Function estimation with Alifanov’s iterative regularization method in linear and nonlinear heat conduction problems

Abstract

Various aspects of a methodology to determine unknown functions representing source terms in inverse heat conduction problems are presented. The methodology is centered on gradient based iterative procedures for optimization problems and we consider specifically Landweber iteration and the conjugate gradient method. The formulation is given for inverse problems with both linear and nonlinear direct heat conduction problems. Test case results are presented and the performance of the estimation results of a nonlinear equation, using linear and nonlinear models, are compared.