ON INVERSE COEFFICIENT HEAT-CONDUCTION PROBLEMS ON RECONSTRUCTION OF NONLINEAR COMPONENTS OF THE THERMAL-CONDUCTIVITY TENSOR OF ANISOTROPIC BODIES

The authors are the fi rst to present a closed procedure for numerical solution of inverse coeffi cient problems of heat conduction in anisotropic materials used as heat-shielding ones in rocket and space equipment. The reconstructed components of the thermal-conductivity tensor depend on temperature (are nonlinear). The procedure includes the formation of experimental data, the implicit gradient-descent method, the economical absolutely stable method of numerical solution of parabolic problems containing mixed derivatives, the parametric identifi cation, construction, and numerical solution of the problem for elements of sensitivity matrices, the development of a quadratic residual functional and regularizing functionals, and also the development of algorithms and software systems. The implicit gradient-descent method permits expanding the quadratic functional in a Taylor series with retention of the linear terms for the increments of the sought functions. This substantially improves the exactness and stability of solution of the inverse problems. Software systems are developed with account taken of the errors in experimental data and disregarding them. On the basis of a priori assumptions of the qualitative behavior of the functional dependences of the components of the thermal-conductivity tensor on temperature, regularizing functionals are constructed by means of which one can reconstruct the components of the thermal-conductivity tensor with an error no higher than the error of the experimental data. Results of the numerical solution of the inverse coeffi cient problems on reconstruction of nonlinear components of the thermal-conductivity tensor have been obtained and are discussed
   
Author:  V. F. Formalev and S. A. Kolesnik
Keywords:  thermal-conductivity tensor, inverse problems, quadratic and regularizing functionals, gradient-descent method, numerical methods, sensitivity matrix, parametric identifi cation
Page:  1302