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8space with various kinds of obstacles. When modeling the interaction of a substance with an obstacle, each
block in the basic substitution is associated with a binary type parameter, as a result of which all blocks are
subdivided into two types: internal and boundary. The entered parameter in the result determines the need to
rotate the block when performing basic substitution. Wherein, the boundary of the modeling area can be spec-
ified in the form of planes (plates) and parallelepipeds. It is also possible to simulate the effect of wind on the
admixture at a given angle. The transfer of substances in the absence of obstacles is modeled by a synchro-
nous shift of the cells of the state array with probabilities proportional to the corresponding components of
the wind speed vector [2].
This work was partially supported by the FRBR and Administration of Krasnodar Region (grant 19-41-230005).
References
1. Toffolli T., Margolus N. Cellular Automata Machines. USA: MIT Press, 1987. 279 p.
2. Rubtsov S. E., Pavlova A. V., Savenkov S. I. On the cellular automata model convection-diffusion processes
impurities // Ecological Bulletin of Scientific Centers of BSEC. 2016. No. 2. P. 62�68.
Study of the interaction of a reservoir with an ideal compressible fluid with an elastic half-space
A. V. Pavlova1, S. E. Rubtsov1, I. S. Telyatnikov2
1Kuban State University Krasnodar
2Southern Scientific Centre of RAS
Email: ilux_t@list.ru
DOI 10.24412/cl-35065-2021-1-01-40
We solved in a flat formulation the problem of harmonic oscillations for a basin with an ideal compressible
fluid on an elastic half-space exposed to a localized surface vibration load. The problem was reduced to an in-
tegral equation (IE) of the first kind for the amplitude of the contact hydrodynamic pressure with a kernel that
depends on the difference and the sum of arguments [1]. IE was solved by the factorization method [2].
A semi-analytical method is presented for determining the main parameters of the contact interaction in
hydroelastic systems "liquid-soil" taking into account the effect of natural and man-made vibration loads on
them, which makes it possible to identify the conditions for the occurrence of dynamic modes that are dan-
gerous for construction integrity and to estimate their frequencies range depending on the defining character-
istics of the system.
This work was partially supported by the FRBR (grant 19-08-00145) and SSC of the RAS (project No. 01201354241)
References
1. Pavlova A.V., Rubtsov S.E., Telyatnikov I.S. The study of the dynamic problem of vibrations of a reservoir with
liquid on an elastic foundation // IOP Conference Series: Materials Science and Engineering, 918 (2020) 012126.
DOI:10.1088/1757-899X/918/1/012126.
2. Vorovich I. I., Babeshko V. A. Dynamical Mixed Problems of Elasticity for Nonclassical Domains. M.: Nauka, 1979.
Sensitivity-operator-based inverse modeling framework with heterogeneous measurements
A. V. Penenko
Institute of Computational Mathematics and Mathematical Geophysics SB RAS
Novosibirsk State University
Email: aleks@ommgp.sscc.ru
DOI 10.24412/cl-35065-2021-1-01-41
Air quality monitoring systems vary in temporal and spatial coverage, the composition of the observed
chemicals, and the data's accuracy. The developed inverse modeling approach [1] is based on sensitivity oper-
ators and ensembles of adjoint equations solutions. An inverse problem is transformed to a quasi-linear opera-
tor equation with the sensitivity operator. The sensitivity operator is composed of the sensitivity functions,
which are evaluated on the adjoint ensemble members. The members correspond to measurement data ele-
ments. This ensemble construction allows working in a unified way with heterogeneous measurement data in
a single operator equation. The quasi-linear structure of the resulting operator equation allows both solving
and analyzing the inverse problem. More specifically, by analyzing the sensitivity operator's singular structure,
we can estimate the informational content in the measurement data with respect to the considered process
model. This type of analysis can estimate the inverse problem solution before its actual solution and evaluate
the monitoring system efficiency with respect to the considered inverse modeling task [1, 2].
The work was supported by the grant �075-15-2020-787 in the form of a subsidy for a Major scientific project from
Ministry of Science and Higher Education of Russia (project "Fundamentals, methods and technologies for digital monitor-
ing and forecasting of the environmental situation on the Baikal natural territory").
References
1. Penenko, A. Convergence analysis of the adjoint ensemble method in inverse source problems for advection-
diffusion-reaction models with image-type measurements // Inverse Problems & Imaging, American Institute of
Mathematical Sciences (AIMS), 2020, 14, 757-782 doi: 10.3934/ipi.2020035.
2. Penenko, A.; Gochakov, A. & Penenko, V. Algorithms based on sensitivity operators for analyzing and solving
inverse modeling problems of transport and transformation of atmospheric pollutants // IOP Conference Series: Earth
and Environmental Science, IOP Publishing, 2020, 611, 012032 doi: 10.1088/1755-1315/611/1/012032.
Numerical comparison of a sensitivity operator based and metaheuristic algorithms on parameter
identification problems for production-destruction models
A. V. Penenko1,2, V. S. Konopleva1,2, A. V. Bobrovskikh3 and U. S. Zubairova3
1Institute of Computational Mathematics and Mathematical Geophysics SB RAS
2Novosibirsk State University
3Institute of Cytology and Genetics SB RAS
Email: aleks@ommgp.sscc.ru
DOI 10.24412/cl-35065-2021-1-01-42
Various meta-heuristic algorithms are widely to identify parameters of the mathematical models. Usually,
these algorithms take only direct problem solution and can be easily applied to various problems without seri-
ous modifications. The trade-off for this universal character is the use of a limited number of inverse problem
properties. The objective of this paper is to compare the performance of the sensitivity operator-based algo-
rithm [1] and standard implementations of metaheuristic algorithms [2] on a realistic scenario of parameter
identification problems for atmospheric chemistry and bio-chemical models.
The work was supported by Russian Foundation for Basic Research grant 19-07-01135 in part of the development of
algorithms and Russian Foundation for Basic Research grant 19-44-543021 in part of the analysis of the biological models.
References
1. Penenko, A. V.; Mukatova, Z. S. & Salimova, A. B. Numerical study of the coefficient identification algorithm based
on ensembles of adjoint problem solutions for a production-destruction model // International J. of Nonlinear Sciences
and Numerical Simulation, Walter de Gruyter GmbH, 2020, 0, doi: 10.1515/ijnsns-2019-0088.
2. Johnson, S. G. The NLopt nonlinear-optimization package http://github.com/stevengj/nlopt.
