Numerical analytic method for solving the inverse coefficient problem of heat conduction in anisotropic half-space

Abstract

The paper proposes a numerical-analytical method for solving the inverse problem of identification of the components of the thermal conductivity tensor in anisotropic materials on the basis of the earlier analytical solution of the heat conduction problem in anisotropic half-space when heated with a thermal flow. The method is based upon expansion of the residual functional into Taylor series and determination of incremental vectors of the target coefficients which are then used for application of iterative gradient descent algorithms. The solution demonstrates fine iteration convergence even if the initial approximation of the coefficients vector differs from the target one by several times, and even when there is some inaccuracy in the experimental data. The proposed method can be used for a wide range of problems in continuum mechanics.