Abstract
The investigation deals with the choice of a finite-difference scheme for approximating the heat diffusion equation when solving the inverse coefficient problem in a three-dimensional formulation. Using the examples of a number of nonlinear problems for a three-dimensional heat equation whose coefficients depend on temperature, a comparative analysis of several schemes of alternating directions was performed. The following schemes were examined: a locally one-dimensional scheme, a Douglas-Reckford scheme, and a Pisman-Reckford scheme. Each numerical method was used to obtain the temperature distribution inside the parallelepiped. When comparing methods, the accuracy of the obtained solution and the computer time to achieve the required accuracy were taken into account. The inverse coefficient problem was reduced to the variational problem. Based on the carried out research, recommendations were made regarding the choice of a finite-difference scheme for the discretization of the primal problem when solving the inverse coefficient problem.
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Zubov, V., Albu, A. (2020). About Difference Schemes for Solving Inverse Coefficient Problems. In: Olenev, N., Evtushenko, Y., Khachay, M., Malkova, V. (eds) Optimization and Applications. OPTIMA 2020. Lecture Notes in Computer Science(), vol 12422. Springer, Cham. https://doi.org/10.1007/978-3-030-62867-3_23
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