYKH SRHIIri NA EVM [Table Met~iods of
_ Simulating Electronic Circuits on Computers], Riev, Viahcha shkol~a, -
1971, 188 pp.
8. Chen, R. "Solving a Class of Large Sparae Linear Systema of
Equations by Partitioning," PROC. IEEE INT. SYMPOS., Toronto, Can.~
1973~ 520 pp.
9. Tinney~ U.; Uolker~ U. "Direct Solutiona of Quasimodular Circuit
Equations by Optimally Order~d Expansion of the Matrix in Triangular
Cofactora," TR. IN-TA ELERTRON. I RADIOTEKHNIKA [W'orks of the
Institute of Electroni~s and Radio Engineering], No 11, 1957,
pp 1129-1133.
COPYRIGHT: Izdatel'stvo "Naukova dumka". "Elektronnoye modelirovaniye",
1980
[201-10845]
1Q845
CSO: 1863
15
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UDC 681.142-523.8.621.372
= APPLICATION OF MICRO~ROCESSOR SYSTEMS FOR THE SIMUI+ATION OF NONLINEAR
ELECTRONIC CIRCUITS
Kiev ELEKTR4*?NOYE MODELIROVANIYE in Russian No 1, 1980 pp 32-41
[Article by A. I. Petrenko, A. T. Chigrin]
[Excerpta] At thP present time increased interest ie being observed in
the solution of co~plex engiaeering problems on multiprocesaor aystema
and uniform comput~r atructures. These include the problem of the simu-
- lation of electronic nonlinear systema. Here the models of the electronic
circuits considesing the modern methods of solution of noa].inear algebraic
and nonlinear "rigid" differential equatians are reduced to a multiply
svlved system of linearized equations of dimensionality nXn of the type
Ax = b. (1)
In the article a study ia made of the survey of inethods of para~lel solu-
rion of the given system of equations on the multiproceseor system when
the sparaeness of the matrix of equations of tha system A and the number
of multiprocessors m