Adaptive modified alternating triangular iterative method for solving grid equations with a non-self-adjoint operator

Сухинов, А. И.; Chistyakov, A. E.

doi:10.1134/s2070048212040084

Cited by 53 publications

(16 citation statements)

References 3 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…In works [19][20][21][22][23][24] it was shown that the best results, closest to experimental field data, were obtained on the basis of the O.M. Belotserkovsky parametrization.…”

Section: The Vertical Turbulent Viscosity Coefficientmentioning

confidence: 99%

Ecological and hydrophysical research of impact the vertical turbulent exchange coefficient on the concentration of dissolved oxygen in the bottom layer of shallow water

et al. 2017

View full text Add to dashboard Cite

Abstract. The paper presents the results of hydrochemical observations obtained during the expedition on the scientific-research vessel "Deneb" in the Eastern part of the Azov Sea and the Taganrog Bay in July 2017. In the ecological and hydrophysical researches we have found abnormally low levels of dissolved oxygen in the bottom layer of the Azov Sea. Among the various approximations of the vertical turbulent exchange coefficient, the algebraic subgrid models are the most applicable. These models are based on the determination of turbulent flows as averaged multiplication of deviations over space or time (correlation) of the velocity components of the currents and a transferring physical quantity. The numerical experiment for determination of vertical turbulent exchange coefficient for some points of the Azov Sea was performed. Direct dependence between values of the vertical turbulent exchange coefficient and the concentration of dissolved oxygen in the bottom layer was obtained.

show abstract

“…In works [19][20][21][22][23][24] it was shown that the best results, closest to experimental field data, were obtained on the basis of the O.M. Belotserkovsky parametrization.…”

Section: The Vertical Turbulent Viscosity Coefficientmentioning

confidence: 99%

Ecological and hydrophysical research of impact the vertical turbulent exchange coefficient on the concentration of dissolved oxygen in the bottom layer of shallow water

et al. 2017

View full text Add to dashboard Cite

show abstract

“…Game theoretic models of biological resource management with asymmetric players and different planning horizons are studied in [21,22]. Game problems of harvesting in a biological community are considered also in [23].The papers [24][25][26][27] present non-linear differential equation models of the shallow bodies of water (on the example of Azov Sea). The works [28,29] develop these models by the consideration of fish capture as a control impact: in [28] an optimal control problem is solved, and [29] treats a conflict control model which is formalized as a hierarchical differential game (a Stackelberg game).The differential Stackelberg games are described in the monograph [30], and the inverse Stackelberg games (with a feedback by control) are reviewed in [31].…”

mentioning

confidence: 99%

“…The papers [24][25][26][27] present non-linear differential equation models of the shallow bodies of water (on the example of Azov Sea). The works [28,29] develop these models by the consideration of fish capture as a control impact: in [28] an optimal control problem is solved, and [29] treats a conflict control model which is formalized as a hierarchical differential game (a Stackelberg game).…”

mentioning

confidence: 99%

Spatially Distributed Differential Game Theoretic Model of Fisheries

Ougolnitsky¹,

Усов²

2019

Mathematics

View full text Add to dashboard Cite

We consider a differential game of fisheries in a fan-like control structure of the type "supervisor-several agents". The dynamics of the controlled system is described by a non-linear differential equation model which is identified on the Azov Sea data. An averaging by two spatial coordinates is conducted. Different information structures of the game are generated by the control methods of compulsion (supervisor restricts the feasible strategies of agents) and impulsion (she exerts an impact to their payoff functionals). Both Stackerlberg and inverse Stackelberg games are considered. For the numerical investigation we use a discretization of the initial model and the method of qualitatively representative scenarios in simulation modeling.Mathematics 2019, 7, 732 2 of 13 the Stackelberg games to fisheries can be found in [16,[18][19][20]. Game theoretic models of biological resource management with asymmetric players and different planning horizons are studied in [21,22]. Game problems of harvesting in a biological community are considered also in [23].The papers [24][25][26][27] present non-linear differential equation models of the shallow bodies of water (on the example of Azov Sea). The works [28,29] develop these models by the consideration of fish capture as a control impact: in [28] an optimal control problem is solved, and [29] treats a conflict control model which is formalized as a hierarchical differential game (a Stackelberg game).The differential Stackelberg games are described in the monograph [30], and the inverse Stackelberg games (with a feedback by control) are reviewed in [31]. An original approach to the analysis of differential Stackelberg games with consideration of different information structures which determine the order of moves of all players, their knowledge about the strategies of other players, and the state of the controlled dynamical system is presented in [32]. In that paper, the structure of optimal strategies is described and a method of solution of Stackelberg games and inverse Stackelberg games is proposed. The method is based on building of a mutually advantageous program of actions and punishment of the defectors [32].This paper develops the results presented in [28,29]. Unlike them, we consider here a fan-like control system (a differential game of a supervisor and several agents) and closed-loop strategies of the players. In the case of several agents, the set of their best responses to the supervisor's strategy is the set of Nash equilibria in the normal-form game of the agents. Besides, we consider a spatial coordinate [33].The authors' approach to the modeling of fisheries is based on the concept of sustainable management [34][35][36]. In this frame, the hierarchical control mechanisms (compulsion and impulsion methods) are presented as solutions of the Stackelberg games with phase constraints which reflect the requirements to the state of a controlled system (the conditions of sustainable development). Compulsion means the supervisor's impact to the sets of feasible ac...

show abstract

“…It should also be noted that the proposed version of the method of minimum corrections is a separate method. The developed algorithms were applied to solve the grid equations obtained as a result of approximation of the threedimensional mathematical model of hydrodynamics of shallow water bodies [9][10][11][12][13][14][15][16]. A parallel implementation of the adaptive modified iterative alternating-triangular method of minimal corrections is described [17][18][19][20][21][22].…”

mentioning

confidence: 99%

Adaptive modified alternating-triangular method

Сухинов¹,

Chistyakov²

2018

Computational Mathematics and Information Technologies

View full text Add to dashboard Cite

The paper covers the development of adaptive methods for solving convection-diffusion problems. For this class of problems a version of minimal correction adaptive modified alternatingtriangular method was developed, as well the convergence rate of the method was analytically estimated. Numerical results have been presented for solving real hydrodynamical problem in shallow water using parallel algorithm of developed method.Keywords: wave problem; grid equations; adaptive modified alternating triangular iterative method Introduction. Often in applied problems, for example, in the mathematical modeling of hydrodynamics, heat and mass transfer, geofiltration, population dynamics and other processes, it becomes necessary to solve equations of the convection-diffusion type. In the case of using implicit schemes and schemes with weights, such problems lead to linear algebraic equations with a nonselfadjoint operator. One approach to solving such problems is the Gaussian symmetrization method [3]. The disadvantage of this method is the quadratic increase in the number of conditionality of the operator of the problem.

show abstract

Adaptive modified alternating triangular iterative method for solving grid equations with a non-self-adjoint operator

Cited by 53 publications

References 3 publications

Ecological and hydrophysical research of impact the vertical turbulent exchange coefficient on the concentration of dissolved oxygen in the bottom layer of shallow water

Ecological and hydrophysical research of impact the vertical turbulent exchange coefficient on the concentration of dissolved oxygen in the bottom layer of shallow water

Spatially Distributed Differential Game Theoretic Model of Fisheries

Adaptive modified alternating-triangular method

Contact Info

Product

Resources

About