Application of fast automatic differentiation for solving the inverse coefficient problem for the heat equation

Abstract

The problem of determining the thermal conductivity coefficient that depends on temperature is studied. The consideration is based on the initial-boundary value problem for the one-dimensional unsteady heat equation. The mean-root-square deviation of the temperature distribution field and the heat flux from the experimental data on the left boundary of the domain is used as the objective functional. An analytical expression for the gradient of the objective functional is obtained. An algorithm for the numerical solution of the problem based on the modern fast automatic differentiation technique is proposed. Examples of solving the problem are discussed.