• A. A. Tymoshenko Faculty of Computer Science and Cybernetics, Taras Shevchenko National University of Kyiv, Kyiv, Ukraine
  • D. A. Klyushin Faculty of Computer Science and Cybernetics, Taras Shevchenko National University of Kyiv, Kyiv, Ukraine
  • S. I. Lyashko Faculty of Computer Science and Cybernetics, Taras Shevchenko National University of Kyiv, Kyiv, Ukraine
Keywords: Mathematical simulation, Control, Optimization, Richards–Klute equation


The article is dedicated to several gradient based methods for solving a two-dimensional humidification problem, described by Richards equation. Several assumptions are made: water is assumed incompressible, external pressure and temperature are constant. The initial state and desired function are known, while the optimal source power should be calculated. Kirchhoff transformation is applied to the initial equation to simplify the stated problem. Time and space coordinates are scaled to get linear dimensionless equation, which can be easily discretized over space and time. Numerical methods are applied to rewrite and solve the system. Also gradient methods are applied for cases, where it is possible to define the optimization functional for every allowed source power.


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