Identification of the thermal conductivity coefficient in two dimension caseстатьяРецензия
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Дата последнего поиска статьи во внешних источниках: 8 декабря 2019 г.
Аннотация:In the paper the problem of determining the thermal conductivity coefficient that depends on temperature is studied. The consideration is based on the mixed boundary value problem for the two-dimensional unsteady-state heat equation. The inverse coefficient problem is reduced to a variation problem. The mean-root-square deviation of the heat flux obtained by solving initial-boundary value problem from the experimental data on the boundary of the considered domain is used as the objective functional. The optimal control problem is solved numerically. The objective functional is minimized using the gradient methods. It is well known that it is very important for the gradient methods to determine accurate values of the gradients. For this reason, in this paper we used the efficient Fast Automatic Differentiation technique, which gives the exact functional gradient for the discrete optimal control problem. The examples of
solving the inverse coefficient problem confirm the efficiency of the proposed algorithm.