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Article information
2017 , Volume 22, ¹ 3, p.61-70
Marchenko M.A., Ivanov A.A., Smirnov D.D.
Complex of programs AMIKS for the numerical solution of stochastic differential equations using the Monte Carlo method on supercomputers
The paper describes complex of programs named AMIKS for the numerical solution of stochastic differential equations (SDE) systems on supercomputers. In addition to the ability to create new software modules for the numerical solution of the SDE, AMIKS already has ready-made software modules that, when loaded, allow you to recalculate a specific task with new parameters. The block of calculated program modules consists of some SDE systems that arise in the following fields of science: linear and nonlinear oscillatory circuits, SDE with a randomly structure, strange attractors, movement of spacecraft and gyroscopes, self-oscillating regimes in chemical reactions, motion of a charged particle in an electromagnetic field, SDE of fluid and gas motion, SDE with Poisson component. AMIKS is capable to numerically solve SDE in partial derivatives, which reduces to a numerical solution of SDE systems after discretization with respect to spatial variables. With this, SDE system consisting of tens of thousands of equations and more will arise, which requires a long counting time on hundreds of supercomputer cores. As an example, we use Korteweg - de Vries equation, which has a solution in the form of solitary wave for some parameters. In the AMIKS user interface, there is an opportunity of test calculations on a personal computer in order to select the necessary parameters for task setting on a supercomputer. For the Korteweg - de Vries equation, the results of numerical experiments obtained on the NKS-30T cluster of the Siberian Supercomputer Center at the IVMMG SB RAS are presented. To analyze the numerical solution, AMIKS provides a convenient interface for plotting graphs such as frequency characteristics, generalizing the integral curve, phase portrait as well as the spectral portrait of the solution. In particular, the last functional was developed specifically for numerical analysis of SDE in partial derivatives. Later, the authors plan to continue developing tools for the analysis of SDE in partial derivatives.
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Keywords: stochastic differential equations, integral frequency curve, frequency phase portrait, the generalized Euler method, a set of programs, the Monte Carlo method, frequency portrait decisions, soliton
Author(s):
Marchenko Mikhail Aleksandrovich
Dr.
Position: Director
Office: Institute of Computational Mathematics and Mathematical Geophysics SB RAS
Address: 630090, Russia, Novosibirsk, Academician Lavrentieva Avenue, 6
Phone Office: (383) 330 83 53
E-mail: marchenko@sscc.ru
SPIN-code: 5257-8170Ivanov Aleksandr Aleksandrovich
Office: Institute of Computational Mathematics and Mathematical Geophysics SB RAS
Address: 630090, Russia, Novosibirsk, Academician Lavrentieva Avenue, 6
SPIN-code: 5257-8170Smirnov Dmitry Dmitriyevich
Position: Junior Research Scientist
Office: Institute of Computational Mathematics and Mathematical Geophysics SB RAS
Address: 630090, Russia, Novosibirsk, Academician Lavrentieva Avenue, 6
References:
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[5] Artemiev, S.S., Marchenko, M.A., Ivanov, A.A., Korneev, V.D., Smirnov, D.D. AMIKS – programma dlya chislennogo analiza stokhasticheskikh ostsillyatorov na massivno-parallel'nykh vychislitel'- nykh sistemakh. Svidetel'stvo o gosudarstvennoy registratsii programmy dlya EVM ¹2016616439, data gosudarstvennoy registratsii v Reestre programm dlya EVM 10.06.2016 [ AMIKS is a program for the numerical analysis of stochastic oscillators on massively parallel computing systems. The certificate of state registration of the computer program ¹2016616439, the date of state registration in the Register of Computer Programs on 10.06.2016]. (In Russ.)
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Bibliography link:
Marchenko M.A., Ivanov A.A., Smirnov D.D. Complex of programs AMIKS for the numerical solution of stochastic differential equations using the Monte Carlo method on supercomputers // Computational technologies. 2017. V. 22. ¹ 3. P. 61-70
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