Optimal Control of Point Sources in Richards-Klute Equation

Tymoshenko, Andrii; Klyushin, D. A.; Lyashko, S. I.

doi:10.1007/978-3-319-91008-6_20

Cited by 8 publications

(2 citation statements)

References 6 publications

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“…As in previous research for one-dimensional problem [13], the accuracy criterion is based on providing the humidity level as near to target function as possible, but the result of calculations is the optimal source power. Based on theorems from the previous section and [12], the convergence is proven, so it is enough to stop the process in a proper moment, for example by limiting the number of iterations or 98% accuracy level termination.…”

Section: Resultsmentioning

confidence: 99%

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Optimal Control of Point Source Intensity in a Porous Medium

Klyushin

Tymoshenko

2020

Advances in Computer Science for Engineering and Education III

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In this paper, a new combined method for computing the optimal intensity of point sources regulating humidity in a porous medium is proposed. The process is described by Richards-Klute equation. The initial problem is transformed into the linear dimensionless optimal control problem on nonstationary moisture transport in an unsaturated porous medium using Kirchhoff transformation. A variation algorithm is applied to the resulting problem formulation. For this algorithm, the finite difference method is used for both direct and conjugate problems, followed by numerical method application to solve a system of linear algebraic equations. The optimization is achieved by minimizing the deviation of the last state from the target values of this state. The current paper provides theoretical background and solution for a twodimensional drip irrigation problem. Theorems on existence and uniqueness are listed for the target functional. All necessary transitions and calculations are shown and demonstrate high accuracy of the method. The proposed method allows to solve the problem of optimal parameter choice for a drip irrigation system, and to improve its effectiveness.

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Section: Resultsmentioning

confidence: 99%

“…For the problem of moisture transport through the ground, a variation method is used [11][12][13]. So, linearization fits this approach well with further application of numerical methods for the resulting linear system.…”

Section: Literature Reviewmentioning

confidence: 99%