PUBLISHED PAPERS #05.08
| Anar Rahimov, Aziz Zeynalli. An Approach to Numerical Solution to Problem of Determining Piecewise Constant Values and Constancy Domains of Parameters of the Mathematical Model of Oil Filtration |
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| Abstract. The study presents an approach for numerical solving the problem of determining the parameters of a two-dimensional mathematical model of oil filtration. The parameters are determined on the class of piecewise constant functions. It is important that in this case the problem is not only to identify the parameters values, but also to identify the constancy boundaries of the parameters. The proposed method reformulates the initial problem as a finite-dimensional optimization problem with a network structure. Gradient formulas for the functional of the discretized problem are derived for all optimized parameters, allowing the application of effective first-order optimization methods. The paper also includes results from computational experiments conducted on model problems. |
| Keywords: mathematical model of filtration, inverse problem, parametric identification, constancy domain, functional gradient, first-order optimization methods |
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| DOI: https://doi.org/10.30546/MaCoSEP2025.1351 |